  Voting systems typically treat all voters equally. We argue that perhaps they
should not: Voters who have supported good choices in the past should be given
higher weight than voters who have supported bad ones. To develop a formal
framework for desirable weighting schemes, we draw on no-regret learning.
Specifically, given a voting rule, we wish to design a weighting scheme such
that applying the voting rule, with voters weighted by the scheme, leads to
choices that are almost as good as those endorsed by the best voter in
hindsight. We derive possibility and impossibility results for the existence of
such weighting schemes, depending on whether the voting rule and the weighting
scheme are deterministic or randomized, as well as on the social choice axioms
satisfied by the voting rule.
