Bifurcations and Patterns in Compromise Processes

E. Ben-Naim, Los Alamos National Laboratory
P. L. Krapivsky, Boston University
S. Redner, Boston University

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.