### Abstract

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 to k where .

Original language | English (US) |
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Pages (from-to) | 809-829 |

Number of pages | 21 |

Journal | Economic Theory |

Volume | 20 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2002 |

### Keywords

- Leximin
- Non-resolute
- Strategy-proof

### ASJC Scopus subject areas

- Economics and Econometrics

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## Cite this

*Economic Theory*,

*20*(4), 809-829. https://doi.org/10.1007/s00199-001-0239-6