Simplification and analysis of a model of social interaction in voting

TL;DR

This paper simplifies a social voting interaction model to enable mathematical analysis, revealing how social influence, heterogeneity, and noise interact, and identifying a bistability regime to better understand the original model's behavior.

Contribution

It introduces a simplified, analytically tractable version of a social voting model, providing new insights into its dynamics and stability regimes.

Findings

Identification of a bistability regime

Clarification of the roles of social influence, heterogeneity, and noise

Enhanced understanding of the original model's behavior

Abstract

A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the interplay of the different elements present in the system --- social influence, heterogeneity and noise --- and leads to a better understanding of its properties. The origin of a regime of bistability is identified. The insight gained in this way gives further intuition into the behaviour of the original model.