Does Having More Options Mean Harder to Reach Consensus?

TL;DR

This paper extends a binary voting model to a plurality-vote system on adaptive networks, revealing that more initial options can speed up consensus, with diverse scaling behaviors depending on initial opinion distribution.

Contribution

It introduces a generalized plurality-vote model on adaptive networks and analyzes how initial opinion diversity affects consensus time.

Findings

More options in initial opinions can accelerate consensus.

Consensus time scales differently depending on initial opinion distribution.

Finite-size systems can reach consensus faster than in binary models.

Abstract

We generalize a binary majority-vote model on adaptive networks to a plurality-vote counterpart. When opinions are uniformly distributed in the population of voters in the initial state, it is found that having more available opinions in the initial state actually accelerate the time to consensus. In particular, we investigate the three-state plurality-vote model. While time to consensus in two state model scales exponentially with population size $N$, for finite-size system, there is a non-zero probability that either the population reaches the consensus state in a time that is very short and independent of $N$ (in the heterophily regime), or in a time that scales exponentially with $N$ but is still much faster than two-state model.