A variety of preference aggregation schemes and voting rules have been developed in social choice to support group decision making. However, the requirement that participants provide full preference information in the form of a complete ranking of alternatives is a severe impediment to their practical deployment. Only recently have incremental elicitation schemes been proposed that allow winners to be determined with partial preferences; however, while minimizing the amount of information provided, these tend to require repeated rounds of interaction from participants. We propose a probabilistic analysis of vote elicitation that combines the advantages of incremental elicitation schemes—namely, minimizing the amount of information revealed—with those of full information schemes—single (or few) rounds of elicitation. We exploit distributional models of preferences to derive the ideal ranking threshold k, or number of top candidates each voter should provide, to ensure that either ...