Timing interactions in social simulations: The voter model

TL;DR

This paper introduces new update rules for the voter model in social simulations that produce realistic, heavy-tailed interevent time distributions, highlighting the importance of update mechanisms in consensus formation.

Contribution

It proposes two novel update rules based on time since last event, capturing heterogeneous activity patterns and affecting consensus dynamics in the voter model.

Findings

Both update rules produce power-law interevent time distributions.

Endogenous update more robustly generates heavy-tailed activity patterns.

Endogenous update leads to consensus through coarsening, unlike standard rules.

Abstract

The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.