Summary.
We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality \(k^*\) to k where \(1 < k^* < k\).
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Received: November 8, 1999; revised version: September 18, 2001
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Campbell, D., Kelly, J. A leximin characterization of strategy-proof and non-resolute social choice procedures. Econ Theory 20, 809–829 (2002). https://doi.org/10.1007/s00199-001-0239-6
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DOI: https://doi.org/10.1007/s00199-001-0239-6