The Role of Network Structure and Initial Group Norm Distributions in Norm Conflict

TL;DR

This paper uses an agent-based model to analyze how network structure and initial norm distributions influence norm conflict and consensus within and between groups, highlighting the roles of homophily and heterophily.

Contribution

It introduces a novel simulation framework examining the effects of network features and initial norms on conflict and consensus in multi-group settings.

Findings

Norm change is most likely when norms are strongly tied to group membership.

Heterophilic networks lead to similar norm distributions across groups.

Homophilic networks increase intergroup conflict and reduce intragroup conflict.

Abstract

Social norms can facilitate societal coexistence in groups by providing an implicitly shared set of expectations and behavioral guidelines. However, different social groups can hold different norms, and lacking an overarching normative consensus can lead to conflict within and between groups. In this paper, we present an agent-based model that simulates the adoption of norms in two interacting groups. We explore this phenomenon while varying relative group sizes and homophily/heterophily (two features of network structure), and initial group norm distributions. Agents update their norm according to an adapted version of Granovetter's threshold model, using a uniform distribution of thresholds. We study the impact of network structure and initial norm distributions on the process of achieving normative consensus and the resulting potential for intragroup and intergroup conflict. Our results show that norm change is most likely when norms are strongly tied to group membership. Groups end up with the most similar norm distributions when networks are heterophilic, with small to middling minority groups. High homophilic networks show high potential intergroup conflict and low potential intragroup conflict, while the opposite pattern emerges for high heterophilic networks.

Tables

Table 1. Table 1: Range of parameter values of the simulation in the experiment

Parameter	Description	Value(s)
\svhline n	No. of Agents in Network	2000
m	Minimum Agent Degree	2
p1:p2a	Initial Group Norm Distribution	[0.5:0.5][0.6:0.4][0.8:0.2]
t	Individual Agent Threshold	$U(0,1)$ b
g	Group Size	[$0.1,\stackrel{+0.1}{\dots },0.5$]
h	Homophily/Heterophily Parameter	[$0.1,\stackrel{+0.1}{\dots },1$]

Equations

$$p_{ij}=\frac{h_{ij}{k}_i}{\sum h_{lj}{k}_l}.$$

$$C=\left(g\left(1+\frac{hC}{hC+(1-h)(2-C)}\right)+(1-g)\frac{(1-h)C}{h(2-C)+(1-h)C}\right).$$

$$\begin{array}{rl}{p}_{aa}& =\frac{hC}{hC+(1-h)(2-C)},\\ p_{bb}& =\frac{h(2-C)}{h(2-C)+(1-h)C}.\end{array}$$

$$C=g(1+p_{aa})+(1-g)p_{ba}.$$

$$f_{aB}=\frac{p_{aa}{p}_{aB}+p_{ab}{p}_{bB}}{p_{aa}+p_{ab}}.$$

$$f_{aB}=\frac{(\frac{hC}{hC+(1-h)(2-C)})(p_{aB}-p_{bB})+(2-\frac{h(2-C)}{h(2-C)+(1-h)C})p_{bB}}{2-(\frac{h(2-C)}{h(2-C)+(1-h)C})}.$$

