Analytical results for the Sznajd model of opinion formation
F. Slanina, H. Lavicka
TL;DR
This paper provides an analytical study of the Sznajd model on complete graphs, proving phase transition existence in the original model and analyzing opinion dynamics and voting distributions.
Contribution
It offers the first analytical proof of phase transition in the Sznajd model and explores opinion formation and vote distribution behaviors.
Findings
Proves phase transition in the original Sznajd model.
Finds smooth behavior without transition in the Ochrombel modification.
Derives the $1/n$ vote distribution pattern observed in Brazilian elections.
Abstract
The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed dependence in the distribution of votes in Brazilian elections is provided.
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