Majority rule in the absence of a majority

Abstract

Which is the best, impartially most plausible consensus view to serve as the basis of democratic group decision when voters disagree? Assuming that the judgment aggregation problem can be framed as a matter of judging a set of binary propositions (“issues”), we develop a multi-issue majoritarian approach based on the criterion of supermajority efficiency (SME). SME reflects the idea that smaller supermajorities must yield to larger supermajorities so as to obtain better supported, more plausible group judgments. As it is based on a partial ordering, SME delivers unique outcomes only in special cases. In general, one needs to make cardinal, not just ordinal, tradeoffs between different supermajorities. Hence we axiomatically characterize the class of additive majority rules, whose (generically unique) outcome can be interpreted as the “on balance most plausible” consensus judgment.