Reaching a joint decision with minimal elicitation of voter preferences

• Preference elicitation with minimal cost of communication in range voting.
• Determining a necessary winner in incomplete setting by querying voters on items in range voting.
• Heuristics for finding a winner using probability distribution of voter-item preferences.

Sometimes voters are required to reach a joint decision and find an item that best suits the group’s preferences. Voters may wish to state preferences only when necessary, particularly in cases where there are many available options, therefore it is unpractical to assume that all voter preferences are known at all times. In order to elicit voter preferences at a minimal cost, a preference elicitation process is required. We introduce a general approach for reaching a joint decision with minimal elicitation of voter preferences. The approach is probabilistic and uses voting rules to find a necessary winning item which is presented to the group as their best option. We propose computing a voter-item probability distribution and developing methods based on this distribution that can then determine which voter-item pair to query. Computing the optimal minimal set of voter-item queries is computationally intractable; therefore we propose novel heuristic algorithms, named DIG and ES, which proceed iteratively until the identification of a winning item. The probabilistic voting distribution is updated as more information is revealed. Experiments on simulated data examine the benefits of each of the algorithms under different settings. Experiments with the real-world Netflix data show that the proposed algorithms reduce the required number of ratings for identifying the winning item by more than 50%.