Social norms represent fundamental components of human societies, guiding behavior and expectations across nearly all facets of life. They function as informal institutions, wielding significant influence over actions without the necessity of legal structures or explicit enforcement mechanisms. These norms guide a wide array of crucial behaviors, ranging from economic transactions and political participation to everyday practices such as personal hygiene and social etiquette.
Despite their pervasive influence and critical role in societal functioning, establishing a standardized definition of "social norm" has proven to be a persistent challenge for academics. This has resulted in a notable lack of consensus across the field, as acknowledged by various scholars. This definitional fluidity creates substantial hurdles for consistent theoretical modeling, precise measurement, and the effective integration of research findings from diverse studies. The absence of a universally agreed-upon definition means that researchers often operate with different understandings of the core phenomenon they are studying, complicating comparative analysis and cumulative scientific progress. The inherent ambiguity and lack of consensus among prominent scholars underscore a fundamental challenge that any new theoretical model must address if it aims to bring greater rigor and coherence to the field.
Kristopher Overbo's dissertation, 'A Model of Social Norm Dynamics', introduces a deterministic model designed to describe the temporal dynamics of social norm development. This model is firmly rooted in the principles of rational choice and methodological individualism, a doctrine asserting that macro-social outcomes should be explained through interactions at the individual level.
A primary motivation for this model's development is to overcome key limitations observed in traditional game-theoretic approaches. These earlier approaches often concentrate on static outcomes and are typically confined to small-scale situations, which constrains their applicability to real-world, evolving macro-social contexts. In stark contrast, Overbo's model is engineered for effective scalability, enabling it to capture dynamic, large-scale societal phenomena and the temporal processes that characterize the development and stabilization of social norms. This inherent design for dynamic, large-scale analysis offers a significant advantage for scientific inquiry and computational simulation, moving beyond the often qualitative or static nature of prior social norm theories. The model's deterministic nature further means that, given a set of initial conditions and parameters, its future states are precisely determined, enhancing its predictability and reproducibility, which are cornerstones of scientific understanding. Moreover, the model reliably generates long-run equilibria under time-invariant parameters, a characteristic not commonly found in established approaches, ensuring predictable long-term behavior under stable conditions.
The model integrates three primary forces that collectively explain agent-level behavior: native preference, social influence, and habit formation. Native preference accounts for intrinsic and heterogeneous motivations, ensuring a degree of behavioral variety even in highly conforming environments. Social influence reflects the pressure individuals experience from observing the behaviors of others, which drives conformity. Habit formation, on the other hand, stabilizes behavior over time, encouraging actions consistent with past decisions.
A novel and central feature of this model is the concept of "support." Support is introduced as a measure of the degree to which a set of chosen behaviors aligns with a given social norm. Unlike simpler measures that might focus on adherence to a single behavior, support captures the interrelation between various behaviors relevant to a norm, offering a more nuanced understanding of how collective patterns emerge from individual actions.
This comprehensive learning plan is designed to demystify Kristopher Overbo's 'A Model of Social Norm Dynamics'. It aims to break down the dissertation's intricate theoretical and mathematical components into clear, understandable concepts for a non-expert audience. The plan provides a structured learning path, progressively building understanding of the model's core ideas, its intellectual lineage, its unique contributions, and its practical implications. By fostering a deeper appreciation for the complexities of social norm dynamics, this report seeks to make expert-level research accessible and to highlight its relevance to real-world social phenomena.
To fully appreciate the contributions of Overbo's model, it is essential to understand the theoretical landscape from which it emerges. The study of social norms has a rich history, with various scholars offering distinct perspectives and frameworks.
The academic discourse on social norms has long grappled with the challenge of a unified definition. This lack of consensus has hindered consistent modeling and empirical validation across studies.
Coleman's Definition: James Coleman (1990) provided an influential definition, stating that a social norm exists "when the socially defined right to control the action is held not by the actor, but by others". This perspective emphasizes that norms represent a transfer of control over an individual's actions to others in society, typically focusing on specific "focal actions". However, this definition has limitations. It describes the conditions under which a norm exists rather than its inherent nature, which can obscure its more fundamental properties. There is also some ambiguity surrounding what constitutes a "socially defined right." Furthermore, Coleman's framework does not explicitly address the role of behavioral regularity; an unusual action, if socially pressured, could still be categorized as a norm, even if it lacks widespread adoption.
Bicchieri's Definition: Cristina Bicchieri (2005) offered a more ambitious and mathematically precise definition of social norms. She posited that a behavioral rule R qualifies as a social norm in a population if a sufficiently large subset of that population knows the rule exists and applies to a given situation. Crucially, each individual in this subset must prefer to conform to R, under the condition that they believe a sufficiently large subset of the population also conforms (empirical expectations), and that a sufficiently large subset expects them to conform (normative expectations), potentially with sanctions for non-compliance. Despite its admirable nuance, this definition does not encompass all phenomena commonly considered normative. For instance, Bicchieri explicitly excludes descriptive norms, providing fashion trends as an example. She declares that such norms are not social norms, but a distinct phenomenon. Interestingly, she declares that such norms carry no expectation from others that an individual conforms. Moreover, her model's reliance on measuring internal beliefs and expectations, while theoretically rich, can pose significant challenges for empirical observation.
Opp's Classification: Recognizing the difficulty in standardizing a single definition, Karl-Dieter Opp (2001) proposed a framework for classifying existing definitions by identifying three common elements: "Oughtness" (a shared sense of expected behaviors), "Behavioral Regularity" (coordination of behavior across a population), and "Sanctioning" (a system providing incentives or disincentives for certain behaviors). While helpful in organizing the diverse landscape of definitions, Opp's classification nonetheless highlights the disparate elements that a comprehensive model must integrate.
The persistent academic struggle to standardize a definition of "social norm," as evidenced by the varied and often mutually exclusive definitions offered by prominent scholars, reveals a fundamental fragmentation in the field. This fragmentation complicates consistent modeling, measurement, and the integration of research findings. A model that can either reconcile these definitions or propose a superior, more encompassing one would be a substantial contribution. Overbo's model, by later introducing concepts like "support" and "norm strength" and then using them to formally define a social norm, directly attempts to synthesize these disparate elements into a quantifiable and empirically tractable framework, aiming to bridge the gap between abstract theoretical constructs and measurable social phenomena.
In the formal modeling of social norms, game-theoretic approaches have emerged as a dominant framework. Early contributions from economists like Schelling (1960) introduced the idea that social norms could be understood as coordination problems, a concept later extended by Sugden (1986) to micro-scale situations. James Coleman's (1990) Foundations of Social Theory stands out as arguably the most influential work in this area, frequently framing norms as solutions to public goods problems (often modeled as prisoner's dilemmas) or coordination games.
Mechanics of Norm Emergence: Game theory explains norm emergence through strategic interactions. Conventional norms are typically modeled as coordination games where the payoff depends on each player choosing the same strategy (e.g., agreeing to drive on the same side of the road). These games are often resolved through communication or by identifying "focal equilibria"—solutions that stand out as naturally salient or obvious to all parties involved, such as meeting at the Eiffel Tower in Paris. Non-conventional norms are commonly illustrated as prisoner's dilemmas, where the first-order problem is that individual self-interest leads to suboptimal collective outcomes. The "second-order free-rider problem" arises because no one has an incentive to contribute to a system of controls to enforce cooperation. Coleman suggests that in practice, this is resolved through social relationships and the presence of zealous sanctioners, leading to socially beneficial outcomes. Cristina Bicchieri (2005) further extended this by proposing that social expectations—both empirical (belief that others are following the norm) and normative (belief that others expect one to follow the norm)—directly shape individuals' utility functions, thereby influencing their decision-making and norm adherence.
Advantages: Game theory offers a powerful framework for understanding social norms due to its expositional clarity and its ability to provide simple, formal models of human interaction. It simplifies complex social behaviors into strategic games, which helps clarify the exposition of norm formation and adherence. The field benefits from a rich research ecosystem that has developed across disciplines such as economics, sociology, psychology, and political science, allowing scholars to draw on a wealth of existing models, techniques, and empirical findings. Furthermore, game theory grounds the study of social norms in rational choice theory, providing a logical basis for explaining why people conform to norms, even when it requires costly sacrifices. The concept of equilibrium, central to game theory, illustrates how stable patterns of behavior can emerge from individual decision-making processes.
Limitations: Despite its strengths, traditional game theory faces several limitations when applied to social norms. These approaches primarily focus on static equilibria and are often restricted to small-scale interactions, making it difficult to describe the complex, multi-agent dynamics of real-world norms that evolve over time across large populations. Coleman's work, for example, frames norm internalization as a mechanism for cost reduction imposed by others, but it does not fully describe the process or explain why individuals would willingly accept costly norms that contradict their private beliefs. His treatment of disjoint norms (where beneficiaries and targets are separate groups) also heavily emphasizes coercive enforcement, overlooking more subtle forms of social pressure and influence. Moreover, these models often overlook the emergence of norms that are suboptimal or even damaging to collective welfare, often assuming norms must provide some benefit to the group. The highly specialized taxonomy of norms (e.g., conjoint vs. disjoint, prescriptive vs. proscriptive) often arises from the constraints of fitting norms into predefined game structures, which can fragment understanding rather than unify it and complicate empirical application.
Comparison to Overbo: Overbo's model fundamentally differentiates itself from traditional game theory by its inherent capacity to make precise predictions about how the development of norms is influenced by changes in network structure and individual actions over time. The core limitation of traditional game theory—its static nature and difficulty in scaling to large, dynamic social systems—creates a significant explanatory gap that Overbo's model directly aims to fill. By explicitly integrating temporal dynamics and network structures, Overbo's model offers a more practical and realistic framework for analyzing how norms evolve in constantly shifting, real-world environments, rather than merely identifying their stable end-states. This dynamic perspective is crucial for understanding social change and designing effective policy interventions, especially since real-world macro-social systems rarely achieve equilibrium due to constant shocks. While game-theoretic models provide general insights into long-run outcomes, Overbo's approach offers greater precision in forecasting the dynamic evolution of norms in specific social systems. It incorporates social embeddedness, similar to Bicchieri's extension, but focuses on habit and influence as key mechanisms, and explicitly integrates network effects.
Evolutionary Game Theory (EGT) offers a distinct approach to the study of social norms, shifting the focus from static equilibria and individual decision-making to population-level dynamics and intergenerational change. In EGT models, a population of agents is assigned fixed strategies (e.g., whether to follow a norm) that they employ in simulated interactions. The payoffs received from these interactions determine their ability to "replicate" in the next generation. This process leads to an evolution of strategies over time, as exemplified by Axelrod's work.
Advantages: EGT introduces intertemporal dynamics, allowing for the study of how behaviors adapt within a population over successive generations. Its stochastic approach can also circumvent some of the difficulties encountered in finding equilibria. EGT models serve to justify why cooperation or coordination behavior occurs, providing a theoretical basis for assumptions included in other models. Examining the parameter values under which various dominant strategies emerge can provide insights into why certain equilibria are favored over others.
Limitations: Despite its strengths, EGT has notable limitations when applied to social norms. The mechanics of EGT are often abstract and far removed from intuitive understandings of how norms and individuals actually work. Agents are treated as having fixed strategies within their lifetimes, effectively discarding the sense of rational calculation and real-time adaptation at the individual level. A critical input to these models is the "replicator function," which dictates the reproductive process; for social norms, this function often lacks a clear empirical counterpart. While EGT effectively demonstrates population dynamics, it does not capture agent dynamics within a single generation. It is well-suited for exploring macro-level, inter-generational dynamics over very long periods, but less so for explaining how norms appear and disappear within the much shorter, sub-evolutionary timescales relevant to human societies. Furthermore, prominent EGT models, such as Axelrod's, often abstract away from specific social network structures, focusing on aggregate outcomes and end-state equilibria rather than how network topology influences norm adoption and diffusion.
Comparison to Overbo: Overbo's model distinguishes itself by adhering to methodological individualism, explaining macro-social outcomes through individual-level interactions and grounding behavior in rational choice theory. EGT's strength in explaining the long-term evolutionary stability of cooperative behaviors comes at the cost of neglecting real-time individual adaptation and the rapid emergence or disappearance of norms within a single human generation. Overbo's model directly addresses this gap by providing a framework for intra-generational dynamics, where agents adapt their behavior in real-time through social influence and habit, rather than having fixed strategies that only change across generations. This makes his model more relevant for understanding contemporary social change, cultural shifts, and policy interventions that operate on much shorter timescales than evolutionary processes. The model also explicitly incorporates network structures, providing a richer understanding of how specific social contexts shape norm adoption and spread. Its focus is on how coordination occurs, complementing EGT's focus on why it might evolve.
Threshold models, rooted in Granovetter's (1978) seminal work, are computational simulations that frequently employ social network structures to explain how individuals make binary decisions, such as whether to adopt a particular behavior or follow a norm. These models propose that agents adopt a norm based on observing the same behavior in their network neighbors. A key concept is the "individual threshold," which represents the proportion of neighbors who must adopt a norm before the observing agent also does. This heterogeneity in thresholds is central to determining the tipping point at which norm adoption cascades through a population.
Extensions: Building on this foundation, Centola (2005, 2018) introduced the concept of "complex contagions," demonstrating that certain behaviors, particularly those requiring reinforcement from multiple contacts (i.e., strong ties), spread more effectively within dense, tightly connected clusters. This contrasts with "simple contagions," like information, which tend to travel more easily across weak ties in sparsely connected networks. Further extending these models, Mäs & Opp (2016) incorporated flexible thresholds, allowing individuals' decisions to change dynamically based on evolving social and personal contexts.
Limitations: While valuable for exploring the dynamics of norm diffusion in social networks, threshold models exhibit several notable limitations. Their reliance on binary decision-making (an all-or-nothing choice) oversimplifies the complexity of real-world behaviors, which often involve degrees of adherence rather than all-or-nothing choices. Additionally, these models typically assume static thresholds for agents, failing to capture how individual behaviors and social pressures evolve over time. The lack of empirical alignment in many threshold models makes it challenging to validate their assumptions or apply their findings directly to real-world scenarios. Furthermore, they often lack integrated microfoundations that detail the underlying behavioral or rationalized processes driving individual decisions.
Comparison to Overbo: Overbo's model addresses these limitations by allowing for "decision gradients" and "partial adherence" through its novel concept of "support," moving beyond the binary choices of threshold models. This means individuals can fulfill normative obligations in various ways and to varying degrees. The contrast between the "binary decision-making" in threshold models and Overbo's "decision gradients" and the continuous "support" concept is a key differentiator. Real-world social behavior is rarely a simple "yes" or "no" to a norm; there are degrees of adherence and substitution possibilities. This allows Overbo's model to explain more subtle social phenomena like partial conformity or gradual shifts, which are beyond the scope of threshold models. The model also incorporates dynamic individual adaptation and habit formation, allowing agents to adapt their behavior over time, and integrates elements of rational behavior (native preferences, social pressures, habits), bridging network and rational-choice perspectives. This enables it to explain persistent non-conformity or selective norm adoption, which threshold models are less equipped to handle. The absence of explicit rational foundations in many threshold models means they cannot explain why an individual might choose to deviate from a norm despite social pressure, a gap Overbo's model fills by integrating rational choice.
Overbo's model draws on established psychological theories to provide a robust micro-level foundation for individual behavior, notably the Reasoned Action Approach and the concept of habit formation.
Reasoned Action Approach (RAA): While neither a formal model, nor a model of social norms per se, the Reasoned Action Approach (RAA) from social psychology provides a well-studied theoretical basis for how individuals use norms to make decisions about their focal actions at the micro level. RAA, the modern incarnation of the earlier Theory of Planned Behavior and Theory of Reasoned Action (Fishbein & Ajzen, 2010). According to this view, behavior with respect to a specific focal action is determined primarily by what is called behavioral intention which itself is a function of three inputs:
Habit Formation: The concept of habit formation is central to Overbo's model's ability to account for the persistence and stability of social norms over time. It is incorporated as an agent-level tendency for individuals to maintain consistent support levels over time.
Habit is expressed in the model as a single period look-back term. As simple as this implementation is, the recursive nature of the model ensures that when $h_{i}$ $n_{i,i}\ne0,$ current support levels are influenced by all past support choices, with the relative impact of a given period diminishing as t increases. This means that, once established, support has persistence, even when external conditions or preferences change. This framework could be adapted to more sophisticated or longer period habit, however this simple implementation suitably enables the desired dynamics without over-complicating the model.
