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...

Voting procedures are known to be plagued with a variety of difficulties such as strategic voting, or where a voter is rewarded with a better election outcome by not voting, or where a winning candidate can lose by receiving more support. Once we know that these problems can occur, the next...

Economic models as well as aggregation and decision problems with "holes" in the domain can be difficult to analyze because, unexpectedly, they are related to Arrow's Impossibility Theorem: embedded within the model may be "topological dictators." But, just as it is possible to remove the...