Small Worlds and Cultural Polarization

Abstract

Building on Granovetter's theory of the “strength of weak ties,” research on “small-world” networks suggests that bridges between clusters in a social network (long-range ties) promote cultural diffusion, homogeneity, and integration. We show that this macro-level implication of network structure depends on hidden micro-level assumptions. Using a computational model similar to earlier studies, we find that ties between clusters facilitate cultural convergence under the micro-level assumptions of assimilation and attraction to similar others. However, these assumptions also have negative counterparts—differentiation and xenophobia. We found that when these negative possibilities are no longer assumed away, the effect of long-range ties reverses: Even very small amounts of contact between highly clustered communities sharply increased polarization at the population level.

[An appendix to this article is featured as an online supplement at the publisher's website.]

Keywords:

• agent-based models
• cultural dynamics
• micro-macro link
• polarization
• small-world networks
• social influence

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Corrigendum

Acknowledgments

The research of the first author has been supported by the Netherlands Organization for Scientific Research, NWO (VIDI Grant 452-04-351). We thank the special issue editors and two anonymous reviewers for valuable advice on and constructive criticism of earlier versions of this work. Our work has further benefited from stimulating discussions with Michael Mäs, Tobias Stark, Károly Takács, and other members of the discussion group on norms and networks at the Department of Sociology of the University of Groningen.

Notes

¹For example, in the “connected caveman graph” shown in Figure 8a, the local clusters are formed by so-called “caves,” complete subnetworks with five nodes each. Each cave is directly linked to its two neighboring caves in the circular spatial arrangement by exactly one tie but not to any other cave. Thus, in this network a long-range tie links nodes from two caves that are not directly linked in the original graph. In other words, a long-range tie has a range of at least three in this graph.

²Following the standard in the literature, we define network density of a cluster as the number of actual neighborhood ties between members of the cluster divided by the number of theoretically possible ties.

³We initialize states to be uniform randomly distributed in [−1, +1]. This implies that the distances between the agents are not uniform randomly distributed and hence neither are the weights. More precisely, the expected weight in the initial condition is one third. The special issue editors raised the concern that our results might be sensitive to this “positive bias” in the initial distribution of weights. We therefore modified the weight function to allow the expected weight when opinions are randomly distributed to be set arbitrarily at any level from 0 to 1/3. Results of the corresponding robustness test are reported in the online appendix. In most conditions, we observed no qualitative differences with the central results reported below. Moreover, the conditions in which we observed substantial differences confirmed the explanatory mechanism proposed above, that is, that long-range ties foster polarization if ties between agents within short range are less likely to be negative compared to long-range ties. At the end of the online appendix, we also discuss the behavioral assumptions that correspond to different specifications of the weight function and conclude that our original model is to be preferred.

⁴To be precise, with self-distances excluded the value of P for maximal polarization is .

⁵Previous work (e.g., Watts and Strogatz, 1998) “rewired” ties in order to keep density constant. However, rewiring changes the local structure of the access graph in some caves such that caves have no longer the same local structure. To avoid this complication, we left the local structure of all caves intact and add long-range ties, which resulted in a marginal increase in density. In experiment 2, we show that effects of this manipulation are not caused by changes of the network density of the access graph.