Beyond networks: Opinion formation in triplet-based populations

TL;DR

This paper investigates opinion formation in populations where interactions occur within randomly formed triplets, revealing that consensus is reached faster compared to traditional pairwise network interactions, due to structural differences.

Contribution

It introduces a triplet-based interaction model for opinion dynamics and compares its consensus time with that of standard network models, highlighting the impact of interaction structure.

Findings

Full consensus is achieved faster in triplet-based populations.

Discrepancies in consensus times are linked to differences in interaction distribution shapes.

Triplet interactions reduce the time to reach agreement compared to network-based interactions.

Abstract

We study a process of opinion formation in a population of agents whose interaction pattern is defined on the basis of randomly distributed groups of three agents, or triplets -in contrast to networks, which are defined on the basis of agent pairs. Results for the time needed to reach full consensus are compared between a triplet-based structure with a given number of triplets and a random network with the same number of triangles. The full-consensus time in the triplet structure is systematically lower than in the network. This discrepancy can be ascribed to differences in the shape of the probability distribution for the number of triplets and triangles per agent in each interaction pattern.