# Multi-choice opinion dynamics model based on Latane theory

## TL;DR

This paper extends the Nowak--Szamrej-Latané opinion formation model to multiple opinions, demonstrating that phase transition signatures persist and analyzing how the number of opinions affects critical social temperature through computer simulations.

## Contribution

The paper introduces a multi-opinion extension of the Latané social impact model and analyzes phase transition behavior with simulations, expanding understanding of opinion dynamics.

## Key findings

- Signatures of order/disorder phase transition are observed in the multi-opinion model.
- Critical social temperature decreases as the number of opinions increases.
- Model parameters influence the phase transition characteristics.

## Abstract

In this paper Nowak--Szamrej-Latan\'e model is reconsidered. This computerised model of opinion formation bases on Latan\'e theory of social impact. We modify this model to allow for multi (more than two) opinions. With computer simulations we show that in the modified model the signatures of order/disorder phase transition are still observed. The transition may be observed in the average fraction of actors sharing the $i$-th opinion, its variation and also average number of clusters of actors with the same opinion and the average size of the largest cluster of actors sharing the same opinion. Also an influence of model control parameters on simulation results is shortly reviewed. For a homogeneous society with identical actors' supportiveness and persuasiveness the critical social temperature $T_C$ decreases with an increase of available opinions $K$ from $T_C=6.1$ ($K=2$) via 4.7, 4.1 to $T_C=3.6$ for $K=3$, 4, 5, respectively.