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arXiv · 2503.16721

Fine structure of phase diagram for social impact theory

Krzysztof Malarz·Maciej Wołoszyn
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Abstract

In this paper, the social impact theory introduced by Latan\'e is reconsidered. A fully differentiated society is considered; that is, initially every actor has their own opinion. The equivalent of Muller's ratchet guards that -- even for the non-deterministic case (with a positive social temperature) -- any opinion once removed from the opinion space does not appear again. With computer simulation, we construct the phase diagram for Latan\'e model based on the number of surviving opinions after various evolution times. The phase diagram is constructed on the two-dimensional plane of model control parameters responsible for the effective range of interaction among actors and the social temperature. Introducing the Muller's ratchet-like mechanism gives a non-zero chance for any opinion to be removed from the system. We believe that in such a case, for any positive temperature, ultimately a consensus is reached. However, even for a moderate system size, the time to reach consensus is very long. In contrast, for the deterministic case (without social temperature), the system may be frozen with clusters of actors having several different opinions, or even reach the cycle limit (with blinking structures).

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Krzysztof Malarz, Maciej Wołoszyn. 2025-03-20. Fine structure of phase diagram for social impact theory. https://doi.org/10.1063/5.0272091

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