Generalized location problems with n agents are considered, who each report a point in m-dimensional Euclidean space. A solution assigns a compromise point to these n points, and the individual utilities for this compromise point are equal to the negatives of the Euclidean distances to the individual positions. For m = 2 and n odd, it is shown that a solution is Pareto optimal, anonymous, and strategy-proof if, and only if, it is obtained by taking the coordinatewise median with respect to a pair of orthogonal axeL Further, for all other situations with m_> 2, such a solution does not exist. A few results concerning other solution properties, as well as different utility functions, are discussed.
The Kemeny distance for preference orderings is used to determine individual rankings of social preferences. Based on this distance function, the strategy-proofness of social welfare functions is examined. Our main result is an impossibility theorem stating that no social welfare function can be strategyproof, if some additional properties are required.
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