$$f_{bA}=\frac{p_{bb}{p}_{bA}+p_{ba}{p}_{aA}}{p_{bb}+p_{ba}}.$$

Full text

1 Introduction

In this chapter, we study the impact of network structure and initial group norm distributions on the process of arriving at a normative consensus between groups and the potential for intragroup and intergroup conflict that might emerge under different conditions. To this end, we first provide a brief theoretical overview on social norms, normative group conflict and the process of finding consensus trough social influence. Secondly, we give an overview on the role that network structure as well as the initial distributions of norms can play in this process. Specifically, we argue that homophily/heterophily (preference for forming connections to similar/dissimilar others) between members of different groups, relative group sizes, and the initial distribution of norms within groups are all important factors for reaching normative consensus, and consequently relevant determinants of conflict potential. Based on this reasoning, we develop an agent-based model that simulates social networks of agents from two different social groups where each agent holds one of two social norms. In an adapted version of Granovetter’s threshold model Granovetter [1978], each agent updates its social norm by comparing the proportion of norms held by its immediate neighbors to an internal threshold drawn from a uniform distribution. Agents are thus ”observing” the ”openly displayed behavior” of their neighbors and adapt their own behavior accordingly if enough of their neighbors display a different norm. We apply this model to different network structures, defined by relative group sizes and homophily/heterophily between agents from different groups. This allows us to assess the impact of these structural network properties on the process of reaching normative consensus and associated conflict potential. In addition, we run our model for different levels of initial group norm distributions, so that we can also assess the influence of alignment (or independence) of norms and social group membership. We define and examine three relevant outcomes: The degree to which norm distributions change, the degree to which the difference in norm distributions between the two groups changes, and the potential for conflict within and between the groups. Lastly, we discuss our results with respect to their applicability, the limitations of our model and possible directions for future research.

2 Social Norms

Social norms can be defined as unwritten behavioral rules Bicchieri and Mercier [2014] or ”social standards that are accepted by a substantial proportion of the group” Forsyth [2018]. They are a shared set of situation-specific behaviors that facilitate social interaction by providing an implicitly shared set of expectations and behavioral guidelines Bicchieri [2006]. Such behaviors can range from an implicit dress code at work, to the expression of religious and political symbols, or (not) interacting with other social groups. Norms are implicitly negotiated between members of a group and enforced through informal sanctions, such as gossip, censoring or ostracism Bicchieri [2006]. They are passed through generations via socialization processes in childhood House [2018] and are, in contrast to laws, not necessarily enforced by an institution. Norms come in multiple types; for example, prescriptive norms define behaviors that one should enact (e.g. ”offering elderly people a seat on the subway”), while proscriptive norms define undesirable behaviors that one should avoid (e.g. ”interrupting people while they speak”). The most important distinction for our purposes is between injunctive and descriptive norms. Injunctive norms focus on beliefs about how people should act, while descriptive norms are defined by the observation of how people actually do act Melnyk et al. [2010], Cialdini et al. [1990]. For instance, ”everybody should recycle” is an injunctive norm, while the observation that many people do not recycle represents a descriptive norm Cialdini et al. [1990]. Both types of norms are important determinants of behavior, but previous research suggests that injunctive norms primarily elicit behavioral change by changing attitudes Melnyk et al. [2010], Megens and Weerman [2010], while descriptive norms directly impact behavior Cialdini [2007]. In this chapter, we are interested in descriptive norms, because they are directly inferred from the observed behavior of others. Injunctive norms can differ from directly observed behavior, and can involve more complex cognitive processes House [2018], which are beyond the scope of our model. Therefore, when we are referring to social norms with respect to our model, we are specifically addressing descriptive social norms.

2.1 Normative Conflict

A large body of previous research has focused on the potential for positive impact of social norms on behavior. Predominantly, these studies were interested in changing individual beliefs or behavior by presenting normative information at odds with the individual’s current beliefs or behavior. Examples include the reinforcement of non-delinquent behavior through the influence of peers Megens and Weerman [2010], positive effects of punishment on cooperative behavior Fehr and Gächter [2000], effects of social norms on compliance to vaccination programs Oraby et al. [2014], reduction of binge-drinking in college students Haines and Spear [1996] and littering Cialdini et al. [1990]. However, inconsistent norms do not only elicit behavioral change; they can lead to interpersonal and intergroup conflictHogg and Reid [2006]. The potential risk of such normative conflicts is especially high in multicultural contexts where different cultural groups must coexist Wimmer [2013]. A recent example of normative conflict in Europe is women wearing a veil to cover their face in public. This practice is a prescriptive social norm in some predominantly Muslim countries and it has elicited mixed reactions when immigrants engaged in the practice in their new countries Kılıç et al. [2008]. Some western countries such as France, Belgium and Switzerland have banned the practice. In France, lawmakers claimed that a ban was necessary to ensure ”peaceful cohabitation” Zeit Online [2019]. Likewise, in Germany, face veils have been controversially discussed in the past years: For instance, the German Minister of the Interior stated ”[…] we reject this. Not just the headscarf, any full-face veils that only shows eyes of a person […] It does not fit into our society for us, for our communication, for our cohesion in the society … This is why we demand you show your face” McKenzie [2019]. This backlash reflects an underlying normative conflict, with a large majority (81%) of Germans supporting a ban in public institutions and a substantial group (51%) even supporting a general ban. Only a minority of the national population (15%) indicate that they are not in favor of any kind of regulation Infratest Dimap [2018].

