Max-Plus Opinion Dynamics With Temporal Confidence

TL;DR

This paper introduces a novel max-plus algebra-based framework for modeling opinion dynamics that accounts for temporal hierarchies and asynchronous updates influenced by information recency.

Contribution

It presents an efficient method to incorporate temporal information delays into opinion models using lag-vectors within a max-plus algebra structure.

Findings

The model captures the influence of information recency on opinion formation.

It extends the Hegselmann-Krause model to include temporal dynamics.

The approach enables analysis of asynchronous opinion updates in social networks.

Abstract

Often in the setting of human-based interactions, the existence of a temporal hierarchy of information plays an important role in diffusion and opinion dynamics within communities. For example at the individual agent level, more recently acquired information may exert greater influence during decision-making processes. To facilitate further exploration of this effect, we introduce an efficient method for modelling temporally asynchronous opinion updates, where the timing of updates depends on the timing of incoming opinion states received from neighbours. The framework enables the introduction of information arrival-time lag by means of lag-vectors. These are used to weight the relevance of information received by agents, based on the delay between its receipt and the subsequent opinion update. The temporal dynamics (i.e. the times at which information is transmitted) are governed by an underlying algebraic structure called max-plus algebra. We investigate the resulting continuous opinion dynamics under the max-plus regime using a modified Hegselmann-Krause model, replacing the conventional confidence-interval based on the distance between opinions with one based instead on the recency of information received by agents.