Bhat, Deepak and Sidney Redner
We introduce the reputational voter model (RVM) to account for the possibility that there are differing and time-varying abilities of individuals to influence the opinion state of their neighbors. The ith individual can be in one of two voting states and is also endowed with a reputational rank ri that ranges from 1 (highest rank) to N (lowest), where N is the population size. In an interaction where the rank of voter i is greater than voter j, only the opinion of j changes. Additionally, the reputational rank of i increases, while the rank of j does not change. When the population contains equal numbers in the two voting states and the average rank of these two subpopulations are the same, the time to reach consensus in the mean-field limit scales as exp( N). The feature that causes this long consensus time is that the average rank of the minority population is typically higher than that of the majority. Thus whenever consensus is approached, this highly ranked minority tends to drive the population away from consensus.