However, such normative societal conflicts exist not only along established cultural and religious divides, but can cover a wide array of topics and elicit intergroup and intragroup conflicts Hogg and Reid [2006]. For instance, gun ownership is a controversial normative debate within U.S. society Kleck [1996], involving subgroups with different cultural orientations Celinska [2007]. Abortion is another topic debated worldwide, with disagreements concerning womens rights, health care systems and moral constraints Marecek et al. [2017]. Empirical research shows how the controversy around abortion leads to a polarization of opinions within Protestants and Catholic groups in U.S. society Evans [2002]. Other inconsistent norms can concern controversial national traditions such as Zwarte Piet (”Black Pete”), a folklorist character and helper of Sinterklaas (Santa Claus) in the Dutch culture. The character is typically displayed with blackface makeup, bright red lips and colorful clothing. The display has been increasingly criticized as a racist stereotype, predominantly by minority and immigrant groups, while many native Dutch citizens argue that ”Black Pete” is a positive character and part of their national tradition Rodenberg and Wagenaar [2016]. In essence, inconsistent social norms within a larger collective have the potential to lead to intergroup, as well as intragroup conflict. With respect to trends of increasing globalization and migration, effectively resolving these normative conflicts is becoming a striking priority for many societies in the future.

2.2 Finding Consensus

Despite their potential for negative outcomes, normative conflicts are not an indication that a collective is inherently unfit to live together peacefully. In contrast, they can be fundamental to the formation of social units at different scales. Georg Simmel defines shared consensus on social roles and their supporting norms as necessary features of human society Simmel [2009]. Similarly, normative conflicts are frequently observed in the literature on group formation and described as a necessary step towards a common group identity. For example, in Tuckman’s stage model of group development, the norming stage focuses on resolving disagreement and establishing a shared set of behavioral guidelines; it is a crucial step in the formation of an effective group Tuckman [1965]. Some recent, empirically validated models such as the Normative Conflict Model Packer and Miners [2014] confirm this mechanism. According to the model, members strongly identified with the group are more likely to openly express dissent compared to weakly identified members Packer and Miners [2014]. Dissenters help uncover the causes of the conflict and discuss possible solutions. To form an effective group with committed members, it is necessary to effectively resolve conflicts due to incompatible norms and to find a consensus on which most members agree. Failure to reach such a consensus might result in a lack of common group identity and task effectiveness, leading to the dissolution of the group Tuckman [1965].

Interactions between people from different social groups are a steadily increasing occurrence in societies that are socially, economically and culturally diverse Arapoglou [2012]. Such diversity is likely to increase in the future, along with changing relations between majority and minority groups due to demographic and socioeconomic changes Crul [2016]. As ongoing political and societal polarization in Western societies already demonstrate, incompatible social norms associated with different groups have the potential to elicit conflict Fiorina and Abrams [2008]. For these reasons, we argue that it is crucial to understand the conditions enabling social groups to effectively reach a normative consensus and how this process relates to conflict potential within and between social groups.

