Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensus

TL;DR

This paper explores multidimensional continuous opinion dynamics in resource allocation problems, revealing that increasing opinion dimensions enhances the likelihood of consensus despite more clusters forming.

Contribution

It extends existing opinion dynamics models to higher dimensions and analyzes how opinion clustering and consensus are affected by the number of dimensions and confidence bounds.

Findings

Higher dimensions increase chances for majority consensus.

More opinion clusters form as dimensions increase.

Meta-stable states are observed in the Hegselmann-Krause model.

Abstract

We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount of ressource to n projects. We use the opinion dynamics models of Deffuant-Weisbuch and Hegselmann-Krause, which both extend naturally to more dimensional opinions. They both rely on bounded confidence of the agents and differ in their communication regime. We show detailed simulation results regarding $n=2,...,8$ and the bound of confidence $\eps$. Number, location and size of opinion clusters in the stabilized opinion profiles are of interest. Known differences of both models repeat under higher opinion dimensions: Higher number of clusters and more minor clusters in the Deffuant-Weisbuch model, meta-stable states in the Hegselmann-Krause model. But surprisingly, higher dimensions lead to better chances for a vast majority consensus even for lower bounds of confidence. On the other hand, the number of minority clusters rises with n, too.