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The naming game has become an archetype for linguistic evolution andmathematical social behavioral analysis. In the model presented here, there are$N$ individuals and $K$ words. Our contribution is developing a robust methodthat handles the case when $K = O(N)$. The initial condition plays a crucialrole in the ordering of the system. We find that the system with high Shannonentropy has a higher consensus time and a lower critical fraction of zealotscompared to low-entropy states. We also show that the critical number ofcommitted agents decreases with the number of opinions and grows with thecommunity size for each word. These results complement earlier conclusions thatdiversity of opinion is essential for evolution; without it, the systemstagnates in the status quo [S. A. Marvel et al., Phys. Rev. Lett. 109, 118702(2012)]. In contrast, our results suggest that committed minorities can moreeasily conquer highly diverse systems, showing them to be inherently unstable.

Analysis of the high dimensional naming game with committed minorities