Voter model with non-Poissonian interevent intervals

TL;DR

This paper studies how non-Poissonian, long-tailed interevent intervals in human interactions affect opinion formation dynamics, revealing that power-law distributions slow consensus on rings but have less impact on complete graphs.

Contribution

It introduces a variant of the voter model incorporating non-Poissonian interevent intervals and compares how different network structures influence consensus times.

Findings

Power-law interevent intervals slow down consensus on rings.

On complete graphs, consensus time is similar for power-law and exponential distributions.

Higher degree networks reduce the slowing down effect of power-law intervals.

Abstract

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.