Abstract
We consider elections where both voters and candidates can be associated with points in a metric
space and voters prefer candidates that are closer to
those that are farther away. It is often assumed that
the optimal candidate is the one that minimizes the
total distance to the voters. Yet, the voting rules often do not have access to the metric space M and
only see preference rankings induced by M. Consequently, they often are incapable of selecting the
optimal candidate. The distortion of a voting rule
measures the worst-case loss of the quality being
the result of having access only to preference rankings. We extend the idea of distortion to approvalbased preferences. First, we compute the distortion of Approval Voting. Second, we introduce
the concept of acceptability-based distortion—the
main idea behind is that the optimal candidate is
the one that is acceptable to most voters. We
determine acceptability-distortion for a number of
rules, including Plurality, Borda, k-Approval, Veto,
Copeland, Ranked Pairs, the Schulze’s method, and
STV