Selection and Influence in Cultural Dynamics

TL;DR

This paper models the interplay of influence and selection in cultural dynamics, providing a formal analysis of societal outcomes and equilibrium states in a stylized population model.

Contribution

It offers a comprehensive characterization of stable equilibria and convergence in a model combining influence and selection based on type similarity.

Findings

Complete characterization of stable equilibrium outcomes

Proof of convergence from all initial states

Analysis of influence and selection effects on societal diversity

Abstract

One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become similar to others they interact with) and selection (the tendency to be affected most by the behavior of others who are already similar). Influence tends to promote homogeneity within a society, while selection frequently causes fragmentation. When both forces act simultaneously, it becomes an interesting question to analyze which societal outcomes should be expected. To study this issue more formally, we analyze a natural stylized model built upon active lines of work in political opinion formation, cultural diversity, and language evolution. We assume that the population is partitioned into "types" according to some traits (such as language spoken or political affiliation). While all types of people interact with one another, only people with sufficiently similar types can possibly influence one another. The "similarity" is captured by a graph on types in which individuals of the same or adjacent types can influence one another. We achieve an essentially complete characterization of (stable) equilibrium outcomes and prove convergence from all starting states. We also consider generalizations of this model.