Iterative Deliberation via Metric Aggregation

TL;DR

This paper models an iterative decision-making process for agent communities, showing conditions under which repeated deliberation converges to a consensus in various metric spaces.

Contribution

It introduces a general model of iterative deliberation with convergence guarantees for different metric spaces and voting rules.

Findings

Convergence conditions depend on metric space and voting rule.

Iterative process reliably reaches a stable decision under specified conditions.

Applicable to diverse decision-making scenarios in multi-agent systems.

Abstract

We investigate an iterative deliberation process for an agent community wishing to make a joint decision. We develop a general model consisting of a community of n agents, each with their initial ideal point in some metric space (X, d), such that in each iteration of the iterative deliberation process, all agents move slightly closer to the current winner, according to some voting rule R. For several natural metric spaces and suitable voting rules for them, we identify conditions under which such an iterative deliberation process is guaranteed to converge.