3 Network Structure & Group Norm Distributions

Individuals do not adopt norms in isolation; the structure of their social environment is a key determinant of social behavior. The social networks in which we are embedded determine the kinds of people and behavior to which we are exposed, thereby shaping the descriptive norms we hold. Thus, the interpersonal processes which contribute to finding normative consensus Neumann [2008], as well as the intergroup and intragroup processes Hogg and Reid [2006], are crucially contextualized within networks of social interaction. Consequently, we argue that finding normative consensus is a continuous process of group members mutually exerting social influence Cialdini [2007] on each other until a relatively stable equilibrium is reached Latané [1981], Flache et al. [2017]. This often requires that at least some individuals react to social influence exerted on them by their social networks by changing their norms. For instance, Kalesan et al. [2016] show how networks such as family and friends are the best predictors in forging a culture favoring gun ownership. As for the normative conflict of gay marriage in the U.S., a longitudinal time-series study shows how the decision of the U.S. Supreme Court in June 2015 eventually led to an increase in perceived social norms supporting gay marriage independently of individual attitudes Tankard and Paluck [2017]. In short, the social networks people are embedded in appear to play a crucial role in the process of reaching a normative consensus within and between groups.

In this chapter, we will focus on homophily/heterophily between people from different groups and relative group sizes as determinants of network structure, and on the initial distribution of norms within groups when they come into contact.

3.1 Homophily & Heterophily

Homophily is the tendency to preferentially connect and interact with similar others McPherson et al. [2001], while heterophily is the tendency to preferentially connect and interact with dissimilar others Lozares et al. [2014]. Homophily has been observed extensively in many social networks, including school friendships Stehlé et al. [2013], scientific collaborations Jadidi et al. [2017], and online communications Mislove et al. [2010]. It is likely a manifestation of the similarity bias, a fundamental human tendency to like and value others that are similar to the self and to consequently be disproportionally influenced by them Cialdini [2007]. For example, a controlled experimental study on the spread of a health innovation through social networks varied the level of homophily, showing that homophily significantly increased the overall adoption of new health behavior, especially among those in more clustered networks Centola [2010]. Similar effects have been shown in diverse health behaviors in large social networks, such as the spread of smoking Christakis and Fowler [2008] and obesity Christakis and Fowler [2007]. Since social influence is exerted through social ties in networks Aral and Walker [2011], Lewis et al. [2012] and homphily/heterophily determines how these ties are formed, we argue that it is an important factor in the process of negotiating a normative consensus through mutual social influence.

3.2 Group Size

Almost no collective group is made out of completely homogeneous members. Instead, they consist of demographic subgroups, such as those defined by gender, nationality, or education McPherson et al. [2001]. Mostly, these subgroups are not equally sized, so that people are either part of a majority or minority group Blau [1977] with respect to a certain social category. The pervasive influence of majority opinions, customs, and norms is well established in theoretical accounts of group-based social influence Latané [1981]. The dominant role of the majority has been experimentally validated in numerous studies replicating the seminal work by Asch [1951], both for individual social influence Horcajo et al. [2010], Kundu and Cummins [2013] and group influence Meyers et al. [2000], Cohen [2003]. Greater influence of the majority is generally assumed for acculturation processes of minority immigrants in host countries Bourhis et al. [1997], Ward et al. [2010]. Yet, other studies have demonstrated that under certain conditions, minorities can successfully exert social influence on the majority and consequently redefine the normative consensus in their favor Hogg and Reid [2006], Mugny and Papastamou [1982], Nemeth [1986]. For these reasons, we argue that the sizes of interacting subgroups within a larger society are an important factor in the process of negotiating normative consensus.

3.3 Initial Group Norm Distributions

Agreement on social norms is considered to be a part of the collective identity people derive from the social groups to which they belong Hornsey [2008], Hogg and Reid [2006]. Norms vary, however, in how much they align with group membership. Even in the case of German opinions on face veils, a full 15% do not agree with the normative opinion to ban face veils McKenzie [2019], Infratest Dimap [2018]. That is, despite sharing group membership, individuals disagree on this norm. Conversely, in the social group of Muslim immigrants in Germany, some will support the norm of face veils while others will oppose it. People can hold the same norm on face veils even though they are from different social groups, or they can hold different social norms while belonging to the same social group. In terms of our example, there will be some Muslim immigrants agreeing with Germans who oppose face veils. There will also be some Germans agreeing with the Muslim immigrants who do not oppose face veils. In short, even in this case of strong consensus, group membership is not the single determinant of norms held on an individual level. Social norms are often aligned with group membership to a degree, but the two are not synonymous.

