Let's Agree to Agree: Targeting Consensus for Incomplete Preferences through Majority Dynamics

TL;DR

This paper analyzes how majority dynamics influence consensus formation in collective decisions with incomplete preferences, revealing potential drawbacks and control strategies for decision order.

Contribution

It introduces a framework for understanding the impact of majority-based decision processes on consensus, including the effects of issue order control.

Findings

Myopic majority adherence can harm consensus in worst-case scenarios.

Simulations show the damage to consensus is often mild.

Issue order control can influence the existence and identity of consensus.

Abstract

We study settings in which agents with incomplete preferences need to make a collective decision. We focus on a process of majority dynamics where issues are addressed one at a time and undecided agents follow the opinion of the majority. We assess the effects of this process on various consensus notions -- such as the Condorcet winner -- and show that in the worst case, myopic adherence to the majority damages existing consensus; yet, simulation experiments indicate that the damage is often mild. We also examine scenarios where the chair of the decision process can control the existence (or the identity) of consensus, by determining the order in which the issues are discussed.