Awareness of Voter Passion Greatly Improves the Distortion of Metric
  Social Choice
  We develop new voting mechanisms for the case when voters and candidates are
located in an arbitrary unknown metric space, and the goal is to choose a
candidate minimizing social cost: the total distance from the voters to this
candidate. Previous work has often assumed that only ordinal preferences of the
voters are known (instead of their true costs), and focused on minimizing
distortion: the quality of the chosen candidate as compared with the best
possible candidate. In this paper, we instead assume that a (very small) amount
of information is known about the voter preference strengths, not just about
their ordinal preferences. We provide mechanisms with much better distortion
when this extra information is known as compared to mechanisms which use only
ordinal information. We quantify tradeoffs between the amount of information
known about preference strengths and the achievable distortion. We further
provide advice about which type of information about preference strengths seems
to be the most useful. Finally, we conclude by quantifying the ideal candidate
distortion, which compares the quality of the chosen outcome with the best
possible candidate that could ever exist, instead of only the best candidate
that is actually in the running.