By explicitly integrating components from the Reasoned Action Approach into "native preference" and "social influence," Overbo's model provides a strong micro-level psychological grounding that many purely formal models lack. The model gains psychological realism by mapping RAA's "attitude" and "perceived control" to "native preference," and "perceived norm" to "social influence." Furthermore, the inclusion of habit formation as a dynamic, self-reinforcing mechanism offers a powerful and empirically supported explanation for norm persistence and internalization, moving beyond simple external sanctions or static preferences. This synthesis creates a more robust and testable framework for understanding why behaviors, once adopted, exhibit inertia and are difficult to change.
Overbo's model builds upon existing mathematical frameworks, particularly the DeGroot family of models, while introducing significant modifications to suit the complexities of social norm dynamics.
DeGroot Learning: This model, developed by statistician Morris DeGroot (1974), describes how individuals in a social network update their opinions or beliefs about what is true through interpersonal contact. The model captures the process by which a group of agents iteratively adjust their beliefs based on a weighted average of the opinions of their neighbors and their own prior beliefs. This means each person's new opinion is a mix of their old opinion and the opinions of those they listen to. Eventually, agents converge on persistent consensus or disagreement, depending on the network structure and the influence of endogenously set weights. The procedure can be described mathematically as follows:
$s_{i}^{t}=\sum_{j=1}^{n}w_{ij}s_{j}^{t-1}$
Here, $s_{i}^{t}$ is person 'i's opinion at time 't'. The symbol $\sum$ means "sum up" or "add together." So, $s_{i}^{t}$ is the sum of all $w_{ij}$ (how much person 'i' values person 'j's opinion) multiplied by $s_{j}^{t-1}$ (person 'j's opinion from the previous time period). The $w_{ij}$ values represent the weight agent 'i' places on the opinion of agent 'j'. 'n' is the number of agents (people) in the network. Each period, opinions are updated until a stable state is achieved.
This is not generally considered a rational model because there is no deliberate optimization done by the agents to arrive at the weights they assign to each opinion. Despite this, this model is remarkably simple and intuitive. There is also a modest body of empirical evidence emerging that individuals do learn this way (Jadbabaie et al., 2012; Chandrasekhar et al., 2020).
The model presented in this paper is most structurally similar to that of Friedkin & Johnsen (1990), a variant of the DeGroot Learning Model which adds static preferences, though it differs in application, elements of time variance, and theoretical explanation of its components. See Section 7.5 for further discussion.
Comparison to Overbo: Overbo's model is most structurally similar to the Friedkin & Johnsen variant. However, it distinguishes itself by allowing both the network structure ($N^t$) and the anchor position (native support $\dot{s}^t$) of each agent to be time-variant. This time variance is crucial as it allows for the modeling of external shocks and creates long-run equilibrium behavior that is not solely bounded by initial conditions. Furthermore, Overbo's model introduces the novel abstraction layer of "support," which measures the degree of alignment with a social norm, rather than just an opinion or belief. More significantly, while DeGroot models are typically applied to the learning and convergence of information or opinions, Overbo's model is specifically designed to explain the formation and maintenance of social norms. It provides explicit rational foundations for its usage and defines each term differently within this context.
By building upon the mathematical elegance of DeGroot-like models but introducing time-variance in both network structure and native preferences, Overbo's model gains crucial flexibility to simulate real-world social systems that are constantly subject to external shocks and evolving individual inclinations. This dynamic adaptability, combined with an explicit rational foundation and the novel concept of "support," allows it to model complex norm evolution beyond simple opinion convergence. The explicit statement of mathematical similarity to DeGroot models is important, but the modifications are what allow Overbo's model to realistically handle external "shocks" and ongoing "evolution" in a way that static DeGroot models cannot. The introduction of "support" as an abstraction layer also allows the model to capture more complex social phenomena than simple opinion transmission, and the claim of rational foundations provides a deeper theoretical grounding for the observed dynamics.
| Model Type | Key Characteristics | Primary Limitations Addressed by Overbo's Model |
|---|---|---|
| Traditional Game Theory (e.g., Coleman, Bicchieri) | Focus on static equilibria, small-scale interactions, fixed strategies, emphasis on payoffs and sanctions, often struggles with harmful/neutral norms, fragmented taxonomy. | Overcomes static nature and lack of scalability; provides more nuanced internalization; incorporates subtle social pressure; capable of explaining harmful norms. |
| Evolutionary Game Theory (EGT) (e.g., Axelrod) | Population-level dynamics, intergenerational change, fixed strategies within individual lifetimes, no clear empirical analog for replicator function, often abstracts from specific network structures. | Offers strong microfoundations for agent dynamics; focuses on real-time intra-generational adaptation; explicitly integrates network effects. |
| Threshold Models (e.g., Granovetter, Centola) | Binary decision-making, static thresholds (often), focus on network diffusion and cascades, limited explicit microfoundations, oversimplifies behavioral complexity. | Moves beyond binary oversimplification to continuous behavioral measures ("support"); allows for dynamic thresholds and adaptation; integrates rational choice microfoundations. |
| Overbo's Model | Deterministic, scalable to large populations, captures temporal (intra-generational) dynamics, grounded in rational choice, introduces continuous "support" measure, explicitly incorporates dynamic network structures and habit formation, capable of explaining harmful/neutral norms, offers a unified norm definition. | (Integrates strengths and addresses limitations of previous models.) |
Overbo's model is a deterministic framework that describes how individual decisions aggregate to form societal norms over time. It is built upon three primary forces that explain agent-level behavior: native preference, social influence, and habit formation.
The model defines an agent's current "support" ($s_{i}^{t}$) recursively, as a weighted average of these three key forces. The core equation is:
$s_{i}^{t}=n_{i,i}^{t}((1-h_{i})\dot{s}_{i}^{t}+h_{i}s_{i}^{t-1})+\sum_{j=1}^{p}n_{i,j}^{t}s_{j}^{t-1}$
Let's break this down:
So, in simple terms, this equation says: **Your current support for a norm ($s_{i}^{t}$) is a mix of what you naturally prefer ($\dot{s}_{i}^{t}$), what you did last ($s_{i}^{t-1}$), and what your friends or influential people did ($s_{j}^{t-1}$), all weighted by how much each factor matters to you.**
After the $t=0$ initial state, the support chosen by agent i in each period is a weighted average of three other support values that are observable to i: native preference, habit, and social influence. The $n_{i,j}^{t}$ weights indicate the extent to which each agent in the network, including themselves, influences future support, while the $h_{i}$ weights further divide the non-social influences into the other two component parts. The support level generated by this function feeds into the $t+1$ period behaviors through the habit term for the same agent and the social influence term for other agents connected directly via an influence network $N^{t+1}$. Through this social influence channel, the time t support of a given agent affects neighbors at distance d at time $t+d$ and as well as providing some amount of self-feedback in alternating periods. This speed-of-light effect provides additional dynamics and links individual behavior to macrosocial effects. See Figure 4.
This model is generally concerned with dynamics, consistent with an expectation that large social systems frequently experience shocks. Still, it is worth noting that the model itself is not inherently divergent. The model reaches equilibrium in the absence of shocks to $N^{t}$ and $\dot{S}^{t}$ as $t\rightarrow\infty$ This is apparent in the demonstrations in Section 5. See Appendix C for a proof of this convergence.
In the following sections we discuss each major term mentioned in greater detail, beginning with support.
The concept of "support" is not discussed in existing literature on norms; it is introduced with this model. Support serves as a scalar value representing the degree to which an individual's actions reflect adherence to an ideal. In support, we are attempting to capture the nuanced nature of conformity. This section discusses the theoretical underpinnings of support, its relationship to observable behaviors, and its significance in shaping norm dynamics within the social system.
We begin the discussion with an example. Suppose we are interested in studying the social norm one might initially describe as "clapping at the end of a good performance." It may be claimed that, with respect to this norm, either a person claps in a particular instance, or they do not, and thus the individual's behavior is a binary variable for observational purposes. This idea aligns cleanly with the idea of a focal behavior as discussed in existing literature on norms in Section 2. Seldom, however, is this type of social behavior so simply exhibited or interpreted by others. Some clap easily, some enthusiastically, some clap more or less frequently, or pause before beginning to clap. When a researcher considers such variations important, and they seldom do, they may deem it necessary to measure focal behavior as a numeric (scalar) value. To further complicate matters though, there are very close substitutes for clapping. Some may add vocal cheers or whistles. Some might boo, which could be considered a sort of anti-clapping. This range of behaviors is observed by others and serves as a key indicator of an individual's attitude toward the relevant norm.
When applying conventional game theoretic modeling to norms, capturing such nuance is particularly challenging. In principle, it is possible to construct a discrete game which divides the set of strategies available to an individual into "strong clapping", "weak clapping", "booing" etc., but introducing any reasonable amount of strategic variety into such a framework invites intractability for both the theorist and the empiricist even at the micro-scale. Still, the ability to accommodate more nuanced strategies would have an advantage in this regard over one that does not.
It is with this in mind that the concept of support is introduced. It will first be defined informally as the amount of enthusiasm with which one's collection of behaviors aligns to the principles of a norm. Behavior with respect to a particular focal action is typically a component of support, but not the entirety of it. It is quite possible to demonstrate meaningful support for a prescriptive norm while not engaging in the focal action it is built upon (e.g., "I would love dearly to shake your hand, but I have a flu").
Support, as a concept, has the advantage of capturing meaningful relationships among behaviors beyond a single focal behavior. The disadvantage is that by adding this layer of abstraction, the methods of measurement become less obvious. Researchers can, and often do, simply survey a population about their local and subjective estimations of how behaviors relate to social expectations (Jasso & Opp, 1997; Gerber et al., 2008; Fishbein & Ajzen, 2010). In practice, a survey could also be constructed which captures perceptions about how well a particular collection of behaviors align to the expectations of a norm. Still, it is desirable to make the relationship between support and behavior explicit. Doing so clarifies the concept and provides an alternate method for measuring support when surveys are unavailable or unconvincing. To that end, we next define support formally in terms of observables.
Let $\vec{B}_{i}^{t}\in\mathbb{R}^{m}$ be a vector of m measurable observations of person 'i's behaviors in some discrete time period t. Let support weights $\vec{W}\in\mathbb{R}^{n}$ be a vector of weights corresponding to those observations. Let i's support $s_{i}\in\mathbb{R}$ be the dot product of $\vec{W}$ and $\vec{B}_{i}^{t}$
$s_{i}^{t}=\vec{W}\cdot\vec{B}_{i}^{t}$
So, $s_{i}^{t}$ is a single number that summarizes how much a person's actions align with a norm, by giving different importance to different behaviors. For example, if a norm is "being a good student," $\vec{B}_{i}^{t}$ might include behaviors like "attending class," "doing homework," and "participating in discussions." $\vec{W}$ would assign weights to these, perhaps giving more weight to "doing homework" than "attending class." Then, $s_{i}^{t}$ would be your overall "good student" score. The model assumes $\vec{W}$ is stable and known to all. Conceptually, it may be convenient to think of $S_{i}$ as the units of effort an agent i spends in contributing to an ideal specified by $\vec{W}$ with $s_{i}=0$ indicating perfectly neutral behavior. $\vec{W}$ can be thought of as a perceived exchange rate between behaviors in their contribution to that ideal.
One way for agents to coordinate on support is to coordinate on behavior. If one behaves exactly the way another does, applying $\vec{W}$ results in identical support values. Such behavioral mimicry is consistent with the work of Cialdini et al. (1990) on descriptive norms. Kuran (1995) uses the argument of bounded rationality to explain such behavior coordination. It has been found that teenagers often mimic each other's behavior (Robalino & Macy, 2018; Paluck et al., 2016). Repacholi et al. (2014) finds evidence that 15-month-old infants are able to interpret the social interactions of others to effectively mimic acceptable behaviors, suggesting that the phenomenon develops quite early in life.
A utilitarian argument for such mimicry can be expressed as follows: People have a preference for others whose interests appear to be aligned with their own. Agents, knowing this will, to varying degrees, modify their behavior to reflect the interest of people whose favor they seek; a child will mimic the behavior of their parent, an employee will mimic the behaviors of the boss, married couples will seek to mimic each other, etc. Benefits of mimicry can also extend beyond the direct relationship with the agent being mimicked. If agent A aligns their behavior with a successful or popular individual B, agent C may see A's behavior as a signal that A shares qualities with B. In this way, A's reputation may improve with C.
As mentioned, one could mimic support by copying the behaviors of another perfectly. However, there is another possibility. Through $\vec{W}$ the agent is afforded the option of substituting one behavior for another to coordinate on a concept instead of a specific behavior. A roommate who wishes to honor a norm of cooperation among housemates can prepare dinner while another washes the dishes. The model in this paper implies that such conceptual trade-offs are important to understanding complex social norms. This ability to capture nuanced behavioral patterns and the interrelation of multiple behaviors significantly enhances the model's capacity to explain complex social phenomena.
A crucial aspect of Overbo's model is its grounding in rational choice theory, demonstrating that the observed behaviors and norm dynamics emerge from individual utility maximization.
The model's derivation from individual utility begins by characterizing a "happiness score" or "satisfaction level" ($U_{fl}$), which includes native preferences, habit formation, social influence, and expected future happiness. For mathematical convenience, these terms are treated as "additively separable," meaning each part of your happiness (from your natural preference, your habits, and social influence) simply adds up to your total happiness. The model assumes that your happiness changes smoothly, and that the "cost" or "unhappiness" of deviating from your ideal behavior for each factor increases the further you stray. Think of it like walking up a hill: the further you go from the top, the steeper it gets, making it harder to keep going.
The model primarily uses an "immediate utility" function ($U^t$), which is your happiness right now, without worrying about the distant future. There are three main arguments for this simplification:
Assuming that $U^t$ is a good enough approximation of $U_{fl}$, the model defines each of the three components (influence, native preference, habit) as "parabolic functions." Imagine a hill shape: your happiness is highest at the peak (your ideal behavior for that factor), and it decreases as you move away from that ideal, like going down either side of the hill. The further you are from your ideal, the more your happiness drops. For example:
By combining these terms, the model finds the "utility-maximizing support" ($s^{t}$), which is the sweet spot where your overall happiness is highest, by balancing all these forces. This is done by finding where the "first-order condition" is zero, which means that making a tiny change to your support won't make you any happier or unhappier.
After some mathematical steps, the model's core equation for optimal support is derived:
$s^{t}=\frac{a_{K+1}\dot{s}^{t}+a_{K+2}s^{t-1}+\sum_{k=1}^{K}a_{k}\dot{s}_{k}^{t-1}}{\sum_{k=1}^{K+2}a_{k}}$
This equation shows that your best choice for support ($s^{t}$) is a weighted average of your natural preference ($\dot{s}^{t}$), your past behavior ($s^{t-1}$), and the past behavior of your influential neighbors ($\dot{s}_{k}^{t-1}$). The 'a' values ($a_{K+1}$, $a_{K+2}$, $a_k$) are like "importance weights" that tell you how much each factor contributes to your overall happiness. When these weights are organized into a matrix for all agents, we get the full model described by Equation 3, showing how everyone in the network influences each other.
The Role of Information: The model assumes that agents make decisions based on "complete information" from their immediate surroundings. This means they only need to observe their own past actions and the past behaviors of those directly connected to them in their network. They don't need to know everything about the entire network, and they don't need to worry about how their single choice might affect the whole system in the long run.
Connecting Support and Behavior: A critical aspect of the model's rational foundation is that for a given person and their "support weights" ($\vec{W}$), a specific "support score" implies a unique set of behaviors. This is important because it means the model can predict specific actions, not just abstract support levels.
The idea is that if you want to achieve a certain support score, you'll choose from your available behaviors to get there. If your natural behaviors don't perfectly match the target support, you'll make compromises. You'll change the behavior that costs you the least "unhappiness" to adjust towards the target. As that behavior changes, its cost increases, and you might switch to adjusting another behavior that now costs less. This continues until you reach your target support. The thesis mathematically shows this works for any number of behaviors, ensuring that the model can make concrete predictions about specific actions.
$s^{t}=wb^{t}$
This means if you know your target support score and the importance of clapping, you can directly calculate how much you should clap:
$b^{t}=\frac{s^{t}}{w}$
$s^{t}=w_{1}b_{1}^{t}+w_{2}b_{2}^{t}$
Even though many combinations of clapping and cheering could give the same total support, the model uses additional math to figure out the *best* combination for you. This involves minimizing the "unhappiness" from deviating from your natural clapping ($\dot{b}_1^t$) and cheering ($\dot{b}_2^t$) levels. The math helps find the specific amounts of $b_1^t$ and $b_2^t$ that achieve your target support while making you as "happy" as possible.
