### Abstract

A commodity is shared between some individuals: there is an initial allocation; some selection procedures are used to choose an alternative allocation and individuals decide between keeping the initial allocation or shifting to the alternative allocation. The selection procedures are supposed to involve an element of randomness in order to reflect uncertainty about economic, social and political processes. It is shown that for every allocation, λ, there exists a number, ζ(λ)∈[0, 1], such that, if the number of individuals tends to infinity, then the probability that a proportion of the population smaller (resp. larger) than ζ(λ) prefers an allocation chosen by the selection procedure converges to 1 (resp. 0). The index ζ(λ) yields a complete order in the set of Pareto optimal allocations. Illustrations and interpretations of the selection procedures are provided.

Original language | English (US) |
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Pages (from-to) | 295-325 |

Number of pages | 31 |

Journal | Mathematical social sciences |

Volume | 41 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2001 |

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### Keywords

- D72
- Infra-majority voting
- Pareto-optimal allocations

### ASJC Scopus subject areas

- Sociology and Political Science
- Social Sciences(all)
- Psychology(all)
- Statistics, Probability and Uncertainty

### Cite this

*Mathematical social sciences*,

*41*(3), 295-325. https://doi.org/10.1016/S0165-4896(00)00066-4