### 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 |

### Fingerprint

### 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

**Ordering Pareto-optima through majority voting.** / Crès, Hervé; Tvede, Mich.

Research output: Contribution to journal › Article

*Mathematical Social Sciences*, vol. 41, no. 3, pp. 295-325. https://doi.org/10.1016/S0165-4896(00)00066-4

}

TY - JOUR

T1 - Ordering Pareto-optima through majority voting

AU - Crès, Hervé

AU - Tvede, Mich

PY - 2001/5/1

Y1 - 2001/5/1

N2 - 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.

AB - 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.

KW - D72

KW - Infra-majority voting

KW - Pareto-optimal allocations

UR - http://www.scopus.com/inward/record.url?scp=17044461471&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17044461471&partnerID=8YFLogxK

U2 - 10.1016/S0165-4896(00)00066-4

DO - 10.1016/S0165-4896(00)00066-4

M3 - Article

VL - 41

SP - 295

EP - 325

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 3

ER -