System size stochastic resonance in a model for opinion formation

TL;DR

This paper investigates a model for opinion formation incorporating imitation, fashion influence, and randomness, revealing a phenomenon called system size stochastic resonance where an optimal population size enhances opinion alignment with fashion trends.

Contribution

It introduces the concept of system size stochastic resonance in opinion dynamics, showing how population size optimally influences opinion alignment with fashion.

Findings

In the absence of fashion, the model exhibits bistable behavior with Kramer's law distribution of switching times.

Identification of an optimal population size for maximum opinion alignment with fashion.

Demonstration of system size stochastic resonance in the opinion formation model.

Abstract

We study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual: imitation, influence of fashion and randomness. We show that in the absence of fashion, the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following Kramer's law. We also demonstrate the existence of system size stochastic resonance, by which there is an optimal value for the number of individuals N for which the average opinion follows better the fashion.