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

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.