Having established the micro-level foundations of the model, it is now possible to aggregate individual behaviors to derive network-wide measures, providing a quantitative lens through which to understand macro-social phenomena.
The model allows for the application of statistical methods to quantify and compare macrosocial properties of a society. Several key metrics are defined:
$\eta^{t}=\frac{\sigma_{\dot{s}}^{t}}{\sigma_{s}^{t}}$
A higher $\eta^{t}$ means the norm is "stronger." It captures how much the group's behavior is *pulled together* by social forces, compared to how spread out it would be if everyone just did their own thing. It's a way to compare the strength of different norms.
With these macro-level measures in place, the model proposes a formal definition for the existence of a social norm:
The pair $(\vec{W},\tau)$ is said to be a social norm in influence network $N^{t}$ at time t if and only if $\eta^{t}>\eta_{crit}^{t},$ where $\vec{W}$ is the mapping between behavior and support. $\tau$ indicates a target support value. $\eta_{crit}^{t}$ is a critical norm strength which denotes the cutoff indicating when a norm is strong enough to be said to exist. The choice of $\eta_{crit}^{t}$ is somewhat arbitrary, just as the cutoff for calling a person 'tall' is arbitrary. Notably though, when $\eta^{t}>2$ more of the variation in support is accounted for by normative dynamics than native support. A less formal way to express this definition is: A norm is the (nontrivial) force, produced by agents' social embeddedness, acting to modify those agents' behavior from how they would otherwise act.
We will illustrate how this definition is applied by way of example. One's participation in football hooliganism can be measured by taking into account a variety of behaviors, attending football matches, chanting, frequenting certain pubs, engaging in post-match vandalism. All these behaviors and their relative contributions to the idea of hooliganism is captured by a $\vec{W}$ It could be that the norm in a given community is very low levels of football hooliganism, or it could be high, or anything in between. This target value is indicated by T. These two values, $\vec{W}$ and , specify a norm conceptually, but this is only a hypothetical norm of hooliganism. To be relevant, that level of hooliganism must exist in the context of a group of people at a particular time. This time and group are identified by $N^{t}$. Having chosen a norm and a group, we can turn our attention to testing for the existence of the norm in the wild. It is not enough to notice that individuals in $N^{t}$ typically, or on average, engage in hooliganism at the level we are interested in. High(low) hooliganism can be explained by non-social factors such as having few(many) other pastimes available or having low(high) police presence in the area. Such factors are ones of native preference. In order for such behavioral regularity to be caused by a norm for hooliganism, it must be transmitted socially. We test for this by measuring $\eta^{t}$, which is how much cumulative effects of social embeddedness have reduced support variance in the population compared to a world without such influences. If newly joining members of the network show changes in their support levels aligning with the target support, a high $\eta^{t}$ is implied, and we say the norm exists in that network at that time. We have then specified and established the existence of the hooliganism norm.
It is worthwhile to briefly examine this definition through the lens of the classifications provided by Opp (2001).
This definition offers a relatively rigorous and quantifiable way to identify and test for the presence of norms within a population. The distinction between behavioral regularity and normative dynamics is critical, as it highlights that norms are not merely patterns of behavior but forces that actively shape individual actions within social networks.
This section explores dynamic aspects of the proposed model, demonstrating how individual behaviors aggregate to produce evolving social outcomes. Through various simulations, it explores different network structures and their impact on the stabilization and diffusion of social norms. These illustrations offer insights into the conditions under which norms emerge, persist, or fade.
The baseline simulation provides a foundational demonstration of the model's behavior in the absence of shocks, large asymmetries, or complex network topologies. Each example in the following section modifies some aspect of the baseline simulation to illustrate its effect on support. The code used to generate this simulation, as well as all others presented in this paper, can be found in Appendix D.
In figure 5a, each line corresponds to the support value of an agent in the network over time. Initially, all agents start with a support level equal to their time-invariant native preference level, s. Each of these values is randomly determined by an independently and identically distributed (i.i.d.) draw from a uniform probability distribution over the range. Over time t, the agents' support values converge, causing $\eta^{t}$ to increase from its base value of 1. The $\eta^{t}$ value in the last period is displayed on the upper left of the plot.
In Figure 5b, the network layout for this simulation is shown. The network is fully connected in this case, meaning there are two edges between every pair of agents, one in each direction. The connection weight of each edge is selected randomly and i.i.d. from a uniform distribution over the interval. The agents' self-influence values set to be 80% of the total influence. Habit formation terms are chosen from the range [0.75, 1.0]. These two ranges were explicitly selected to ensure that convergence and clustering occur at a rate suitable for the chosen number of time periods. Weights are then normalized to conform with Equation 5. The nodes are numbered in descending order according to initial support values $(\dot{s}^{0})$ values. Agent 1 has the highest $\dot{s}^{0}$, Agent 2 has the second highest, and so on.
Collective instrumentality is not a requirement for a norm to exist. It could be that the $t=0$ states were better for all instrumentally. There is no welfare function applied or included in the model independently. Still, potential welfare gains should improve the likelihood of a norm emerging via s. Collective instrumentality can enter through its impact on global native preferences as we will see in 5.5. Passive transmission of behavior allows for influential people to unintentionally sway $\tau^{t}$ and create a norm. In general, a norm will emerge when an influential subset of society has coordinated support. This coordination could be coincidental, intentional, or incidental.
Here we explore three degenerate forms of the model by removing each of the three primary components (native preferences, habit, and influence) from the model in turn. Studying these degenerate forms illustrates the impact of each term on the model. This approach also tests the robustness of the model by exploring how it behaves under extreme or simplified conditions, helping to reveal its limitations or potential weaknesses.
These degenerate forms demonstrate the individual contributions of each component to the model's overall dynamics and the emergence of social norms.
The model's simulations illustrate how different network structures significantly impact the development and persistence of social norms.
The model is designed to account for the dynamic nature of social systems, including the impact of external shocks and the persistence of behaviors over time.
While Overbo's research is theoretical, it lays a foundation for future empirical work by offering conceptual tools and practical insights into how social norm dynamics might be observed in the real world. This section explores several complementary aspects of how the model connects to empirical research, including testable propositions and guidance on parameter measurement.
The proposed model offers a structured account of how individual decision-making gives rise to collective normative behavior. It generates a number of broad claims that lend themselves to empirical testing, allowing researchers to evaluate major aspects of the model without needing to account for its full complexity in a single study.
Proposition 1: Substitution Under Behavioral Restriction
When a norm-supporting behavior is externally restricted, individuals will compensate in the short run by increasing complementary behaviors that serve the same normative function. The magnitude of this compensatory shift is proportional to the normative importance of the restricted behavior relative to the availability and cost of substitutes. This proposition follows from the inclusion of habit and multi-behavior support in the model. When a norm-associated behavior becomes restricted (e.g., by law or increased cost), it is effectively no longer available to signal support. Nonetheless, because habit reinforces prior support levels in the short run, agents will choose alternative behaviors in order to maintain support requirements. This leads to a temporary increase in complementary support behaviors before moving toward a new equilibrium. The practical consequence of this is that individuals do not immediately abandon a norm when a focal behavior is restricted. Instead, they adjust by engaging in alternative behaviors that fulfill a similar normative function. For instance, if the right to vote were taken away, the immediate effect would not be a decrease in support for democratic ideals. Rather, there would be an increase in pro-democratic discussion and demonstration among those who value democracy as they make use of these alternative outlets to express normative support. The magnitude of this compensatory shift depends on the extent to which the restricted behavior is integral to the norm and whether viable substitutes are available. On a smaller scale, Proposition 1 could be used to study the effects of workplace break restrictions. In this context, if socializing breaks for a company's employees were banned, any existing norm of informal workplace socializing would, at least temporarily, cause a shift toward other related behaviors. Suppose a company implements a stricter break policy, which severely hinders workplace socializing. According to the proposition, employees who previously relied on these breaks for social bonding and informal collaboration will immediately compensate by increasing engagement in alternative forms of workplace interaction. Examples of this include sending more informal messages, lingering longer at the water cooler, or turning routine meetings into more social interactions. A quasi-experimental study could analyze employee behavior before and after such a policy is introduced, tracking changes in messaging volume, meeting length, and informal in-office interactions. A difference-in-differences approach could then compare offices with and without such restrictions, measuring whether employees in restricted offices increase substitute social behaviors. Such a hypothesis might also be tested through an observational study. Researchers could track whether employees shift to alternative break-like behaviors by comparing organizations that recently implemented break-restricting rules to those that have not. If Proposition 1 holds, employees will find ways to compensate for the removal of informal breaks by increasing other behaviors that fulfill the same normative function, at least temporarily. Beck et al. (2024) provides an existing study that, with slight modification, could be conducted to empirically test this aspect of the model. They examined compensatory behavior in adolescents physical activity by tracking natural deviations from habitual exercise levels and identifying instances where individuals compensated for reductions in activity with increased alternative physical behaviors. Their study employed a mixed-methods crossover design, using self-reported habitual activity schedules, smartphone-based activity diaries, and follow-up interviews to analyze compensation patterns. To test Proposition 1, a similar methodology could be employed, but with a systematically imposed restriction on a norm-supporting behavior rather than relying on natural and idiosyncratic fluctuations.
Proposition 2: Long-Term Effects of Policy
In the long run, policies aimed at norm modification are most effective when alternative norm-supporting behaviors are costly or difficult to adopt. When substitutes are low-cost and accessible, individuals shift toward these alternatives, sustaining the norm despite efforts to restrict focal behaviors. Whereas Proposition 1 addresses short-term effects, Proposition 2 concerns itself with long-term or equilibrium consequences of compensatory behaviors. The extent to which the norm ultimately persists depends on the availability and cost of alternative norm-supporting behaviors. This is because in the long run, native support dominates habit. If substitute behaviors are cheap and readily available, individuals can easily transition to these alternatives, mitigating the long-term impact of the policy on the norm. In contrast, if substitutes are expensive, inconvenient, or otherwise very costly, norm adherence will ultimately decline as individuals find it too taxing to maintain. For example, researchers could examine smoking rates in communities that ban public smoking, chewing tobacco, and vaping versus those that banned only smoking, to determine whether restricting substitute behaviors better leads to a long-run decline in nicotine use. Even without direct restrictions on substitute behaviors, researchers can still explore alternative testing opportunities. A natural experiment could analyze consumer behavior in regions where a ban on a norm-supporting behavior was introduced, with and without easy access to substitutes. When smoking is banned indoors, people may be forced to smoke outside in designated areas, but for smokers in Florida, such an alternative is more attractive than it would be for smokers in Alaska, particularly during winter months. By tracking behavioral adaptation over time, researchers could assess whether very costly substitution is merely a temporary adjustment or whether it sustains the targeted norm in the long run, contradicting this proposition. This suggests that empirical tests of long-run policy effectiveness should focus on whether norms shift or change over time, conditional on the cost of alternative behaviors. A robust empirical test would involve a longitudinal comparison of policy interventions that restrict a norm-supporting behavior, with variation in the availability and cost of substitutes. A strong research design would control for pre-policy trends and economic conditions over time to isolate the policy's effect on norm persistence.
A study like that of Akee et al. (2010) would be a strong candidate for testing Proposition 2. This longitudinal analysis leveraged a natural experiment in which an exogenous increase in household income from casino revenue distributions allowed researchers to observe long-term behavioral changes. For the relevant test, a comparable design could be used, incorporating the additional step of collecting data on the availability and cost of alternative behaviors associated with previously established norms.
The findings of such studies would have important implications for policymakers designing norm-diminishing interventions. To ensure the long-term effectiveness of such policies, regulators must not only restrict certain behaviors but also consider whether alternative norm-supporting behaviors will emerge to replace them. If substitution effects are anticipated, additional policy mechanisms, such as raising the cost of substitutes through taxation or restricting their availability through complementary regulations, may be necessary to prevent the long-run persistence of the undesired norm. Understanding these substitution effects will help in crafting policies that not only create immediate behavioral change but also weaken or strengthen norm adherence in the long run, leading to more lasting social transformation.
Proposition 3: The Role of Influencers
Individuals with high social leverage who gain high exposure can shift population target support toward their own. Sustaining this effect in the long run requires continued exposure. In this paper's model, when a high-leverage individual receives substantial exposure, others who observe this directly shift their own support to more closely align with that individual, all else being equal. If this exposure is widespread enough, the macro-social effect can be substantial. The model further implies that this effect is time-sensitive. Without continued reinforcement, the impact of a high-leverage individual's actions will diminish at a rate inversely proportional to habit. This diminishing effect, illustrated in Figure 10, occurs because habit formation alone cannot sustain a new norm indefinitely. Once this exposure is removed, native preferences begin to reassert themselves, gradually reducing long-term adherence to the newly shifted support. If a high-leverage individual demonstrates a specific norm through a single widely covered media event, for example, there is expected to be a temporary increase in the norm's adoption, which will decay unless reinforced through sustained exposure. Empirically, this should be clearest if the high-leverage individual is relatively uninfluenced by others. This is because if they are also subject to heavy influence themselves, the feedback influence will mute the difference between their support and that of the audience prior to exposure. For example, between two public figures of equal stature and sustained exposure, the one over whom the audience has less leverage will have a greater normative impact in their respective network. Proposition 3 suggests that the news cycle can drive large changes in collective behavior. Media coverage enables widespread and unidirectional exposure of individuals who are frequently of high status. See the discussion of the "Angelina Jolie Effect" in Section 8.2.1 for a more detailed example of this effect. Possible tests include a longitudinal survey to track behavioral shifts in a population exposed to high-leverage influencers over time or a field experiment in which different social groups receive norm-promoting messages from either high-leverage influencers or low-leverage peers. Additionally, social media data could be analyzed to examine how changes in influencer advocacy impact public sentiment over time.
A study such as that of Jackson & Darrow (2005) could be modified to empirically test Proposition 3. This experiment exposed young adults to political endorsements from celebrities through controlled media presentations, including televised interviews and campaign advertisements. Participants' political opinions were measured before and after exposure to assess the immediate impact of celebrity influence and strong evidence was found for the effectiveness of such exposure. However, the study examined only short-term reactions and did not explore whether these effects persisted over time. To test Proposition 3, a similar methodology could be employed with a more longitudinal design, where some participants are repeatedly exposed to norm-promoting messages from the same high-leverage individuals over an extended period. By tracking changes in participants' behaviors and support levels at multiple time points, researchers could assess whether continued exposure is necessary to sustain the initial influence of high-leverage individuals, thereby providing empirical validation for the proposition's emphasis on the importance of sustained visibility for long-term normative change.
Proposition 4: Endowment and Social Influence
In any interaction where exposure occurs $(e_{i,j}^{t}\ne0)$ the social influence of individual j over individual i increases in j's endowment. Given that influence is a function of exposure and leverage, and that leverage increases in endowment, we arrive at Proposition 4 directly from Equations 4 and 11. In the model, endowment amplifies an individual's ability to shape the normative choices of others by increasing the influence their previously expressed support carries. When two individuals interact, the one with greater endowment has a larger effect on the behavior of the other when controlling for exposure. While endowments salient to the norm can be expected to have the most practical impact, (e.g., fashion guidance would be more well-received from a successful fashion designer) this assertion applies to all forms of endowment. All else being equal, the impact one agent's support has on others increases in wealth, beauty, power, authority, or any other observable asset or right. As this proposition is micro-focused, it may be well-suited to a lab experiment. A researcher might pair participants with differing levels of perceived authority, knowledge, or material resources and assign them a task requiring norm formation, such as deciding on the appropriate response to a novel social etiquette scenario. By tracking changes in behavior after interactions, researchers could measure the extent to which the lower-endowed individual shifts toward the norm expressed by the higher-endowed individual.
A study such as that of Asch (1956) could be modified to empirically test Proposition 4. In the original experiment, participants were placed in a group setting with confederates who intentionally provided incorrect answers to simple perceptual tasks. The study measured the extent to which individuals conformed to the majority opinion, demonstrating the power of social influence. However, the experiment did not specifically examine the role of individual endowments, such as authority or expertise, in influencing conformity. To test Proposition 4, a similar experimental design could be employed where participants are paired with confederates who are presented as having varying levels of endowment relevant to the task such as differing levels of expertise or status. By systematically varying the perceived endowment of the confederates and measuring the degree of conformity exhibited by participants, researchers could assess whether individuals with higher endowments exert greater social influence during interactions, thereby offering empirical support for the proposition.
