Social Structure and Opinion Formation

TL;DR

This paper introduces a dynamical model of opinion formation that incorporates social network structure, predicting stable coexistence of opinions and highlighting the roles of network topology and influential individuals.

Contribution

It develops a novel theory linking social network topology to opinion dynamics, including a martingale property and opinion coexistence, supported by computer simulations.

Findings

Opinions tend to coexist rather than reach consensus.

Highly connected individuals significantly influence opinion dynamics.

The model's predictions align with observed locality effects in social networks.

Abstract

We present a dynamical theory of opinion formation that takes explicitly into account the structure of the social network in which in- dividuals are embedded. The theory predicts the evolution of a set of opinions through the social network and establishes the existence of a martingale property, i.e. that the expected weighted fraction of the population that holds a given opinion is constant in time. Most importantly, this weighted fraction is not either zero or one, but corresponds to a non-trivial distribution of opinions in the long time limit. This co-existence of opinions within a social network is in agreement with the often observed locality effect, in which an opinion or a fad is localized to given groups without infecting the whole society. We verified these predictions, as well as those concerning the fragility of opinions and the importance of highly connected individuals in opinion formation, by performing computer experiments on a number of social networks.