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We generalize a binary majority-vote model on adaptive networks to itsplurality-vote counterpart and analyze the time scale to consensus when votersare given more than two options. When opinions are uniformly distributed in thepopulation of voters in the initial state, we find that the time scale toconsensus is shorter than the binary vote model from both numerical simulationsand mathematical analysis using the master equation for the three-stateplurality-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 effortneeded to push the fragmented three-opinion population in the thermodynamiclimit to the consensus state, measured in minimal intervention cost, is lessthan that needed to push a polarized two-opinion population to the consensusstate, when the degree ($p$) of homophily is less than 0.8. For finite system,the fragmented three-opinion population will spontaneously reach the consensusstate, with faster time to consensus, compared to polarized two-opinionpopulation, for a broad range of $p$.

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