Proposition 5: The Role of Deviation Costs in Norm Strength
A social norm will be stronger when the cost of deviating from native preference toward behaviors that support the norm is lower. This proposition follows from the inclusion of a coefficient on the native preference term in utility, which represents the cost of deviating from intrinsically desired behaviors. Because an individual's native behavior preferences will typically be misaligned with the prevailing norm, adherence requires individuals to adjust their expressed behaviors at some personal cost. If the cost of deviation from native preferences is high, individuals are less likely to make large adjustments to coordinate with the norm. Conversely, when the cost of deviation is low, individuals will more readily shift toward behaviors that reinforce the norm, making it stronger. At the micro scale, this suggests that if the norm is something a person would have followed in the absence of social pressure, or if the person does not intrinsically care much about the relevant behaviors, they will adhere more closely to the norm. At the macro scale, this means that a social group will adhere more strongly to the norm if there is generally little instrumental harm in aligning their behavior. Empirical testing of this proposition could focus on contexts where behavioral shifts occur with varying levels of cost. For example, recycling norms are expected to be stronger in environments where waste sorting is simple, with clearly labeled bins and minimal effort required from individuals. However, in areas where recycling requires complex sorting, extra fees, or special drop-off locations, the norm is predicted to be weaker. This weakness is expected to be observable not only in focal behavior but also in support behaviors such as recycling advocacy.
An empirical study that supports Proposition 5 in this manner is Niu et al. (2023), which investigates the influence of personal costs on adherence to pro-environmental social norms. In this study, participants were asked to engage in environmentally friendly behaviors such as recycling, reducing energy consumption, and minimizing single-use plastics, with varying levels of personal cost imposed such as time, effort, and financial burden. The researchers found that participants were more likely to adhere to pro-environmental norms when personal costs were low, while higher costs led to reduced adherence. This aligns with Proposition 5 by demonstrating that lower costs of deviating from native preferences facilitate stronger adherence to social norms. To test the proposition more directly, future studies could manipulate the cost of deviating from self-interest in controlled environments, such as by varying the complexity of recycling tasks or the financial incentives for non-recyclable waste disposal, and measuring subsequent adherence to recycling norms. This approach would isolate the causal effect of deviation costs on norm strength, providing direct evidence that when the cost of ignoring the norm is high, adherence diminishes, while lower costs encourage stronger norm-following behavior. Additionally, measuring not just overt behavior but also attitudes and advocacy for the norm under different cost conditions would capture the broader social reinforcement effects that the proposition anticipates. Proposition 5 is also particularly relevant to voting norms because the costs related to participation are so low. See Sections 8.2.2 and 8.2.3 for further discussion of how these low costs aid in norm formation and adaptability.
The following topics illustrate some strengths of the proposed model by highlighting its capability to address certain social phenomena that other models struggle to capture. This is not to claim that other models cannot accommodate these observations with modification, nor was the primary aim of this research to resolve such issues. Rather, the idea is to convey that explanations for these observations emerge more naturally from this model than the alternatives. This indicates that the model may be especially well-suited for empirical study of such issues and can also be effectively tested and refined through them.
Celebrity Influence: In Section 5.5, we show how an influential individual can sway behavior across a society under the proposed model. This illustrates how community behavior can shift rapidly due to the involvement of celebrities or other prominent figures. Traditional game theory, EGT, and Threshold models do not natively account for such asymmetric influence in descriptive norms, though such effects are quite apparent empirically (Cialdini et al., 1990). A specific example that demonstrates this issue is the so-called "Angelina effect". This refers to the surge in preventative healthcare behaviors, particularly genetic testing for cancer risks, following American celebrity Angelina Jolie's public announcement that she underwent a preventative double mastectomy in 2013. The number of women interested in BRCA1 and BRCA2 genetic testing rose significantly after Jolie's announcement, demonstrating how celebrity behavior can influence societal priorities related to health practices. The influence occurred quickly and spread through media channels, reshaping health-seeking behaviors within months (Kosenko et al., 2016). It is common knowledge that breast cancer should be screened for regularly, so arguments that Jolie's announcement constituted meaningful new information about cancer risk are not convincing explanations of such a shift. If the effect were primarily due to such learning, it would persist as the topic faded from public discourse, though that does not seem to be the case. Jolie herself has little to gain from others screening for cancer, so it also cannot be explained as a disjoint problem in the vein of Coleman. The only remaining conventional rational explanation for such shifts is that the public figure acted as a focal point to signal which strategy everyone should choose in a coordination game. If the benefit were entirely from such conventional norm effects, there would be little reason to shift behavior based on the actions of one individual over any established equilibrium for cancer screening in society at large. Under the model presented, this shift in behavior is explained by a temporary shock to the network, where Jolie's experience with cancer received wide exposure. This, combined with her high social leverage, meant that the effort she made to protect herself from cancer led others to do the same shortly afterward. Of course, the social outcome was not that there was a massive increase in the focal action (double mastectomies). Rather, in line with the concept of support, individually appropriate measures were taken to combat cancer, the most common of these being to screen for breast cancer. To illustrate the advantage more clearly, consider a hypothetical sub-population with a low baseline rate of cancer screening that is exposed to news on Jolie's announcement and health progress for some finite period of time. The proposed model predicts a shock upward in screening due to exposure which is sustained so long as exposure continues and decreasing gradually after exposure is removed. Game theory models generally predict no change due to exposure unless the news transmits information which updates utility estimates. In that case, there would be a change in behavior that would be sustained even after exposure is removed. Threshold models would also predict a sustained increase, but only if Jolie's participation happened to be in a position to cause a network cascade. Otherwise, they would predict no change. EGT says nothing in this case. Only this paper's model is consistent with what occurred.
This example aligns strongly with Proposition 3 and illustrates one of the advantages this type of modeling has over other approaches. In this case, by explicitly modeling singular, asymmetric influences, such as those exerted by celebrities, the resulting volatility in norms is explained.
The Emergence of a Voting Norm: This section argues that alternative theoretical methods are less likely to predict the emergence of norms under certain conditions. We will use voter participation as an illustrative case.
Each theoretical framework we have discussed provides a different perspective on the emergence of widespread voter participation. Coleman's reasoning suggests that a coalition of individuals who benefit from high voter participation coordinate their efforts to sanction others into voting, thereby establishing voting as a norm. Bicchieri's model, on the other hand, focuses on expectations. In this view, a voting norm occurs because people expect others to vote and believe they are expected to do so themselves, leading them to vote as a behavioral response. EGT posits that the predisposition to vote could be bred into us through evolutionary processes. Threshold models propose that voting begins with a small number of individuals who vote because they enjoy it or have some other idiosyncratic motivation, which causes a cascade through the social network. In contrast, the model presented in this paper tells a story of shared understanding, such as the belief that "democracy is good." Demonstrating appropriate support for this value becomes socially important for each citizen. In the absence of any election, one can demonstrate such support in a variety of other ways, such as speaking about the benefits of democracy or participating in political protests. In cases where democratic elections are available, voting emerges as a cheap and accessible way to display one's alignment with this shared value. This aligns with Proposition 5, which suggests that norms become stronger when the cost of deviation is low.
The various explanations these different models provide for the emergence of a voting norm are different, but not fundamentally so. Determining which framework is most useful is partly an empirical question, but it is also true that the stories being told do not inherently contradict each other. Nevertheless, the nature of the model proposed in this paper does makes it better suited to predict the emergence of voter participation. It provides clearer guidance on how to measure factors related to the relevant norm and makes more precise predictions about both short-term and long-term outcomes. Unlike other frameworks, it better addresses the practical challenges of empirical application and provides greater specificity. First, compared to alternatives, this model offers greater empirical applicability to voting norms. This stems from the greater detail in the proposed utility function. Game theory-based approaches often leave the underlying utility functions undefined to maintain generality, making them difficult to operationalize. Bicchieri's model, though somewhat specific, relies heavily on measuring internal beliefs, which are inherently harder to observe and quantify than behaviors or other external factors. While the model in this paper also generalizes, most notably in its treatment of native preferences, this factor is relatively unimportant in the context of voting, where direct self-interest plays a negligible role. This is because there are few reasons to vote which satisfy simple self-interest. This topic is discussed in greater detail in Appendix A. Instead, the habit formation and social influence components of this model are expected to dominate, and these components are given an explicit functional form. This reduces the burden on empiricists by offering clearer guidelines for measurement and analysis.
Furthermore, conventional game theory and EGT approaches introduce additional challenges by requiring empiricists to identify equilibrium states, a task that is as much art as science. There is no guarantee that such equilibria exist, and even when they do, their identification often involves significant uncertainty. In this sense, the model presented provides a prediction where many alternative models do not. Alternative approaches provide limited insight into short-term behavioral shifts. Conventional game theory offers no dynamic framework, and EGT focuses on the evolution of coordination rather than the mechanisms driving it. Threshold models, while dynamic, often rely on overly simplistic mechanisms for explaining behavioral shifts. By contrast, this model provides precise predictions for individual agents at every point in time, rather than merely estimating the likelihood of a particular outcome or direction of movement, as game-theoretic solutions often do. By making predictions that are both precise and dynamic, this model is uniquely equipped to explain the emergence and stabilization of voting norms in ways that other frameworks cannot.
Variations in Voter Participation: Even in cases where high voter participation is already established, the proposed model appears to offer some additional empirical insight over the alternatives. One way the model distinguishes itself is by explaining the empirical observation that voters are more likely to participate in high-profile elections. In the United States, for example, voter turnout is significantly higher during presidential races than interim elections. The proposed model attributes this variability to dynamic changes in exposure across the network. That is, during presidential elections, there is significantly more discussion around the importance and stakes of voting in both the media and interpersonal communication. This difference is significant and regular even though the outcome of certain local elections may have more direct and practical impact on an individual voter and their community. Furthermore, a single vote in such elections is more likely to influence the outcome. This problem challenges traditional rational-choice explanations, including Coleman's framework.
In the literature on norms, such variance would typically be handled as an exception by saying the norm is conditional, and that it is more important to vote if it is not an interim election. However, such conditionality is difficult to explain in this context as it is not clear why such a condition should exist, or how it comes about. Whatever established model one wishes to apply, the source of this conditionality is left purely to conjecture. The presented model, however, points to increased exposure to election topics from influential individuals as the driving force. The effect of the changes in exposure to the topic of voting pre- and post-presidential election could operate in a manner similar to that shown in Figure 10. During the interim election, the influence network is weak. Then, as the presidential election approaches and media around the importance of voter participation is maximized, conformity peaks. After the election, social influence on the topic decreases and so does the corresponding coordination on support until the next presidential election.
Harmful Behaviors: A central challenge in understanding apparently harmful norms is explaining why they persist despite their evident inefficiencies or detriments to individual and collective welfare. Traditional models, such as those grounded in evolutionary game theory or coordination games, often presume that norms emerge and persist because they optimize group welfare. These models struggle to account for norms like hazing rituals, smoking, or self-injury, which endure despite widespread acknowledgment of their harmfulness. This model addresses these gaps by incorporating the concept of support, which captures how behaviors align with a norm not solely through individual adherence but as part of a broader signaling process. Unlike simpler models that view norm adherence as a binary comply-or-defect decision, this model recognizes that individuals engage in a constellation of interrelated behaviors that collectively indicate their support for a norm. For example, in the case of hazing rituals, enduring physical or psychological harm serves as a public signal of loyalty to the group.
These actions not only align with the group's expectations but also reinforce the individual's identity as a committed member. By emphasizing the interconnectedness of behaviors under a single norm, the model explains how even costly or harmful actions can accrue net personal benefit, such as increased status or belonging, even though the practice it is costly for all involved when considered in isolation. Additionally, the model integrates habit formation and social influence to illustrate how harmful norms become stabilized over time. Habit formation ensures that a support level, once established, becomes a default response, reducing the likelihood of deviation even when external conditions change. Social influence can magnify this effect by creating a feedback loop, where observing others' adherence to the norm reinforces an individual's interest in conforming. Together, these forces create a mechanism for norm persistence that does not rely on the assumption of group-level optimality, setting this model apart from alternatives. Unlike traditional frameworks, which often assume that norms dissolve when they no longer serve a clear utility, this model demonstrates how harmful norms can persist due to their role in signaling and social cohesion. This signaling reinforces the norm's legitimacy, even as external campaigns highlight its harms. The model's nuanced understanding of support as a dynamic, multidimensional measure enables it to capture these complexities, offering a superior explanation for the endurance of harmful norms. By addressing both individual motivations and network-level dynamics, this framework provides insights that other models fail to deliver.
Pluralistic Ignorance: This model potentially resolves a notable conflict between rational choice theory and the concept of pluralistic ignorance discussed in Section 2.6.1. Pluralistic ignorance, as defined by Perkins & Berkowitz (1986), suggests that individuals systematically misperceive others' behaviors and attitudes, resulting in erroneous beliefs about how others behave and biased choices. However, rational choice models typically assume that individuals should have no such persistent biases.
This inherent tension arises from the belief that rational agents should, in theory, correct misperception through something like Bayesian updating. Even if the estimates made are not precise because of incomplete information, the expectation should at least remain unbiased. Yet, empirical evidence of persistent norms, such as alcohol use, suggests that these misperceptions are stable and endure, contradicting the assertions of conventional rational choice theory. The model presented in this paper potentially reconciles these seemingly opposed perspectives by suggesting that the conflict may be the result of the difference between mean and target support. That is, the survey was interpreted as measuring estimates of mean behavior across all college students without accounting for how the influence network weights the behavior of each student differently. What was relevant to the students desires to fit in, and what they were actually responding to, may have been behavior weighted by influence. If that is the case, there is no misperception on the part of the students. Given the survey results, the model predicts that students with higher social influence are, in fact, more likely to consume alcohol, and that in turn should drive a general elevation in consumption.
Persistence of Behaviors in Changing Social Contexts: When individuals move to a new cultural setting and sever ties with their previous social environment, they do not immediately shed old behaviors. As individuals make these transitions, established habits exhibit inertia that slows down adaptation to the new environment, influencing their interactions within the new context until new behaviors take root through repeated exposure. Traditional game-theoretic models struggle to account for the persistence of behaviors during social transitions. These models often assume that behaviors are determined by immediate payoffs and fixed strategies, which makes them more suited to explaining equilibrium states or short-term coordination problems rather than dynamic, long-term behavioral change. They do not adequately capture the stabilizing effects of habituation or the cumulative influence of social exposure over time. As a result, game-theoretic approaches fail to conclusively address why some individuals might continue to engage in familiar behaviors after a significant change in cultural context, particularly when those behaviors no longer provide clear utility or align with the new environment's norms. The model discussed here not only predicts such lag, it also shows how one's social placement in the new society predicts the speed at which such adaptation occurs.
A significant difficulty in the approach presented in this paper arises in the large number of parameters involved. Given a population size p, a maximum number of time periods $t_{max}$, a number of measurable behaviors m, as well as network density , suppose we aim to fully test the model on a real-world community. To do so, we may require up to the following:
Thus, the maximum number of measurements required to make a precise prediction with the model can be expressed as
[Max measurement count] $=\delta t_{max}p^{2}+(2+t_{max}+mt_{max}-\delta t_{max})p+m$
For instance, in a system with 100 people, 10 behaviors, 10 time periods, and a network density of 0.1, the upper bound on the number of scalar values needed to input or compare is 21,110. This number can be reduced by about an order of magnitude if shocks are limited, but since at least one complete social network is required for the model to function, the parameter count grows at a rate of $O(p^{2})$ for tightly connected networks.
If the influence network values are taken as given, the parameter growth rate becomes $O(pmt_{max})$, which is an improvement as p would typically be the largest value. However, this situation remains far from practical. Ignoring the network variables, the maximum number of scalars in the 100-agent example above reduces to 11,200. In a system with few shocks, this number could be as low as 1,400. While the model is testable directly in principle, this large number of parameters makes such tests impractical on all but the sparsest of networks.
Still, less direct methods are available. Most obviously, agent-level testing is a crucial first step in model validation which does not require extensive data collection. By verifying that agents' actions at the micro-level reflect realistic decision-making and social dynamics, researchers can ensure that the foundation of the model is accurate before moving on to broader system-level validation. This step ensures that agent behaviors are grounded in empirical evidence. Tests of propositions derived from the model, such as those highlighted in Section 8.1 can also help validate and refine the model. From there, calibration and sensitivity tests can be conducted based on known data to test larger scale predictions.
Measurement of Parameters (New to Literature): The thesis provides conceptual groundwork for measuring parameters that are new to the literature, highlighting that they can be operationalized in principle.
