  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.
