Analysis of Time Scale to Consensus in Voting Dynamics with more than Two Options

TL;DR

This paper extends binary voting models to multiple options, showing faster consensus formation and lower intervention costs in three-opinion populations compared to two-opinion ones, with implications for understanding opinion dynamics.

Contribution

It introduces a generalized plurality-vote model on adaptive networks and analyzes the time to consensus and intervention effort for multiple opinions.

Findings

Faster consensus in three-opinion models than binary models.

Lower intervention effort needed for three-opinion populations to reach consensus.

Spontaneous consensus occurs more rapidly in three-opinion populations for various homophily levels.

Abstract

We generalize a binary majority-vote model on adaptive networks to its plurality-vote counterpart and analyze the time scale to consensus when voters are given more than two options. When opinions are uniformly distributed in the population of voters in the initial state, we find that the time scale to consensus is shorter than the binary vote model from both numerical simulations and mathematical analysis using the master equation for the three-state plurality-vote model. When intervention such as opinion conversion is allowed, as in the case of sudden change of mind of voter for any reason, the effort needed to push the fragmented three-opinion population in the thermodynamic limit to the consensus state, measured in minimal intervention cost, is less than that needed to push a polarized two-opinion population to the consensus state, when the degree ($p$) of homophily is less than 0.8. For finite system, the fragmented three-opinion population will spontaneously reach the consensus state, with faster time to consensus, compared to polarized two-opinion population, for a broad range of $p$.