Lack of consensus in social systems

TL;DR

This paper introduces an exactly solvable model for voter dynamics on evolving networks, revealing that large social systems often do not reach consensus due to metastable states.

Contribution

It presents a novel solvable model capturing opinion dynamics with evolving social connections, highlighting metastability and the rarity of consensus in large systems.

Findings

Consensus emerges in the long run for any initial state.

Metastable states can persist exponentially long, preventing consensus.

Lack of consensus is typical in large social systems.

Abstract

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.