Consensus Formation on Simplicial Complex of Opinions

TL;DR

This paper models opinion formation as a simplicial complex on a scale-free network, incorporating novel interaction mechanisms and analyzing consensus through topological features and quantum analogies.

Contribution

It introduces a new geometric and topological framework for opinion dynamics using simplicial complexes and extends social interaction models with additional local mechanisms.

Findings

Consensus formation depends on topological features of opinion complexes

The model reveals new insights into opinion overlap and social influence

Quantum analogies provide a novel perspective on opinion states

Abstract

Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically located on the nodes of the scale-free network. Social interactions include all concepts of social dynamics present in the mainstream models augmented by four additional interaction mechanisms which depend on the local properties of opinions and their overlapping properties. The results pertaining to the formation of consensus are of particular interest. An analogy with quantum mechanical pure states is established through the application of the high dimensional combinatorial Laplacian.