Does Having More Options Mean Harder to Reach Consensus?

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.

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