A dynamical model for competing opinions

TL;DR

This paper introduces a spatial opinion model where agents on a lattice interact, leading to self-organized criticality with power-law cluster size distributions, and explores how interaction range influences consensus and opinion diversity.

Contribution

It presents a novel dynamical model of competing opinions incorporating spatial structure and interaction range, revealing critical behavior and conditions for consensus.

Findings

Power-law distribution of opinion cluster sizes for sufficiently long-range interactions.

Short-range interactions produce exponential cutoff and spatially clustered opinions.

Non-consensus dynamics occur with two opinions unless long-range interactions enable consensus.

Abstract

We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time it interacts with another agent who has a different opinion. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short, i.e. the system self-organizes into a critical state. Short range interactions lead to an exponential cut off in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, non-consensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those which are located far from them.