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This paper studies the design of voting mechanisms. There are
multiple alternatives, and the voters have generalized single-peaked
preferences derived from median spaces as introduced in Nehring
and Puppe (2007b). This class of preferences covers a wide range
of economically relevant domains, and it is much larger than the
well-known single-peaked preferences on a line. I characterize the
welfare-maximizing voting rules among all social choice functions
satisfying strategy-proofness, anonymity, and surjectivity. The optimal
mechanisms are composed of binary votes on subsets of alternatives
involving flexible majority requirements.
