  We study single-candidate voting embedded in a metric space, where both
voters and candidates are points in the space, and the distances between voters
and candidates specify the voters' preferences over candidates. In the voting,
each voter is asked to submit her favorite candidate. Given the collection of
favorite candidates, a mechanism for eliminating the least popular candidate
finds a committee containing all candidates but the one to be eliminated. Each
committee is associated with a social value that is the sum of the costs
(utilities) it imposes (provides) to the voters. We design mechanisms for
finding a committee to optimize the social value. We measure the quality of a
mechanism by its distortion, defined as the worst-case ratio between the social
value of the committee found by the mechanism and the optimal one. We establish
new upper and lower bounds on the distortion of mechanisms in this
single-candidate voting, for both general metrics and well-motivated special
cases.
