Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy nonimposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by misrepresenting their preferences) are dictatorships. In...

Social decision schemes (SDSs) map the ordinal preferences of voters over multiple alternatives to a probability distribution over the alternatives. To study the axiomatic properties of SDSs, we lift preferences over alternatives to preferences over lotteries using the natural---but little...