  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.