Social norms represent fundamental components of human societies, guiding behavior and expectations across nearly all facets of life. They function as informal institutions, wielding significant influence over actions without the necessity of legal structures or explicit enforcement mechanisms. These norms guide a wide array of crucial behaviors, ranging from economic transactions and political participation to everyday practices such as personal hygiene and social etiquette.
Despite their pervasive influence and critical role in societal functioning, establishing a standardized definition of "social norm" has proven to be a persistent challenge for academics. This has resulted in a notable lack of consensus across the field, as acknowledged by various scholars. This definitional fluidity creates substantial hurdles for consistent theoretical modeling, precise measurement, and the effective integration of research findings from diverse studies. The absence of a universally agreed-upon definition means that researchers often operate with different understandings of the core phenomenon they are studying, complicating comparative analysis and cumulative scientific progress. The inherent ambiguity and lack of consensus among prominent scholars underscore a fundamental challenge that any new theoretical model must address if it aims to bring greater rigor and coherence to the field.
Kristopher Overbo's dissertation, 'A Model of Social Norm Dynamics', introduces a deterministic model designed to describe the temporal dynamics of social norm development. This model is firmly rooted in the principles of rational choice and methodological individualism, a doctrine asserting that macro-social outcomes should be explained through interactions at the individual level.
A primary motivation for this model's development is to overcome key limitations observed in traditional game-theoretic approaches. These earlier approaches often concentrate on static outcomes and are typically confined to small-scale situations, which constrains their applicability to real-world, evolving macro-social contexts. In stark contrast, Overbo's model is engineered for effective scalability, enabling it to capture dynamic, large-scale societal phenomena and the temporal processes that characterize the development and stabilization of social norms. This inherent design for dynamic, large-scale analysis offers a significant advantage for scientific inquiry and computational simulation, moving beyond the often qualitative or static nature of prior social norm theories. The model's deterministic nature further means that, given a set of initial conditions and parameters, its future states are precisely determined, enhancing its predictability and reproducibility, which are cornerstones of scientific understanding. Moreover, the model reliably generates long-run equilibria under time-invariant parameters, a characteristic not commonly found in established approaches, ensuring predictable long-term behavior under stable conditions.
The model integrates three primary forces that collectively explain agent-level behavior: native preference, social influence, and habit formation. Native preference accounts for intrinsic and heterogeneous motivations, ensuring a degree of behavioral variety even in highly conforming environments. Social influence reflects the pressure individuals experience from observing the behaviors of others, which drives conformity. Habit formation, on the other hand, stabilizes behavior over time, encouraging actions consistent with past decisions.
A novel and central feature of this model is the concept of "support." Support is introduced as a measure of the degree to which a set of chosen behaviors aligns with a given social norm. Unlike simpler measures that might focus on adherence to a single behavior, support captures the interrelation between various behaviors relevant to a norm, offering a more nuanced understanding of how collective patterns emerge from individual actions.
This comprehensive learning plan is designed to demystify Kristopher Overbo's 'A Model of Social Norm Dynamics'. It aims to break down the dissertation's intricate theoretical and mathematical components into clear, understandable concepts for a non-expert audience. The plan provides a structured learning path, progressively building understanding of the model's core ideas, its intellectual lineage, its unique contributions, and its practical implications. By fostering a deeper appreciation for the complexities of social norm dynamics, this report seeks to make expert-level research accessible and to highlight its relevance to real-world social phenomena.
To fully appreciate the contributions of Overbo's model, it is essential to understand the theoretical landscape from which it emerges. The study of social norms has a rich history, with various scholars offering distinct perspectives and frameworks.
The academic discourse on social norms has long grappled with the challenge of a unified definition. This lack of consensus has hindered consistent modeling and empirical validation across studies.
Coleman's Definition: James Coleman (1990) provided an influential definition, stating that a social norm exists "when the socially defined right to control the action is held not by the actor, but by others". This perspective emphasizes that norms represent a transfer of control over an individual's actions to others in society, typically focusing on specific "focal actions". However, this definition has limitations. It describes the conditions under which a norm exists rather than its inherent nature, which can obscure its more fundamental properties. There is also some ambiguity surrounding what constitutes a "socially defined right." Furthermore, Coleman's framework does not explicitly address the role of behavioral regularity; an unusual action, if socially pressured, could still be categorized as a norm, even if it lacks widespread adoption.
Bicchieri's Definition: Cristina Bicchieri (2005) offered a more ambitious and mathematically precise definition of social norms. She posited that a behavioral rule R qualifies as a social norm in a population if a sufficiently large subset of that population knows the rule exists and applies to a given situation. Crucially, each individual in this subset must prefer to conform to R, under the condition that they believe a sufficiently large subset of the population also conforms (empirical expectations), and that a sufficiently large subset expects them to conform (normative expectations), potentially with sanctions for non-compliance. Despite its admirable nuance, this definition does not encompass all phenomena commonly considered normative. For instance, Bicchieri explicitly excludes descriptive norms, providing fashion trends as an example. She declares that such norms are not social norms, but a distinct phenomenon. Interestingly, she declares that such norms carry no expectation from others that an individual conforms. Moreover, her model's reliance on measuring internal beliefs and expectations, while theoretically rich, can pose significant challenges for empirical observation.
Opp's Classification: Recognizing the difficulty in standardizing a single definition, Karl-Dieter Opp (2001) proposed a framework for classifying existing definitions by identifying three common elements: "Oughtness" (a shared sense of expected behaviors), "Behavioral Regularity" (coordination of behavior across a population), and "Sanctioning" (a system providing incentives or disincentives for certain behaviors). While helpful in organizing the diverse landscape of definitions, Opp's classification nonetheless highlights the disparate elements that a comprehensive model must integrate.
The persistent academic struggle to standardize a definition of "social norm," as evidenced by the varied and often mutually exclusive definitions offered by prominent scholars, reveals a fundamental fragmentation in the field. This fragmentation complicates consistent modeling, measurement, and the integration of research findings. A model that can either reconcile these definitions or propose a superior, more encompassing one would be a substantial contribution. Overbo's model, by later introducing concepts like "support" and "norm strength" and then using them to formally define a social norm, directly attempts to synthesize these disparate elements into a quantifiable and empirically tractable framework, aiming to bridge the gap between abstract theoretical constructs and measurable social phenomena.
In the formal modeling of social norms, game-theoretic approaches have emerged as a dominant framework. Early contributions from economists like Schelling (1960) introduced the idea that social norms could be understood as coordination problems, a concept later extended by Sugden (1986) to micro-scale situations. James Coleman's (1990) Foundations of Social Theory stands out as arguably the most influential work in this area, frequently framing norms as solutions to public goods problems (often modeled as prisoner's dilemmas) or coordination games.
Mechanics of Norm Emergence: Game theory explains norm emergence through strategic interactions. Conventional norms are typically modeled as coordination games where the payoff depends on each player choosing the same strategy (e.g., agreeing to drive on the same side of the road). These games are often resolved through communication or by identifying "focal equilibria"—solutions that stand out as naturally salient or obvious to all parties involved, such as meeting at the Eiffel Tower in Paris. Non-conventional norms are commonly illustrated as prisoner's dilemmas, where the first-order problem is that individual self-interest leads to suboptimal collective outcomes. The "second-order free-rider problem" arises because no one has an incentive to contribute to a system of controls to enforce cooperation. Coleman suggests that in practice, this is resolved through social relationships and the presence of zealous sanctioners, leading to socially beneficial outcomes. Cristina Bicchieri (2005) further extended this by proposing that social expectations—both empirical (belief that others are following the norm) and normative (belief that others expect one to follow the norm)—directly shape individuals' utility functions, thereby influencing their decision-making and norm adherence.
Advantages: Game theory offers a powerful framework for understanding social norms due to its expositional clarity and its ability to provide simple, formal models of human interaction. It simplifies complex social behaviors into strategic games, which helps clarify the exposition of norm formation and adherence. The field benefits from a rich research ecosystem that has developed across disciplines such as economics, sociology, psychology, and political science, allowing scholars to draw on a wealth of existing models, techniques, and empirical findings. Furthermore, game theory grounds the study of social norms in rational choice theory, providing a logical basis for explaining why people conform to norms, even when it requires costly sacrifices. The concept of equilibrium, central to game theory, illustrates how stable patterns of behavior can emerge from individual decision-making processes.
Limitations: Despite its strengths, traditional game theory faces several limitations when applied to social norms. These approaches primarily focus on static equilibria and are often restricted to small-scale interactions, making it difficult to describe the complex, multi-agent dynamics of real-world norms that evolve over time across large populations. Coleman's work, for example, frames norm internalization as a mechanism for cost reduction imposed by others, but it does not fully describe the process or explain why individuals would willingly accept costly norms that contradict their private beliefs. His treatment of disjoint norms (where beneficiaries and targets are separate groups) also heavily emphasizes coercive enforcement, overlooking more subtle forms of social pressure and influence. Moreover, these models often overlook the emergence of norms that are suboptimal or even damaging to collective welfare, often assuming norms must provide some benefit to the group. The highly specialized taxonomy of norms (e.g., conjoint vs. disjoint, prescriptive vs. proscriptive) often arises from the constraints of fitting norms into predefined game structures, which can fragment understanding rather than unify it and complicate empirical application.
Comparison to Overbo: Overbo's model fundamentally differentiates itself from traditional game theory by its inherent capacity to make precise predictions about how the development of norms is influenced by changes in network structure and individual actions over time. The core limitation of traditional game theory—its static nature and difficulty in scaling to large, dynamic social systems—creates a significant explanatory gap that Overbo's model directly aims to fill. By explicitly integrating temporal dynamics and network structures, Overbo's model offers a more practical and realistic framework for analyzing how norms evolve in constantly shifting, real-world environments, rather than merely identifying their stable end-states. This dynamic perspective is crucial for understanding social change and designing effective policy interventions, especially since real-world macro-social systems rarely achieve equilibrium due to constant shocks. While game-theoretic models provide general insights into long-run outcomes, Overbo's approach offers greater precision in forecasting the dynamic evolution of norms in specific social systems. It incorporates social embeddedness, similar to Bicchieri's extension, but focuses on habit and influence as key mechanisms, and explicitly integrates network effects.
Evolutionary Game Theory (EGT) offers a distinct approach to the study of social norms, shifting the focus from static equilibria and individual decision-making to population-level dynamics and intergenerational change. In EGT models, a population of agents is assigned fixed strategies (e.g., whether to follow a norm) that they employ in simulated interactions. The payoffs received from these interactions determine their ability to "replicate" in the next generation. This process leads to an evolution of strategies over time, as exemplified by Axelrod's work.
Advantages: EGT introduces intertemporal dynamics, allowing for the study of how behaviors adapt within a population over successive generations. Its stochastic approach can also circumvent some of the difficulties encountered in finding equilibria. EGT models serve to justify why cooperation or coordination behavior occurs, providing a theoretical basis for assumptions included in other models. Examining the parameter values under which various dominant strategies emerge can provide insights into why certain equilibria are favored over others.
Limitations: Despite its strengths, EGT has notable limitations when applied to social norms. The mechanics of EGT are often abstract and far removed from intuitive understandings of how norms and individuals actually work. Agents are treated as having fixed strategies within their lifetimes, effectively discarding the sense of rational calculation and real-time adaptation at the individual level. A critical input to these models is the "replicator function," which dictates the reproductive process; for social norms, this function often lacks a clear empirical counterpart. While EGT effectively demonstrates population dynamics, it does not capture agent dynamics within a single generation. It is well-suited for exploring macro-level, inter-generational dynamics over very long periods, but less so for explaining how norms appear and disappear within the much shorter, sub-evolutionary timescales relevant to human societies. Furthermore, prominent EGT models, such as Axelrod's, often abstract away from specific social network structures, focusing on aggregate outcomes and end-state equilibria rather than how network topology influences norm adoption and diffusion.
Comparison to Overbo: Overbo's model distinguishes itself by adhering to methodological individualism, explaining macro-social outcomes through individual-level interactions and grounding behavior in rational choice theory. EGT's strength in explaining the long-term evolutionary stability of cooperative behaviors comes at the cost of neglecting real-time individual adaptation and the rapid emergence or disappearance of norms within a single human generation. Overbo's model directly addresses this gap by providing a framework for intra-generational dynamics, where agents adapt their behavior in real-time through social influence and habit, rather than having fixed strategies that only change across generations. This makes his model more relevant for understanding contemporary social change, cultural shifts, and policy interventions that operate on much shorter timescales than evolutionary processes. The model also explicitly incorporates network structures, providing a richer understanding of how specific social contexts shape norm adoption and spread. Its focus is on how coordination occurs, complementing EGT's focus on why it might evolve.
Threshold models, rooted in Granovetter's (1978) seminal work, are computational simulations that frequently employ social network structures to explain how individuals make binary decisions, such as whether to adopt a particular behavior or follow a norm. These models propose that agents adopt a norm based on observing the same behavior in their network neighbors. A key concept is the "individual threshold," which represents the proportion of neighbors who must adopt a norm before the observing agent also does. This heterogeneity in thresholds is central to determining the tipping point at which norm adoption cascades through a population.
Extensions: Building on this foundation, Centola (2005, 2018) introduced the concept of "complex contagions," demonstrating that certain behaviors, particularly those requiring reinforcement from multiple contacts (i.e., strong ties), spread more effectively within dense, tightly connected clusters. This contrasts with "simple contagions," like information, which tend to travel more easily across weak ties in sparsely connected networks. Further extending these models, Mäs & Opp (2016) incorporated flexible thresholds, allowing individuals' decisions to change dynamically based on evolving social and personal contexts.
Limitations: While valuable for exploring the dynamics of norm diffusion in social networks, threshold models exhibit several notable limitations. Their reliance on binary decision-making (an all-or-nothing choice) oversimplifies the complexity of real-world behaviors, which often involve degrees of adherence rather than all-or-nothing choices. Additionally, these models typically assume static thresholds for agents, failing to capture how individual behaviors and social pressures evolve over time. The lack of empirical alignment in many threshold models makes it challenging to validate their assumptions or apply their findings directly to real-world scenarios. Furthermore, they often lack integrated microfoundations that detail the underlying behavioral or rationalized processes driving individual decisions.
Comparison to Overbo: Overbo's model addresses these limitations by allowing for "decision gradients" and "partial adherence" through its novel concept of "support," moving beyond the binary choices of threshold models. This means individuals can fulfill normative obligations in various ways and to varying degrees. The contrast between the "binary decision-making" in threshold models and Overbo's "decision gradients" and the continuous "support" concept is a key differentiator. Real-world social behavior is rarely a simple "yes" or "no" to a norm; there are degrees of adherence and substitution possibilities. This allows Overbo's model to explain more subtle social phenomena like partial conformity or gradual shifts, which are beyond the scope of threshold models. The model also incorporates dynamic individual adaptation and habit formation, allowing agents to adapt their behavior over time, and integrates elements of rational behavior (native preferences, social pressures, habits), bridging network and rational-choice perspectives. This enables it to explain persistent non-conformity or selective norm adoption, which threshold models are less equipped to handle. The absence of explicit rational foundations in many threshold models means they cannot explain why an individual might choose to deviate from a norm despite social pressure, a gap Overbo's model fills by integrating rational choice.
Overbo's model draws on established psychological theories to provide a robust micro-level foundation for individual behavior, notably the Reasoned Action Approach and the concept of habit formation.
Reasoned Action Approach (RAA): While neither a formal model, nor a model of social norms per se, the Reasoned Action Approach (RAA) from social psychology provides a well-studied theoretical basis for how individuals use norms to make decisions about their focal actions at the micro level. RAA, the modern incarnation of the earlier Theory of Planned Behavior and Theory of Reasoned Action (Fishbein & Ajzen, 2010). According to this view, behavior with respect to a specific focal action is determined primarily by what is called behavioral intention which itself is a function of three inputs:
Habit Formation: The concept of habit formation is central to Overbo's model's ability to account for the persistence and stability of social norms over time. It is incorporated as an agent-level tendency for individuals to maintain consistent support levels over time.
Habit is expressed in the model as a single period look-back term. As simple as this implementation is, the recursive nature of the model ensures that when $h_{i}$ $n_{i,i}\ne0,$ current support levels are influenced by all past support choices, with the relative impact of a given period diminishing as t increases. This means that, once established, support has persistence, even when external conditions or preferences change. This framework could be adapted to more sophisticated or longer period habit, however this simple implementation suitably enables the desired dynamics without over-complicating the model.
