This article establishes versions of Moulin's (Public Choice 35:437-455, 1980) 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...

In general, the optimal provision of a good requires the simultaneous choice of (a)the optimal scale of output given the proportions in which consumers are allocated this total, and (b)the optimal consumption shares given the total available. With public goods the shares are not variable. The...