Bifurcations and Patterns in Compromise Processes
E. Ben-Naim, P.L. Krapivsky, F. Vazquez, and S. Redner
We study opinion dynamics models where agents evolve via repeated pairwise
interactions. In the compromise model, agents with sufficiently close
real-valued opinions average their opinions. A steady state is reached
with a finite number of isolated, noninteracting opinion clusters
(``parties''). As the initial opinion range increases, the number of such
parties undergoes a periodic bifurcation sequence, with alternating major
and minor parties. In the constrained voter model, there are leftists,
centrists, and rightists. A centrist and an extremist can both become
centrists or extremists in an interaction, while leftists and rightists do
not affect each other. The final state is either consensus or a frozen
population of leftists and rightists. The evolution in one dimension is
mapped onto a constrained spin-1 Ising chain with zero-temperature Glauber
kinetics. The approach to the final state exhibits a non-universal
long-time tail.
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