### Abstract

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation (Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an "almost" fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.

Original language | English |
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Pages (from-to) | 877-883 |

Number of pages | 7 |

Journal | Journal of Mathematical Economics |

Volume | 46 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2010 Sep 20 |

Externally published | Yes |

### Fingerprint

### Keywords

- D63
- D71
- Diamond's impossibility theorem
- Finite length anonymity
- Infinite dimension
- Intergenerational equity
- Social choice

### ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics

### Cite this

**A characterization and an impossibility of finite length anonymity for infinite generations.** / Sakai, Toyotaka.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A characterization and an impossibility of finite length anonymity for infinite generations

AU - Sakai, Toyotaka

PY - 2010/9/20

Y1 - 2010/9/20

N2 - In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation (Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an "almost" fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.

AB - In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation (Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an "almost" fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.

KW - D63

KW - D71

KW - Diamond's impossibility theorem

KW - Finite length anonymity

KW - Infinite dimension

KW - Intergenerational equity

KW - Social choice

UR - http://www.scopus.com/inward/record.url?scp=78649629491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649629491&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2010.07.003

DO - 10.1016/j.jmateco.2010.07.003

M3 - Article

AN - SCOPUS:78649629491

VL - 46

SP - 877

EP - 883

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 5

ER -