This interplay of social group membership versus agreement in moral or normative issues has been shown to be influential in previous studies. For instance, the influence that a group exerts on individuals is not only a function of its size, but also of its unanimity, with stronger pressure towards conformity for more unanimous groups Asch [1956]. Furthermore, studies have shown that people react more negatively to dissenters from their own in-group Marques et al. [1988] and consequently punish them harder. The initial distribution of norms within groups thus seems to be important for negotiating a normative consensus, even though it is not necessarily influencing the structure of the social network.

4 Agent-Based Model

Agent-based modeling can be of particular interest to understand social phenomena because it enables researchers to study complex macro-level outcomes that emerge from a clearly defined set of micro-level processes Macy and Willer [2002], Flache et al. [2017]. In addition, simulations allow us to systematically vary agents’ behavioral rules or the circumstances in which they act Squazzoni et al. [2014]. In short, agent-based models help us to gain insight into the emergence of complex systems by systematically testing a variety of different parameters and the combined impact they exert on the emergent system Macy and Willer [2002]. Previous research has extensively used agent-based models to study phenomena such as spatial segregation Schelling [1971], opinion diffusion Lorenz [2007], the adoption of innovation Zhang and Vorobeychik [2017], and cascade effects Watts [2002].

For the purpose of modeling normative conflict in social networks with respect to relative group sizes, homophily/heterophily, and group norm differences, we developed a modular simulation framework based on a network generation algorithm using preferential attachment, group size and homophily/heterophily Karimi et al. [2018], and Granovetter’s threshold model Granovetter [1978]. We utilized R R Core Team [2019] for our model as it appears to be more widespread among the social science community than Python and offers more customizability, better parallelization and scalability than NetLogo. Consequently, probabilistic processes in our model are implemented using the sample() function in R, which relies on the current system time to generate a seed for pseudo-random number generation. All code, documentation and an animated visualization are available on GitHub Kohne [2019] under the MIT License.

4.1 Simulating Norm Conflict

In our agent-based model, we aim to simulate the impact of group size, homophily/heterophily between agents from different groups, and initial group norm distributions on the process of reaching normative consensus and resulting conflict potential. To this end, we generated networks with 2000 agents each, where network structure is determined by one parameter for relative group size ($g$) and one parameter for homophilic/heterophilic preferences of agents ($h$) Karimi et al. [2018]. In addition, initial norms for agents were assigned based on three different pairs of binomial probabilities, resulting in three conditions for initial group norm distributions. Once the network structure is generated and agents are assigned their initial norms, each agent is assigned a threshold from a uniform distribution Granovetter [1978] and the model simulates normative social influence processes between agents by repeating 50 iterations of Granovetter’s threshold model. Once the simulation is complete, we extract the percentage of agents holding each norm for each group, and the number of ties between agents within each group and between the groups. Crucially, we differentiate ties between agents holding the same norm and ties between agents with incompatible norms. Our model thus consists of four subsequent steps: Generation of network structure, initialization of group norm distributions, the norm updating process, and the extraction of outcome metrics.

In total, we simulate 150 unique parameter combinations with 20 networks per combination, resulting in 3000 unique networks (for an overview of the parameter space, see Table 4.1). For each of these networks, we are saving each iteration of Granovetter’s threshold model as an individual network object, resulting in 150.000 networks with 2000 agents each. Simulation was carried out on the High Performance Computing Cluster of the University of Cologne on 150 MPI nodes. We opted for 50 iterations of Granovetter’s threshold model because it was the highest number of feasible iterations in the maximum computation time limit for the MPI nodes (360 hours) of the High Performance Computing Cluster. The simulation took approximately 13 days (315 hours) and resulted in approximately 40GB of output data.