By explicitly integrating components from the Reasoned Action Approach into "native preference" and "social influence," Overbo's model provides a strong micro-level psychological grounding that many purely formal models lack. The model gains psychological realism by mapping RAA's "attitude" and "perceived control" to "native preference," and "perceived norm" to "social influence." Furthermore, the inclusion of habit formation as a dynamic, self-reinforcing mechanism offers a powerful and empirically supported explanation for norm persistence and internalization, moving beyond simple external sanctions or static preferences. This synthesis creates a more robust and testable framework for understanding why behaviors, once adopted, exhibit inertia and are difficult to change.
Overbo's model builds upon existing mathematical frameworks, particularly the DeGroot family of models, while introducing significant modifications to suit the complexities of social norm dynamics.
DeGroot Learning: This model, developed by statistician Morris DeGroot (1974), describes how individuals in a social network update their opinions or beliefs about what is true through interpersonal contact. The model captures the process by which a group of agents iteratively adjust their beliefs based on a weighted average of the opinions of their neighbors and their own prior beliefs. This means each person's new opinion is a mix of their old opinion and the opinions of those they listen to. Eventually, agents converge on persistent consensus or disagreement, depending on the network structure and the influence of endogenously set weights. The procedure can be described mathematically as follows:
$s_{i}^{t}=\sum_{j=1}^{n}w_{ij}s_{j}^{t-1}$
Here, $s_{i}^{t}$ is person 'i's opinion at time 't'. The symbol $\sum$ means "sum up" or "add together." So, $s_{i}^{t}$ is the sum of all $w_{ij}$ (how much person 'i' values person 'j's opinion) multiplied by $s_{j}^{t-1}$ (person 'j's opinion from the previous time period). The $w_{ij}$ values represent the weight agent 'i' places on the opinion of agent 'j'. 'n' is the number of agents (people) in the network. Each period, opinions are updated until a stable state is achieved.
This is not generally considered a rational model because there is no deliberate optimization done by the agents to arrive at the weights they assign to each opinion. Despite this, this model is remarkably simple and intuitive. There is also a modest body of empirical evidence emerging that individuals do learn this way (Jadbabaie et al., 2012; Chandrasekhar et al., 2020).
The model presented in this paper is most structurally similar to that of Friedkin & Johnsen (1990), a variant of the DeGroot Learning Model which adds static preferences, though it differs in application, elements of time variance, and theoretical explanation of its components. See Section 7.5 for further discussion.
Comparison to Overbo: Overbo's model is most structurally similar to the Friedkin & Johnsen variant. However, it distinguishes itself by allowing both the network structure ($N^t$) and the anchor position (native support $\dot{s}^t$) of each agent to be time-variant. This time variance is crucial as it allows for the modeling of external shocks and creates long-run equilibrium behavior that is not solely bounded by initial conditions. Furthermore, Overbo's model introduces the novel abstraction layer of "support," which measures the degree of alignment with a social norm, rather than just an opinion or belief. More significantly, while DeGroot models are typically applied to the learning and convergence of information or opinions, Overbo's model is specifically designed to explain the formation and maintenance of social norms. It provides explicit rational foundations for its usage and defines each term differently within this context.
By building upon the mathematical elegance of DeGroot-like models but introducing time-variance in both network structure and native preferences, Overbo's model gains crucial flexibility to simulate real-world social systems that are constantly subject to external shocks and evolving individual inclinations. This dynamic adaptability, combined with an explicit rational foundation and the novel concept of "support," allows it to model complex norm evolution beyond simple opinion convergence. The explicit statement of mathematical similarity to DeGroot models is important, but the modifications are what allow Overbo's model to realistically handle external "shocks" and ongoing "evolution" in a way that static DeGroot models cannot. The introduction of "support" as an abstraction layer also allows the model to capture more complex social phenomena than simple opinion transmission, and the claim of rational foundations provides a deeper theoretical grounding for the observed dynamics.
| Model Type | Key Characteristics | Primary Limitations Addressed by Overbo's Model |
|---|---|---|
| Traditional Game Theory (e.g., Coleman, Bicchieri) | Focus on static equilibria, small-scale interactions, fixed strategies, emphasis on payoffs and sanctions, often struggles with harmful/neutral norms, fragmented taxonomy. | Overcomes static nature and lack of scalability; provides more nuanced internalization; incorporates subtle social pressure; capable of explaining harmful norms. |
| Evolutionary Game Theory (EGT) (e.g., Axelrod) | Population-level dynamics, intergenerational change, fixed strategies within individual lifetimes, no clear empirical analog for replicator function, often abstracts from specific network structures. | Offers strong microfoundations for agent dynamics; focuses on real-time intra-generational adaptation; explicitly integrates network effects. |
| Threshold Models (e.g., Granovetter, Centola) | Binary decision-making, static thresholds (often), focus on network diffusion and cascades, limited explicit microfoundations, oversimplifies behavioral complexity. | Moves beyond binary oversimplification to continuous behavioral measures ("support"); allows for dynamic thresholds and adaptation; integrates rational choice microfoundations. |
| Overbo's Model | Deterministic, scalable to large populations, captures temporal (intra-generational) dynamics, grounded in rational choice, introduces continuous "support" measure, explicitly incorporates dynamic network structures and habit formation, capable of explaining harmful/neutral norms, offers a unified norm definition. | (Integrates strengths and addresses limitations of previous models.) |
Overbo's model is a deterministic framework that describes how individual decisions aggregate to form societal norms over time. It is built upon three primary forces that explain agent-level behavior: native preference, social influence, and habit formation.
The model defines an agent's current "support" ($s_{i}^{t}$) recursively, as a weighted average of these three key forces. The core equation is:
$s_{i}^{t}=n_{i,i}^{t}((1-h_{i})\dot{s}_{i}^{t}+h_{i}s_{i}^{t-1})+\sum_{j=1}^{p}n_{i,j}^{t}s_{j}^{t-1}$
Let's break this down:
So, in simple terms, this equation says: **Your current support for a norm ($s_{i}^{t}$) is a mix of what you naturally prefer ($\dot{s}_{i}^{t}$), what you did last ($s_{i}^{t-1}$), and what your friends or influential people did ($s_{j}^{t-1}$), all weighted by how much each factor matters to you.**
After the $t=0$ initial state, the support chosen by agent i in each period is a weighted average of three other support values that are observable to i: native preference, habit, and social influence. The $n_{i,j}^{t}$ weights indicate the extent to which each agent in the network, including themselves, influences future support, while the $h_{i}$ weights further divide the non-social influences into the other two component parts. The support level generated by this function feeds into the $t+1$ period behaviors through the habit term for the same agent and the social influence term for other agents connected directly via an influence network $N^{t+1}$. Through this social influence channel, the time t support of a given agent affects neighbors at distance d at time $t+d$ and as well as providing some amount of self-feedback in alternating periods. This speed-of-light effect provides additional dynamics and links individual behavior to macrosocial effects. See Figure 4.
This model is generally concerned with dynamics, consistent with an expectation that large social systems frequently experience shocks. Still, it is worth noting that the model itself is not inherently divergent. The model reaches equilibrium in the absence of shocks to $N^{t}$ and $\dot{S}^{t}$ as $t\rightarrow\infty$ This is apparent in the demonstrations in Section 5. See Appendix C for a proof of this convergence.
In the following sections we discuss each major term mentioned in greater detail, beginning with support.
The concept of "support" is not discussed in existing literature on norms; it is introduced with this model. Support serves as a scalar value representing the degree to which an individual's actions reflect adherence to an ideal. In support, we are attempting to capture the nuanced nature of conformity. This section discusses the theoretical underpinnings of support, its relationship to observable behaviors, and its significance in shaping norm dynamics within the social system.
We begin the discussion with an example. Suppose we are interested in studying the social norm one might initially describe as "clapping at the end of a good performance." It may be claimed that, with respect to this norm, either a person claps in a particular instance, or they do not, and thus the individual's behavior is a binary variable for observational purposes. This idea aligns cleanly with the idea of a focal behavior as discussed in existing literature on norms in Section 2. Seldom, however, is this type of social behavior so simply exhibited or interpreted by others. Some clap easily, some enthusiastically, some clap more or less frequently, or pause before beginning to clap. When a researcher considers such variations important, and they seldom do, they may deem it necessary to measure focal behavior as a numeric (scalar) value. To further complicate matters though, there are very close substitutes for clapping. Some may add vocal cheers or whistles. Some might boo, which could be considered a sort of anti-clapping. This range of behaviors is observed by others and serves as a key indicator of an individual's attitude toward the relevant norm.
When applying conventional game theoretic modeling to norms, capturing such nuance is particularly challenging. In principle, it is possible to construct a discrete game which divides the set of strategies available to an individual into "strong clapping", "weak clapping", "booing" etc., but introducing any reasonable amount of strategic variety into such a framework invites intractability for both the theorist and the empiricist even at the micro-scale. Still, the ability to accommodate more nuanced strategies would have an advantage in this regard over one that does not.
It is with this in mind that the concept of support is introduced. It will first be defined informally as the amount of enthusiasm with which one's collection of behaviors aligns to the principles of a norm. Behavior with respect to a particular focal action is typically a component of support, but not the entirety of it. It is quite possible to demonstrate meaningful support for a prescriptive norm while not engaging in the focal action it is built upon (e.g., "I would love dearly to shake your hand, but I have a flu").
Support, as a concept, has the advantage of capturing meaningful relationships among behaviors beyond a single focal behavior. The disadvantage is that by adding this layer of abstraction, the methods of measurement become less obvious. Researchers can, and often do, simply survey a population about their local and subjective estimations of how behaviors relate to social expectations (Jasso & Opp, 1997; Gerber et al., 2008; Fishbein & Ajzen, 2010). In practice, a survey could also be constructed which captures perceptions about how well a particular collection of behaviors align to the expectations of a norm. Still, it is desirable to make the relationship between support and behavior explicit. Doing so clarifies the concept and provides an alternate method for measuring support when surveys are unavailable or unconvincing. To that end, we next define support formally in terms of observables.
Let $\vec{B}_{i}^{t}\in\mathbb{R}^{m}$ be a vector of m measurable observations of person 'i's behaviors in some discrete time period t. Let support weights $\vec{W}\in\mathbb{R}^{n}$ be a vector of weights corresponding to those observations. Let i's support $s_{i}\in\mathbb{R}$ be the dot product of $\vec{W}$ and $\vec{B}_{i}^{t}$
$s_{i}^{t}=\vec{W}\cdot\vec{B}_{i}^{t}$
So, $s_{i}^{t}$ is a single number that summarizes how much a person's actions align with a norm, by giving different importance to different behaviors. For example, if a norm is "being a good student," $\vec{B}_{i}^{t}$ might include behaviors like "attending class," "doing homework," and "participating in discussions." $\vec{W}$ would assign weights to these, perhaps giving more weight to "doing homework" than "attending class." Then, $s_{i}^{t}$ would be your overall "good student" score. The model assumes $\vec{W}$ is stable and known to all. Conceptually, it may be convenient to think of $S_{i}$ as the units of effort an agent i spends in contributing to an ideal specified by $\vec{W}$ with $s_{i}=0$ indicating perfectly neutral behavior. $\vec{W}$ can be thought of as a perceived exchange rate between behaviors in their contribution to that ideal.
One way for agents to coordinate on support is to coordinate on behavior. If one behaves exactly the way another does, applying $\vec{W}$ results in identical support values. Such behavioral mimicry is consistent with the work of Cialdini et al. (1990) on descriptive norms. Kuran (1995) uses the argument of bounded rationality to explain such behavior coordination. It has been found that teenagers often mimic each other's behavior (Robalino & Macy, 2018; Paluck et al., 2016). Repacholi et al. (2014) finds evidence that 15-month-old infants are able to interpret the social interactions of others to effectively mimic acceptable behaviors, suggesting that the phenomenon develops quite early in life.
A utilitarian argument for such mimicry can be expressed as follows: People have a preference for others whose interests appear to be aligned with their own. Agents, knowing this will, to varying degrees, modify their behavior to reflect the interest of people whose favor they seek; a child will mimic the behavior of their parent, an employee will mimic the behaviors of the boss, married couples will seek to mimic each other, etc. Benefits of mimicry can also extend beyond the direct relationship with the agent being mimicked. If agent A aligns their behavior with a successful or popular individual B, agent C may see A's behavior as a signal that A shares qualities with B. In this way, A's reputation may improve with C.
As mentioned, one could mimic support by copying the behaviors of another perfectly. However, there is another possibility. Through $\vec{W}$ the agent is afforded the option of substituting one behavior for another to coordinate on a concept instead of a specific behavior. A roommate who wishes to honor a norm of cooperation among housemates can prepare dinner while another washes the dishes. The model in this paper implies that such conceptual trade-offs are important to understanding complex social norms. This ability to capture nuanced behavioral patterns and the interrelation of multiple behaviors significantly enhances the model's capacity to explain complex social phenomena.
A crucial aspect of Overbo's model is its grounding in rational choice theory, demonstrating that the observed behaviors and norm dynamics emerge from individual utility maximization.
The model's derivation from individual utility begins by characterizing a "happiness score" or "satisfaction level" ($U_{fl}$), which includes native preferences, habit formation, social influence, and expected future happiness. For mathematical convenience, these terms are treated as "additively separable," meaning each part of your happiness (from your natural preference, your habits, and social influence) simply adds up to your total happiness. The model assumes that your happiness changes smoothly, and that the "cost" or "unhappiness" of deviating from your ideal behavior for each factor increases the further you stray. Think of it like walking up a hill: the further you go from the top, the steeper it gets, making it harder to keep going.
The model primarily uses an "immediate utility" function ($U^t$), which is your happiness right now, without worrying about the distant future. There are three main arguments for this simplification:
Assuming that $U^t$ is a good enough approximation of $U_{fl}$, the model defines each of the three components (influence, native preference, habit) as "parabolic functions." Imagine a hill shape: your happiness is highest at the peak (your ideal behavior for that factor), and it decreases as you move away from that ideal, like going down either side of the hill. The further you are from your ideal, the more your happiness drops. For example:
By combining these terms, the model finds the "utility-maximizing support" ($s^{t}$), which is the sweet spot where your overall happiness is highest, by balancing all these forces. This is done by finding where the "first-order condition" is zero, which means that making a tiny change to your support won't make you any happier or unhappier.
After some mathematical steps, the model's core equation for optimal support is derived:
$s^{t}=\frac{a_{K+1}\dot{s}^{t}+a_{K+2}s^{t-1}+\sum_{k=1}^{K}a_{k}\dot{s}_{k}^{t-1}}{\sum_{k=1}^{K+2}a_{k}}$
This equation shows that your best choice for support ($s^{t}$) is a weighted average of your natural preference ($\dot{s}^{t}$), your past behavior ($s^{t-1}$), and the past behavior of your influential neighbors ($\dot{s}_{k}^{t-1}$). The 'a' values ($a_{K+1}$, $a_{K+2}$, $a_k$) are like "importance weights" that tell you how much each factor contributes to your overall happiness. When these weights are organized into a matrix for all agents, we get the full model described by Equation 3, showing how everyone in the network influences each other.
The Role of Information: The model assumes that agents make decisions based on "complete information" from their immediate surroundings. This means they only need to observe their own past actions and the past behaviors of those directly connected to them in their network. They don't need to know everything about the entire network, and they don't need to worry about how their single choice might affect the whole system in the long run.
Connecting Support and Behavior: A critical aspect of the model's rational foundation is that for a given person and their "support weights" ($\vec{W}$), a specific "support score" implies a unique set of behaviors. This is important because it means the model can predict specific actions, not just abstract support levels.
The idea is that if you want to achieve a certain support score, you'll choose from your available behaviors to get there. If your natural behaviors don't perfectly match the target support, you'll make compromises. You'll change the behavior that costs you the least "unhappiness" to adjust towards the target. As that behavior changes, its cost increases, and you might switch to adjusting another behavior that now costs less. This continues until you reach your target support. The thesis mathematically shows this works for any number of behaviors, ensuring that the model can make concrete predictions about specific actions.
$s^{t}=wb^{t}$
This means if you know your target support score and the importance of clapping, you can directly calculate how much you should clap:
$b^{t}=\frac{s^{t}}{w}$
$s^{t}=w_{1}b_{1}^{t}+w_{2}b_{2}^{t}$
Even though many combinations of clapping and cheering could give the same total support, the model uses additional math to figure out the *best* combination for you. This involves minimizing the "unhappiness" from deviating from your natural clapping ($\dot{b}_1^t$) and cheering ($\dot{b}_2^t$) levels. The math helps find the specific amounts of $b_1^t$ and $b_2^t$ that achieve your target support while making you as "happy" as possible.
