Bifurcations and Patterns in Compromise Processes

TL;DR

This paper analyzes an opinion dynamics model where agents form opinion clusters through pairwise compromises, revealing bifurcation patterns and the emergence of multiple parties as initial opinion range varies.

Contribution

It introduces a model showing how opinion clusters form and bifurcate, highlighting the organized pattern of emergent parties in compromise processes.

Findings

Finite number of opinion clusters at steady state

Bifurcation sequence as initial opinion range increases

Emergence of major and minor parties in alternating patterns

Abstract

We study an opinion dynamics model in which agents reach compromise via pairwise interactions. When the opinions of two agents are sufficiently close, they both acquire the average of their initial opinions; otherwise, they do not interact. Generically, the system reaches a steady state with a finite number of isolated, noninteracting opinion clusters (``parties''). As the initial opinion range increases, the number of such parties undergoes a periodic sequence of bifurcations. Both major and minor parties emerge, and these are organized in alternating pattern. This behavior is illuminated by considering discrete opinion states.