Weymark, John A.2020-09-142020-09-142011http://hdl.handle.net/1803/15899This article establishes versions of Moulin's [On strategy-proofness and single peakedness, Public Choice 35 (1980), 31-38] characterizations of various classes of strategy-proof social choice functions when the domain consists of all profiles of single-peaked preferences on an arbitrary subset of the real line. Two results are established that show that the median of 2n+1 numbers can be expressed using a combination of minimization and maximization operations applied to subsets of these numbers when either these subsets or the numbers themselves are restricted in a particular way. These results are used to show how Moulin's characterizations of generalized median social choice functions can be obtained as corollaries of his characterization of min-max social choice functions.en-USgeneralized median social choice functionsMoulin min-max rulessingle-peaked preferencesstrategy-proofnessJEL Classification Number: D71JEL Classification Number: D82Working Paper