Having established the micro-level foundations of the model, it is now possible to aggregate individual behaviors to derive network-wide measures, providing a quantitative lens through which to understand macro-social phenomena.
The model allows for the application of statistical methods to quantify and compare macrosocial properties of a society. Several key metrics are defined:
$\eta^{t}=\frac{\sigma_{\dot{s}}^{t}}{\sigma_{s}^{t}}$
A higher $\eta^{t}$ means the norm is "stronger." It captures how much the group's behavior is *pulled together* by social forces, compared to how spread out it would be if everyone just did their own thing. It's a way to compare the strength of different norms.
With these macro-level measures in place, the model proposes a formal definition for the existence of a social norm:
The pair $(\vec{W},\tau)$ is said to be a social norm in influence network $N^{t}$ at time t if and only if $\eta^{t}>\eta_{crit}^{t},$ where $\vec{W}$ is the mapping between behavior and support. $\tau$ indicates a target support value. $\eta_{crit}^{t}$ is a critical norm strength which denotes the cutoff indicating when a norm is strong enough to be said to exist. The choice of $\eta_{crit}^{t}$ is somewhat arbitrary, just as the cutoff for calling a person 'tall' is arbitrary. Notably though, when $\eta^{t}>2$ more of the variation in support is accounted for by normative dynamics than native support. A less formal way to express this definition is: A norm is the (nontrivial) force, produced by agents' social embeddedness, acting to modify those agents' behavior from how they would otherwise act.
We will illustrate how this definition is applied by way of example. One's participation in football hooliganism can be measured by taking into account a variety of behaviors, attending football matches, chanting, frequenting certain pubs, engaging in post-match vandalism. All these behaviors and their relative contributions to the idea of hooliganism is captured by a $\vec{W}$ It could be that the norm in a given community is very low levels of football hooliganism, or it could be high, or anything in between. This target value is indicated by T. These two values, $\vec{W}$ and , specify a norm conceptually, but this is only a hypothetical norm of hooliganism. To be relevant, that level of hooliganism must exist in the context of a group of people at a particular time. This time and group are identified by $N^{t}$. Having chosen a norm and a group, we can turn our attention to testing for the existence of the norm in the wild. It is not enough to notice that individuals in $N^{t}$ typically, or on average, engage in hooliganism at the level we are interested in. High(low) hooliganism can be explained by non-social factors such as having few(many) other pastimes available or having low(high) police presence in the area. Such factors are ones of native preference. In order for such behavioral regularity to be caused by a norm for hooliganism, it must be transmitted socially. We test for this by measuring $\eta^{t}$, which is how much cumulative effects of social embeddedness have reduced support variance in the population compared to a world without such influences. If newly joining members of the network show changes in their support levels aligning with the target support, a high $\eta^{t}$ is implied, and we say the norm exists in that network at that time. We have then specified and established the existence of the hooliganism norm.
It is worthwhile to briefly examine this definition through the lens of the classifications provided by Opp (2001).
This definition offers a relatively rigorous and quantifiable way to identify and test for the presence of norms within a population. The distinction between behavioral regularity and normative dynamics is critical, as it highlights that norms are not merely patterns of behavior but forces that actively shape individual actions within social networks.
This section explores dynamic aspects of the proposed model, demonstrating how individual behaviors aggregate to produce evolving social outcomes. Through various simulations, it explores different network structures and their impact on the stabilization and diffusion of social norms. These illustrations offer insights into the conditions under which norms emerge, persist, or fade.
The baseline simulation provides a foundational demonstration of the model's behavior in the absence of shocks, large asymmetries, or complex network topologies. Each example in the following section modifies some aspect of the baseline simulation to illustrate its effect on support. The code used to generate this simulation, as well as all others presented in this paper, can be found in Appendix D.
In figure 5a, each line corresponds to the support value of an agent in the network over time. Initially, all agents start with a support level equal to their time-invariant native preference level, s. Each of these values is randomly determined by an independently and identically distributed (i.i.d.) draw from a uniform probability distribution over the range. Over time t, the agents' support values converge, causing $\eta^{t}$ to increase from its base value of 1. The $\eta^{t}$ value in the last period is displayed on the upper left of the plot.
In Figure 5b, the network layout for this simulation is shown. The network is fully connected in this case, meaning there are two edges between every pair of agents, one in each direction. The connection weight of each edge is selected randomly and i.i.d. from a uniform distribution over the interval. The agents' self-influence values set to be 80% of the total influence. Habit formation terms are chosen from the range [0.75, 1.0]. These two ranges were explicitly selected to ensure that convergence and clustering occur at a rate suitable for the chosen number of time periods. Weights are then normalized to conform with Equation 5. The nodes are numbered in descending order according to initial support values $(\dot{s}^{0})$ values. Agent 1 has the highest $\dot{s}^{0}$, Agent 2 has the second highest, and so on.
Collective instrumentality is not a requirement for a norm to exist. It could be that the $t=0$ states were better for all instrumentally. There is no welfare function applied or included in the model independently. Still, potential welfare gains should improve the likelihood of a norm emerging via s. Collective instrumentality can enter through its impact on global native preferences as we will see in 5.5. Passive transmission of behavior allows for influential people to unintentionally sway $\tau^{t}$ and create a norm. In general, a norm will emerge when an influential subset of society has coordinated support. This coordination could be coincidental, intentional, or incidental.
Here we explore three degenerate forms of the model by removing each of the three primary components (native preferences, habit, and influence) from the model in turn. Studying these degenerate forms illustrates the impact of each term on the model. This approach also tests the robustness of the model by exploring how it behaves under extreme or simplified conditions, helping to reveal its limitations or potential weaknesses.
These degenerate forms demonstrate the individual contributions of each component to the model's overall dynamics and the emergence of social norms.
The model's simulations illustrate how different network structures significantly impact the development and persistence of social norms.
The model is designed to account for the dynamic nature of social systems, including the impact of external shocks and the persistence of behaviors over time.
While Overbo's research is theoretical, it lays a foundation for future empirical work by offering conceptual tools and practical insights into how social norm dynamics might be observed in the real world. This section explores several complementary aspects of how the model connects to empirical research, including testable propositions and guidance on parameter measurement.
The proposed model offers a structured account of how individual decision-making gives rise to collective normative behavior. It generates a number of broad claims that lend themselves to empirical testing, allowing researchers to evaluate major aspects of the model without needing to account for its full complexity in a single study.
Proposition 1: Substitution Under Behavioral Restriction
When a norm-supporting behavior is externally restricted, individuals will compensate in the short run by increasing complementary behaviors that serve the same normative function. The magnitude of this compensatory shift is proportional to the normative importance of the restricted behavior relative to the availability and cost of substitutes. This proposition follows from the inclusion of habit and multi-behavior support in the model. When a norm-associated behavior becomes restricted (e.g., by law or increased cost), it is effectively no longer available to signal support. Nonetheless, because habit reinforces prior support levels in the short run, agents will choose alternative behaviors in order to maintain support requirements. This leads to a temporary increase in complementary support behaviors before moving toward a new equilibrium. The practical consequence of this is that individuals do not immediately abandon a norm when a focal behavior is restricted. Instead, they adjust by engaging in alternative behaviors that fulfill a similar normative function. For instance, if the right to vote were taken away, the immediate effect would not be a decrease in support for democratic ideals. Rather, there would be an increase in pro-democratic discussion and demonstration among those who value democracy as they make use of these alternative outlets to express normative support. The magnitude of this compensatory shift depends on the extent to which the restricted behavior is integral to the norm and whether viable substitutes are available. On a smaller scale, Proposition 1 could be used to study the effects of workplace break restrictions. In this context, if socializing breaks for a company's employees were banned, any existing norm of informal workplace socializing would, at least temporarily, cause a shift toward other related behaviors. Suppose a company implements a stricter break policy, which severely hinders workplace socializing. According to the proposition, employees who previously relied on these breaks for social bonding and informal collaboration will immediately compensate by increasing engagement in alternative forms of workplace interaction. Examples of this include sending more informal messages, lingering longer at the water cooler, or turning routine meetings into more social interactions. A quasi-experimental study could analyze employee behavior before and after such a policy is introduced, tracking changes in messaging volume, meeting length, and informal in-office interactions. A difference-in-differences approach could then compare offices with and without such restrictions, measuring whether employees in restricted offices increase substitute social behaviors. Such a hypothesis might also be tested through an observational study. Researchers could track whether employees shift to alternative break-like behaviors by comparing organizations that recently implemented break-restricting rules to those that have not. If Proposition 1 holds, employees will find ways to compensate for the removal of informal breaks by increasing other behaviors that fulfill the same normative function, at least temporarily. Beck et al. (2024) provides an existing study that, with slight modification, could be conducted to empirically test this aspect of the model. They examined compensatory behavior in adolescents physical activity by tracking natural deviations from habitual exercise levels and identifying instances where individuals compensated for reductions in activity with increased alternative physical behaviors. Their study employed a mixed-methods crossover design, using self-reported habitual activity schedules, smartphone-based activity diaries, and follow-up interviews to analyze compensation patterns. To test Proposition 1, a similar methodology could be employed, but with a systematically imposed restriction on a norm-supporting behavior rather than relying on natural and idiosyncratic fluctuations.
Proposition 2: Long-Term Effects of Policy
In the long run, policies aimed at norm modification are most effective when alternative norm-supporting behaviors are costly or difficult to adopt. When substitutes are low-cost and accessible, individuals shift toward these alternatives, sustaining the norm despite efforts to restrict focal behaviors. Whereas Proposition 1 addresses short-term effects, Proposition 2 concerns itself with long-term or equilibrium consequences of compensatory behaviors. The extent to which the norm ultimately persists depends on the availability and cost of alternative norm-supporting behaviors. This is because in the long run, native support dominates habit. If substitute behaviors are cheap and readily available, individuals can easily transition to these alternatives, mitigating the long-term impact of the policy on the norm. In contrast, if substitutes are expensive, inconvenient, or otherwise very costly, norm adherence will ultimately decline as individuals find it too taxing to maintain. For example, researchers could examine smoking rates in communities that ban public smoking, chewing tobacco, and vaping versus those that banned only smoking, to determine whether restricting substitute behaviors better leads to a long-run decline in nicotine use. Even without direct restrictions on substitute behaviors, researchers can still explore alternative testing opportunities. A natural experiment could analyze consumer behavior in regions where a ban on a norm-supporting behavior was introduced, with and without easy access to substitutes. When smoking is banned indoors, people may be forced to smoke outside in designated areas, but for smokers in Florida, such an alternative is more attractive than it would be for smokers in Alaska, particularly during winter months. By tracking behavioral adaptation over time, researchers could assess whether very costly substitution is merely a temporary adjustment or whether it sustains the targeted norm in the long run, contradicting this proposition. This suggests that empirical tests of long-run policy effectiveness should focus on whether norms shift or change over time, conditional on the cost of alternative behaviors. A robust empirical test would involve a longitudinal comparison of policy interventions that restrict a norm-supporting behavior, with variation in the availability and cost of substitutes. A strong research design would control for pre-policy trends and economic conditions over time to isolate the policy's effect on norm persistence.
A study like that of Akee et al. (2010) would be a strong candidate for testing Proposition 2. This longitudinal analysis leveraged a natural experiment in which an exogenous increase in household income from casino revenue distributions allowed researchers to observe long-term behavioral changes. For the relevant test, a comparable design could be used, incorporating the additional step of collecting data on the availability and cost of alternative behaviors associated with previously established norms.
The findings of such studies would have important implications for policymakers designing norm-diminishing interventions. To ensure the long-term effectiveness of such policies, regulators must not only restrict certain behaviors but also consider whether alternative norm-supporting behaviors will emerge to replace them. If substitution effects are anticipated, additional policy mechanisms, such as raising the cost of substitutes through taxation or restricting their availability through complementary regulations, may be necessary to prevent the long-run persistence of the undesired norm. Understanding these substitution effects will help in crafting policies that not only create immediate behavioral change but also weaken or strengthen norm adherence in the long run, leading to more lasting social transformation.
Proposition 3: The Role of Influencers
Individuals with high social leverage who gain high exposure can shift population target support toward their own. Sustaining this effect in the long run requires continued exposure. In this paper's model, when a high-leverage individual receives substantial exposure, others who observe this directly shift their own support to more closely align with that individual, all else being equal. If this exposure is widespread enough, the macro-social effect can be substantial. The model further implies that this effect is time-sensitive. Without continued reinforcement, the impact of a high-leverage individual's actions will diminish at a rate inversely proportional to habit. This diminishing effect, illustrated in Figure 10, occurs because habit formation alone cannot sustain a new norm indefinitely. Once this exposure is removed, native preferences begin to reassert themselves, gradually reducing long-term adherence to the newly shifted support. If a high-leverage individual demonstrates a specific norm through a single widely covered media event, for example, there is expected to be a temporary increase in the norm's adoption, which will decay unless reinforced through sustained exposure. Empirically, this should be clearest if the high-leverage individual is relatively uninfluenced by others. This is because if they are also subject to heavy influence themselves, the feedback influence will mute the difference between their support and that of the audience prior to exposure. For example, between two public figures of equal stature and sustained exposure, the one over whom the audience has less leverage will have a greater normative impact in their respective network. Proposition 3 suggests that the news cycle can drive large changes in collective behavior. Media coverage enables widespread and unidirectional exposure of individuals who are frequently of high status. See the discussion of the "Angelina Jolie Effect" in Section 8.2.1 for a more detailed example of this effect. Possible tests include a longitudinal survey to track behavioral shifts in a population exposed to high-leverage influencers over time or a field experiment in which different social groups receive norm-promoting messages from either high-leverage influencers or low-leverage peers. Additionally, social media data could be analyzed to examine how changes in influencer advocacy impact public sentiment over time.
A study such as that of Jackson & Darrow (2005) could be modified to empirically test Proposition 3. This experiment exposed young adults to political endorsements from celebrities through controlled media presentations, including televised interviews and campaign advertisements. Participants' political opinions were measured before and after exposure to assess the immediate impact of celebrity influence and strong evidence was found for the effectiveness of such exposure. However, the study examined only short-term reactions and did not explore whether these effects persisted over time. To test Proposition 3, a similar methodology could be employed with a more longitudinal design, where some participants are repeatedly exposed to norm-promoting messages from the same high-leverage individuals over an extended period. By tracking changes in participants' behaviors and support levels at multiple time points, researchers could assess whether continued exposure is necessary to sustain the initial influence of high-leverage individuals, thereby providing empirical validation for the proposition's emphasis on the importance of sustained visibility for long-term normative change.
Proposition 4: Endowment and Social Influence
In any interaction where exposure occurs $(e_{i,j}^{t}\ne0)$ the social influence of individual j over individual i increases in j's endowment. Given that influence is a function of exposure and leverage, and that leverage increases in endowment, we arrive at Proposition 4 directly from Equations 4 and 11. In the model, endowment amplifies an individual's ability to shape the normative choices of others by increasing the influence their previously expressed support carries. When two individuals interact, the one with greater endowment has a larger effect on the behavior of the other when controlling for exposure. While endowments salient to the norm can be expected to have the most practical impact, (e.g., fashion guidance would be more well-received from a successful fashion designer) this assertion applies to all forms of endowment. All else being equal, the impact one agent's support has on others increases in wealth, beauty, power, authority, or any other observable asset or right. As this proposition is micro-focused, it may be well-suited to a lab experiment. A researcher might pair participants with differing levels of perceived authority, knowledge, or material resources and assign them a task requiring norm formation, such as deciding on the appropriate response to a novel social etiquette scenario. By tracking changes in behavior after interactions, researchers could measure the extent to which the lower-endowed individual shifts toward the norm expressed by the higher-endowed individual.
A study such as that of Asch (1956) could be modified to empirically test Proposition 4. In the original experiment, participants were placed in a group setting with confederates who intentionally provided incorrect answers to simple perceptual tasks. The study measured the extent to which individuals conformed to the majority opinion, demonstrating the power of social influence. However, the experiment did not specifically examine the role of individual endowments, such as authority or expertise, in influencing conformity. To test Proposition 4, a similar experimental design could be employed where participants are paired with confederates who are presented as having varying levels of endowment relevant to the task such as differing levels of expertise or status. By systematically varying the perceived endowment of the confederates and measuring the degree of conformity exhibited by participants, researchers could assess whether individuals with higher endowments exert greater social influence during interactions, thereby offering empirical support for the proposition.
