Local Convergence and Global Diversity: The Robustness of Cultural Homophily

Recent extensions of the Axelrod model of cultural dissemination (Klemm et al 2003) showed that global diversity is extremely fragile with small amounts of cultural mutation. This seemed to undermine the original Axelrod theory that homophily preserves diversity. We show that cultural diversity is surprisingly robust if we increase the tendency towards homophily as follows. First, we raised the threshold of similarity below which influence is precluded. Second, we allowed agents to be influenced by all neighbors simultaneously, instead of only one neighbor as assumed in the orginal model. Computational experiments show how both modifications strongly increase the robustness of diversity against mutation. We also find that our extensions may reverse at least one of the main results of Axelrod. While Axelrod predicted that a larger number of cultural dimensions (features) reduces diversity, we find that more features may entail higher levels of diversity.Comment: 21 pages, 8 figures, Submitted for presentation in Mathematical Sociology Session, Annual Meeting of the American Sociological Association (ASA), 200

Small Worlds and Cultural Polarization

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

Learning

Learning and evolution are adaptive or “backward-looking” models of social and biological systems. Learning changes the probability distribution of traits within an individual through direct and vicarious reinforcement, while evolution changes the probability distribution of traits within a population through reproduction and selection. Compared to forward-looking models of rational calculation that identify equilibrium outcomes, adaptive models pose fewer cognitive requirements and reveal both equilibrium and out-of-equilibrium dynamics. However, they are also less general than analytical models and require relatively stable environments. In this chapter, we review the conceptual and practical foundations of several approaches to models of learning that offer powerful tools for modeling social processes. These include the Bush-Mosteller stochastic learning model, the Roth-Erev matching model, feed-forward and attractor neural networks, and belief learning. Evolutionary approaches include replicator dynamics and genetic algorithms. A unifying theme is showing how complex patterns can arise from relatively simple adaptive rules.</p

The social contagion of generosity

Why do people help strangers when there is a low probability that help will be directly reciprocated or socially rewarded? A possible explanation is that these acts are contagious: those who receive or observe help from a stranger become more likely to help others. We test two mechanisms for the social contagion of generosity among strangers: generalized reciprocity (a recipient of generosity is more likely to pay it forward) and third-party influence (an observer of generous behavior is more likely to emulate it). We use an online experiment with randomized trials to test the two hypothesized mechanisms and their interaction by manipulating the extent to which participants receive and observe help. Results show that receiving help can increase the willingness to be generous towards others, but observing help can have the opposite effect, especially among those who have not received help. These results suggest that observing widespread generosity may attenuate the belief that one’s own efforts are needed

Cascade Dynamics of Multiplex Propagation

Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However we show that when the propagation requires simultaneous exposure to multiple sources of activation, called multiplex propagation, the effect of random links is just the opposite: it makes the propagation more difficult to achieve. We calculate analytical and numerically critical points for a threshold model in several classes of complex networks, including an empirical social network.Comment: 4 pages, 5 figures, for similar work visit http://hsd.soc.cornell.edu and http://www.imedea.uib.es/physdep

Local Convergence and Global Diversity: From Interpersonal to Social Influence

Axelrod (1997) showed how local convergence in cultural influence can preserve cultural diversity. We argue that central implications of Axelrod's model may change profoundly, if his model is integrated with the assumption of social influence as assumed by an earlier generation of modelers. Axelrod and all follow up studies employed instead the assumption that influence is interpersonal (dyadic). We show how the combination of social influence with homophily allows solving two important problems. Our integration of social influence yields monoculture in small societies and diversity increasing in population size, consistently with empirical evidence but contrary to earlier models. The second problem was identified by Klemm et al.(2003a,b), an extremely narrow window of noise levels in which diversity with local convergence can be obtained at all. Our model with social influence generates stable diversity with local convergence across a much broader interval of noise levels than models based on interpersonal influence.Comment: 20 pages, 3 figures, Paper presented at American Sociological Association 103rd Annual Meeting, August 1-4, 2008, Boston, MA. Session on Mathematical Sociolog