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We develop new voting mechanisms for the case when voters and candidates arelocated in an arbitrary unknown metric space, and the goal is to choose acandidate minimizing social cost: the total distance from the voters to thiscandidate. Previous work has often assumed that only ordinal preferences of thevoters are known (instead of their true costs), and focused on minimizingdistortion: the quality of the chosen candidate as compared with the bestpossible candidate. In this paper, we instead assume that a (very small) amountof information is known about the voter preference strengths, not just abouttheir ordinal preferences. We provide mechanisms with much better distortionwhen this extra information is known as compared to mechanisms which use onlyordinal information. We quantify tradeoffs between the amount of informationknown about preference strengths and the achievable distortion. We furtherprovide advice about which type of information about preference strengths seemsto be the most useful. Finally, we conclude by quantifying the ideal candidatedistortion, which compares the quality of the chosen outcome with the bestpossible candidate that could ever exist, instead of only the best candidatethat is actually in the running.

Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice