Candidate Voter Dynamics

TL;DR

This paper models the dynamic behavior of candidates in elections with changing voter preferences using a continuous Hegselmann-Krause framework, revealing possible abrupt shifts and complex multi-candidate interactions.

Contribution

It introduces a novel dynamic model for candidate-voter interactions using a space-time-continuous approach and extends analysis to multiple candidates, highlighting complex behaviors.

Findings

Candidates can exhibit discontinuous jumps in position.

Candidate clustering is not guaranteed; they may remain separate.

Model demonstrates complex dynamics depending on parameters.

Abstract

We model dynamically changing candidate positions in the face of a dynamic electorate. To formulate our equations, we use a space-time-continuous Hegselmann-Krause equation, which we solve using a particle method. We use the combined candidate-voter model to demonstrate the possibility of discontinuous jumps in candidate behavior as parameters of the model are varied. We also extend the analysis to a three candidate scenario. We observe that depending on the parameters, candidates do not always come or stay together at their dynamically evolving position.