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The effect of zealotry in the naming game model of opinion dynamics

An individual in the process of forming or updating an opinion on any given subject is heavily influenced by the opinions expressed by others in his/her social network. However, not all individuals are flexible or open-minded; some are zealots, proselytizing an opinion in hopes of convincing others, while themselves completely immune to influence. Zealotry is a common phenomenon surrounding opinions involving significant personal investment, such as political or religious affiliation. In this work, we study the effect of zealotry in the context of binary opinion dynamics (denoted as opinions A and B, such as for/against increasing taxes). We derive several key results as a function of the zealot fractions backing each of the two opinions, including the number and nature of steady state solutions. We present analytically-grounded answers to questions such as: Does the opinion with larger zealot backing always win a majority of the non-zealot population, or are there conditions under which the opinion with smaller zealot backing can win? We extend our analysis with simulations to finite population and networks with finite connectivity.