Vote Elicitation with Probabilistic Preference Models: Empirical Estimation and Cost Tradeoffs

Abstract. 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 a winning or a high quality candidate (as measured by max regret) can be found with high probability. Our main contribution is a general empirical methodology, which uses preference profile samples to determine the ideal ranking threshold for many common voting rules. We develop probably approximately correct (PAC) sample complexity results for one-round protocols with any voting rule and demonstrate the efficacy of our approach empirically on one-round protocols with Borda scoring.