Universality of opinions disappearing in sociophysical models of opinion dynamics: From initial multitude of opinions to ultimate consensus

TL;DR

This study uses computer simulations of well-known sociophysical models to demonstrate that, despite initial fragmentation, opinions tend to converge to consensus over time, with the dynamics varying across models.

Contribution

It provides a comparative analysis of opinion dynamics in voter, Sznajd, and Latané models, highlighting the conditions and timescales for consensus formation.

Findings

Opinions almost always converge to a single consensus.

Voter and Latané models show power-law decrease in opinions over time.

Sznajd model exhibits a complex three-stage opinion evolution.

Abstract

Possibility of reaching a consensus in social systems with strong initial fragmentation is one of the most interesting issues in sociopysics. It is also intriguing what the dynamics of such processes is. To address those problems, we performed computer simulations using well-established models of social opinion formation, namely the voter, Sznajd, and Latan\'e models. We investigated opinion dynamics in cases where the initial number of opinions is very large, equal to the number of actors (the voter and Latan\'e models) or when every second actor has their own opinion (Sznajd model), with some variations on the update schemes, lattice topologies, effective ranges of interaction, and information noise levels. For all considered models, the number of opinions assumed by the actors is finally almost always reduced to only one. However, while the voter and Latan\'e models exhibit a power-law time decrease in the number of opinions, the Sznajd model follows a complex three-stage behavior. We also demonstrated that the mean/median time of reaching the consensus scales with system size according to a power law for voter and Sznajd models, while for the Latan\'e model this increase is even faster. Our results show that in the studied models the consensus is possible, provided that a long enough and model-dependent time to reach this state is available.