Proposition 5: The Role of Deviation Costs in Norm Strength
A social norm will be stronger when the cost of deviating from native preference toward behaviors that support the norm is lower. This proposition follows from the inclusion of a coefficient on the native preference term in utility, which represents the cost of deviating from intrinsically desired behaviors. Because an individual's native behavior preferences will typically be misaligned with the prevailing norm, adherence requires individuals to adjust their expressed behaviors at some personal cost. If the cost of deviation from native preferences is high, individuals are less likely to make large adjustments to coordinate with the norm. Conversely, when the cost of deviation is low, individuals will more readily shift toward behaviors that reinforce the norm, making it stronger. At the micro scale, this suggests that if the norm is something a person would have followed in the absence of social pressure, or if the person does not intrinsically care much about the relevant behaviors, they will adhere more closely to the norm. At the macro scale, this means that a social group will adhere more strongly to the norm if there is generally little instrumental harm in aligning their behavior. Empirical testing of this proposition could focus on contexts where behavioral shifts occur with varying levels of cost. For example, recycling norms are expected to be stronger in environments where waste sorting is simple, with clearly labeled bins and minimal effort required from individuals. However, in areas where recycling requires complex sorting, extra fees, or special drop-off locations, the norm is predicted to be weaker. This weakness is expected to be observable not only in focal behavior but also in support behaviors such as recycling advocacy.
An empirical study that supports Proposition 5 in this manner is Niu et al. (2023), which investigates the influence of personal costs on adherence to pro-environmental social norms. In this study, participants were asked to engage in environmentally friendly behaviors such as recycling, reducing energy consumption, and minimizing single-use plastics, with varying levels of personal cost imposed such as time, effort, and financial burden. The researchers found that participants were more likely to adhere to pro-environmental norms when personal costs were low, while higher costs led to reduced adherence. This aligns with Proposition 5 by demonstrating that lower costs of deviating from native preferences facilitate stronger adherence to social norms. To test the proposition more directly, future studies could manipulate the cost of deviating from self-interest in controlled environments, such as by varying the complexity of recycling tasks or the financial incentives for non-recyclable waste disposal, and measuring subsequent adherence to recycling norms. This approach would isolate the causal effect of deviation costs on norm strength, providing direct evidence that when the cost of ignoring the norm is high, adherence diminishes, while lower costs encourage stronger norm-following behavior. Additionally, measuring not just overt behavior but also attitudes and advocacy for the norm under different cost conditions would capture the broader social reinforcement effects that the proposition anticipates. Proposition 5 is also particularly relevant to voting norms because the costs related to participation are so low. See Sections 8.2.2 and 8.2.3 for further discussion of how these low costs aid in norm formation and adaptability.
The following topics illustrate some strengths of the proposed model by highlighting its capability to address certain social phenomena that other models struggle to capture. This is not to claim that other models cannot accommodate these observations with modification, nor was the primary aim of this research to resolve such issues. Rather, the idea is to convey that explanations for these observations emerge more naturally from this model than the alternatives. This indicates that the model may be especially well-suited for empirical study of such issues and can also be effectively tested and refined through them.
Celebrity Influence: In Section 5.5, we show how an influential individual can sway behavior across a society under the proposed model. This illustrates how community behavior can shift rapidly due to the involvement of celebrities or other prominent figures. Traditional game theory, EGT, and Threshold models do not natively account for such asymmetric influence in descriptive norms, though such effects are quite apparent empirically (Cialdini et al., 1990). A specific example that demonstrates this issue is the so-called "Angelina effect". This refers to the surge in preventative healthcare behaviors, particularly genetic testing for cancer risks, following American celebrity Angelina Jolie's public announcement that she underwent a preventative double mastectomy in 2013. The number of women interested in BRCA1 and BRCA2 genetic testing rose significantly after Jolie's announcement, demonstrating how celebrity behavior can influence societal priorities related to health practices. The influence occurred quickly and spread through media channels, reshaping health-seeking behaviors within months (Kosenko et al., 2016). It is common knowledge that breast cancer should be screened for regularly, so arguments that Jolie's announcement constituted meaningful new information about cancer risk are not convincing explanations of such a shift. If the effect were primarily due to such learning, it would persist as the topic faded from public discourse, though that does not seem to be the case. Jolie herself has little to gain from others screening for cancer, so it also cannot be explained as a disjoint problem in the vein of Coleman. The only remaining conventional rational explanation for such shifts is that the public figure acted as a focal point to signal which strategy everyone should choose in a coordination game. If the benefit were entirely from such conventional norm effects, there would be little reason to shift behavior based on the actions of one individual over any established equilibrium for cancer screening in society at large. Under the model presented, this shift in behavior is explained by a temporary shock to the network, where Jolie's experience with cancer received wide exposure. This, combined with her high social leverage, meant that the effort she made to protect herself from cancer led others to do the same shortly afterward. Of course, the social outcome was not that there was a massive increase in the focal action (double mastectomies). Rather, in line with the concept of support, individually appropriate measures were taken to combat cancer, the most common of these being to screen for breast cancer. To illustrate the advantage more clearly, consider a hypothetical sub-population with a low baseline rate of cancer screening that is exposed to news on Jolie's announcement and health progress for some finite period of time. The proposed model predicts a shock upward in screening due to exposure which is sustained so long as exposure continues and decreasing gradually after exposure is removed. Game theory models generally predict no change due to exposure unless the news transmits information which updates utility estimates. In that case, there would be a change in behavior that would be sustained even after exposure is removed. Threshold models would also predict a sustained increase, but only if Jolie's participation happened to be in a position to cause a network cascade. Otherwise, they would predict no change. EGT says nothing in this case. Only this paper's model is consistent with what occurred.
This example aligns strongly with Proposition 3 and illustrates one of the advantages this type of modeling has over other approaches. In this case, by explicitly modeling singular, asymmetric influences, such as those exerted by celebrities, the resulting volatility in norms is explained.
The Emergence of a Voting Norm: This section argues that alternative theoretical methods are less likely to predict the emergence of norms under certain conditions. We will use voter participation as an illustrative case.
Each theoretical framework we have discussed provides a different perspective on the emergence of widespread voter participation. Coleman's reasoning suggests that a coalition of individuals who benefit from high voter participation coordinate their efforts to sanction others into voting, thereby establishing voting as a norm. Bicchieri's model, on the other hand, focuses on expectations. In this view, a voting norm occurs because people expect others to vote and believe they are expected to do so themselves, leading them to vote as a behavioral response. EGT posits that the predisposition to vote could be bred into us through evolutionary processes. Threshold models propose that voting begins with a small number of individuals who vote because they enjoy it or have some other idiosyncratic motivation, which causes a cascade through the social network. In contrast, the model presented in this paper tells a story of shared understanding, such as the belief that "democracy is good." Demonstrating appropriate support for this value becomes socially important for each citizen. In the absence of any election, one can demonstrate such support in a variety of other ways, such as speaking about the benefits of democracy or participating in political protests. In cases where democratic elections are available, voting emerges as a cheap and accessible way to display one's alignment with this shared value. This aligns with Proposition 5, which suggests that norms become stronger when the cost of deviation is low.
The various explanations these different models provide for the emergence of a voting norm are different, but not fundamentally so. Determining which framework is most useful is partly an empirical question, but it is also true that the stories being told do not inherently contradict each other. Nevertheless, the nature of the model proposed in this paper does makes it better suited to predict the emergence of voter participation. It provides clearer guidance on how to measure factors related to the relevant norm and makes more precise predictions about both short-term and long-term outcomes. Unlike other frameworks, it better addresses the practical challenges of empirical application and provides greater specificity. First, compared to alternatives, this model offers greater empirical applicability to voting norms. This stems from the greater detail in the proposed utility function. Game theory-based approaches often leave the underlying utility functions undefined to maintain generality, making them difficult to operationalize. Bicchieri's model, though somewhat specific, relies heavily on measuring internal beliefs, which are inherently harder to observe and quantify than behaviors or other external factors. While the model in this paper also generalizes, most notably in its treatment of native preferences, this factor is relatively unimportant in the context of voting, where direct self-interest plays a negligible role. This is because there are few reasons to vote which satisfy simple self-interest. This topic is discussed in greater detail in Appendix A. Instead, the habit formation and social influence components of this model are expected to dominate, and these components are given an explicit functional form. This reduces the burden on empiricists by offering clearer guidelines for measurement and analysis.
Furthermore, conventional game theory and EGT approaches introduce additional challenges by requiring empiricists to identify equilibrium states, a task that is as much art as science. There is no guarantee that such equilibria exist, and even when they do, their identification often involves significant uncertainty. In this sense, the model presented provides a prediction where many alternative models do not. Alternative approaches provide limited insight into short-term behavioral shifts. Conventional game theory offers no dynamic framework, and EGT focuses on the evolution of coordination rather than the mechanisms driving it. Threshold models, while dynamic, often rely on overly simplistic mechanisms for explaining behavioral shifts. By contrast, this model provides precise predictions for individual agents at every point in time, rather than merely estimating the likelihood of a particular outcome or direction of movement, as game-theoretic solutions often do. By making predictions that are both precise and dynamic, this model is uniquely equipped to explain the emergence and stabilization of voting norms in ways that other frameworks cannot.
Variations in Voter Participation: Even in cases where high voter participation is already established, the proposed model appears to offer some additional empirical insight over the alternatives. One way the model distinguishes itself is by explaining the empirical observation that voters are more likely to participate in high-profile elections. In the United States, for example, voter turnout is significantly higher during presidential races than interim elections. The proposed model attributes this variability to dynamic changes in exposure across the network. That is, during presidential elections, there is significantly more discussion around the importance and stakes of voting in both the media and interpersonal communication. This difference is significant and regular even though the outcome of certain local elections may have more direct and practical impact on an individual voter and their community. Furthermore, a single vote in such elections is more likely to influence the outcome. This problem challenges traditional rational-choice explanations, including Coleman's framework.
In the literature on norms, such variance would typically be handled as an exception by saying the norm is conditional, and that it is more important to vote if it is not an interim election. However, such conditionality is difficult to explain in this context as it is not clear why such a condition should exist, or how it comes about. Whatever established model one wishes to apply, the source of this conditionality is left purely to conjecture. The presented model, however, points to increased exposure to election topics from influential individuals as the driving force. The effect of the changes in exposure to the topic of voting pre- and post-presidential election could operate in a manner similar to that shown in Figure 10. During the interim election, the influence network is weak. Then, as the presidential election approaches and media around the importance of voter participation is maximized, conformity peaks. After the election, social influence on the topic decreases and so does the corresponding coordination on support until the next presidential election.
Harmful Behaviors: A central challenge in understanding apparently harmful norms is explaining why they persist despite their evident inefficiencies or detriments to individual and collective welfare. Traditional models, such as those grounded in evolutionary game theory or coordination games, often presume that norms emerge and persist because they optimize group welfare. These models struggle to account for norms like hazing rituals, smoking, or self-injury, which endure despite widespread acknowledgment of their harmfulness. This model addresses these gaps by incorporating the concept of support, which captures how behaviors align with a norm not solely through individual adherence but as part of a broader signaling process. Unlike simpler models that view norm adherence as a binary comply-or-defect decision, this model recognizes that individuals engage in a constellation of interrelated behaviors that collectively indicate their support for a norm. For example, in the case of hazing rituals, enduring physical or psychological harm serves as a public signal of loyalty to the group.
These actions not only align with the group's expectations but also reinforce the individual's identity as a committed member. By emphasizing the interconnectedness of behaviors under a single norm, the model explains how even costly or harmful actions can accrue net personal benefit, such as increased status or belonging, even though the practice it is costly for all involved when considered in isolation. Additionally, the model integrates habit formation and social influence to illustrate how harmful norms become stabilized over time. Habit formation ensures that a support level, once established, becomes a default response, reducing the likelihood of deviation even when external conditions change. Social influence can magnify this effect by creating a feedback loop, where observing others' adherence to the norm reinforces an individual's interest in conforming. Together, these forces create a mechanism for norm persistence that does not rely on the assumption of group-level optimality, setting this model apart from alternatives. Unlike traditional frameworks, which often assume that norms dissolve when they no longer serve a clear utility, this model demonstrates how harmful norms can persist due to their role in signaling and social cohesion. This signaling reinforces the norm's legitimacy, even as external campaigns highlight its harms. The model's nuanced understanding of support as a dynamic, multidimensional measure enables it to capture these complexities, offering a superior explanation for the endurance of harmful norms. By addressing both individual motivations and network-level dynamics, this framework provides insights that other models fail to deliver.
Pluralistic Ignorance: This model potentially resolves a notable conflict between rational choice theory and the concept of pluralistic ignorance discussed in Section 2.6.1. Pluralistic ignorance, as defined by Perkins & Berkowitz (1986), suggests that individuals systematically misperceive others' behaviors and attitudes, resulting in erroneous beliefs about how others behave and biased choices. However, rational choice models typically assume that individuals should have no such persistent biases.
This inherent tension arises from the belief that rational agents should, in theory, correct misperception through something like Bayesian updating. Even if the estimates made are not precise because of incomplete information, the expectation should at least remain unbiased. Yet, empirical evidence of persistent norms, such as alcohol use, suggests that these misperceptions are stable and endure, contradicting the assertions of conventional rational choice theory. The model presented in this paper potentially reconciles these seemingly opposed perspectives by suggesting that the conflict may be the result of the difference between mean and target support. That is, the survey was interpreted as measuring estimates of mean behavior across all college students without accounting for how the influence network weights the behavior of each student differently. What was relevant to the students desires to fit in, and what they were actually responding to, may have been behavior weighted by influence. If that is the case, there is no misperception on the part of the students. Given the survey results, the model predicts that students with higher social influence are, in fact, more likely to consume alcohol, and that in turn should drive a general elevation in consumption.
Persistence of Behaviors in Changing Social Contexts: When individuals move to a new cultural setting and sever ties with their previous social environment, they do not immediately shed old behaviors. As individuals make these transitions, established habits exhibit inertia that slows down adaptation to the new environment, influencing their interactions within the new context until new behaviors take root through repeated exposure. Traditional game-theoretic models struggle to account for the persistence of behaviors during social transitions. These models often assume that behaviors are determined by immediate payoffs and fixed strategies, which makes them more suited to explaining equilibrium states or short-term coordination problems rather than dynamic, long-term behavioral change. They do not adequately capture the stabilizing effects of habituation or the cumulative influence of social exposure over time. As a result, game-theoretic approaches fail to conclusively address why some individuals might continue to engage in familiar behaviors after a significant change in cultural context, particularly when those behaviors no longer provide clear utility or align with the new environment's norms. The model discussed here not only predicts such lag, it also shows how one's social placement in the new society predicts the speed at which such adaptation occurs.
A significant difficulty in the approach presented in this paper arises in the large number of parameters involved. Given a population size p, a maximum number of time periods $t_{max}$, a number of measurable behaviors m, as well as network density , suppose we aim to fully test the model on a real-world community. To do so, we may require up to the following:
Thus, the maximum number of measurements required to make a precise prediction with the model can be expressed as
[Max measurement count] $=\delta t_{max}p^{2}+(2+t_{max}+mt_{max}-\delta t_{max})p+m$
For instance, in a system with 100 people, 10 behaviors, 10 time periods, and a network density of 0.1, the upper bound on the number of scalar values needed to input or compare is 21,110. This number can be reduced by about an order of magnitude if shocks are limited, but since at least one complete social network is required for the model to function, the parameter count grows at a rate of $O(p^{2})$ for tightly connected networks.
If the influence network values are taken as given, the parameter growth rate becomes $O(pmt_{max})$, which is an improvement as p would typically be the largest value. However, this situation remains far from practical. Ignoring the network variables, the maximum number of scalars in the 100-agent example above reduces to 11,200. In a system with few shocks, this number could be as low as 1,400. While the model is testable directly in principle, this large number of parameters makes such tests impractical on all but the sparsest of networks.
Still, less direct methods are available. Most obviously, agent-level testing is a crucial first step in model validation which does not require extensive data collection. By verifying that agents' actions at the micro-level reflect realistic decision-making and social dynamics, researchers can ensure that the foundation of the model is accurate before moving on to broader system-level validation. This step ensures that agent behaviors are grounded in empirical evidence. Tests of propositions derived from the model, such as those highlighted in Section 8.1 can also help validate and refine the model. From there, calibration and sensitivity tests can be conducted based on known data to test larger scale predictions.
Measurement of Parameters (New to Literature): The thesis provides conceptual groundwork for measuring parameters that are new to the literature, highlighting that they can be operationalized in principle.