Dynamics of Majority Rule with Differential Latencies

TL;DR

This paper studies how differential latencies in voters affect majority-rule opinion dynamics, revealing a bias towards faster-latency opinions and providing analytical results on consensus probability and timing.

Contribution

It introduces a model incorporating opinion-dependent latencies into majority-rule dynamics and derives analytical expressions for consensus probabilities and times.

Findings

Bias towards opinions with shorter latency.

Derived formulas for exit probability and consensus time.

Asymptotic continuum model characterizing consensus timing.

Abstract

We investigate the dynamics of the majority-rule opinion formation model when voters experience differential latencies. With this extension, voters that just adopted an opinion go into a latent state during which they are excluded from the opinion formation process. The duration of the latent state depends on the opinion adopted by the voter. The net result is a bias towards consensus on the opinion that is associated with the shorter latency. We determine the exit probability and time to consensus for systems of $N$ voters. Additionally, we derive an asymptotic characterisation of the time to consensus by means of a continuum model.