Sommaire:

If opinions spread by interactions between reasonable individuals, why is consensus hard to achieve? I present some idealized social dynamics models to understand this dichotomy between consensus and diversity. Consensus always arises in the voter model and its natural extensions. For the voter model, I'll discuss some basic features of the time to reach consensus. Diversity can arise when an individual may not be influenced by some of its neighbors. One such example is a 3-state voter model of leftists, centrists, and rightists, in which a centrist and an extremist influence each other but extremists of the opposite persuasion do not. Depending on the initial condition, the population may or may not reach consensus. In the bounded confidence model, I'll discuss how a population becomes increasingly fragmented as the political range of interaction of an individual decreases. A related phenomenon occurs in the voter model when individuals are also influenced by competing external news sources.

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