Consensus formation times in fully connected societies

TL;DR

This paper uses a statistical mechanics model with perceptrons to analyze how consensus forms in fully connected societies, revealing conditions under which agents align with or oppose social rules based on interaction strength and temperature.

Contribution

It introduces a perceptron-based model for opinion dynamics in social systems, exploring the effects of interaction strength and temperature on consensus formation.

Findings

Weak interactions lead to consensus with social rules.

Strong interactions can oppose the established social status quo.

Consensus timing depends on information volume and interaction parameters.

Abstract

We developed a statistical mechanics approach to the problem of opinion formation in interacting agents, constrained by a set of social rules, $B$. To provide the agents with an adaptive quality, we represented both the social agents and the social rule by perceptrons. For fully connected societies we find that if the agents' interaction is weak, all agents adapt to the social rule $B$, with which they form a consensus; but if the interaction is sufficiently strong a consensus is built against the established $status$ $quo$. This behavior is observed for all temperatures $T$ and for all values of the agents' interaction parameter $H_{0}$, except in the limit $T\to\infty$ or when the interaction reaches the critical value $H_{0}=1,$ where no consensus is formed. The agents follow a path where, after a time $\alpha_{c},$ they disregard their peers' opinions on socially neutral issues and reach a full consensus at time $\alpha_{d}>\alpha_{c}.$ The measure of time $\alpha$ is proportional to the volume of information provided to the agents.