Dynamics of discrete opinions without compromise

TL;DR

This paper introduces a new agent-based model for discrete opinion dynamics without compromise, analyzing how opinions evolve and stabilize based on bounded confidence and interaction rules.

Contribution

It presents a novel discrete opinion model with analytical results, including bounds on final opinions and absorption times, and provides software for simulation.

Findings

Homogeneous system reaches absorbing states with multiple opinions

Final number of opinions is bounded and depends on initial conditions

Absorption times follow a generalized extreme value distribution

Abstract

A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly selected, converts to the opinion of the other. The model can be used to simulate cases where no compromise is possible, such as choices of substitute goods, or other exclusive choices. The homogeneous case with maximum tolerance is equivalent to the Gambler's Ruin problem. A homogeneous system always ends up in an absorbing state, which can have one or more surviving opinions. An upper bound for the final number of opinions is given. The distribution of absorption times fits the generalized extreme value distribution. The diffusion coefficient of an opinion increases linearly with the number of opinions within the tolerance parameter. A general master equation and specific Markov matrices are given. The software code developed for this study is provided as a supplement.