### Abstract

The paper examines the problem of explicit description of a social welfare order over infinite utility streams, which respects anonymity and weak Pareto axioms. It provides a complete characterization of the domains of one period utilities, for which it is possible to explicitly describe a weak Paretian social welfare order satisfying the anonymity axiom. For domains containing any set of order type similar to the set of positive and negative integers, every equitable social welfare order satisfying the weak Pareto axiom is non-constructive. The paper resolves a conjecture by Fleurbaey and Michel (2003) that there exists no explicit (that is, avoiding the axiom of choice or similar contrivances) description of an ordering which satisfies weak Pareto and indifference to finite permutations. It also provides an interesting connection between the existence of social welfare function and the constructive nature of social welfare order by showing that the domain restrictions for the two are identical.

Original language | English |
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Pages (from-to) | 434-439 |

Number of pages | 6 |

Journal | Journal of Mathematical Economics |

Volume | 47 |

Issue number | 4-5 |

DOIs | |

State | Published - 1 Aug 2011 |

### Fingerprint

### Keywords

- Anonymity
- Non-Ramsey set
- Order type
- Social welfare order
- Weak Pareto

### Cite this

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*Journal of Mathematical Economics*, vol. 47, no. 4-5, pp. 434-439. https://doi.org/10.1016/j.jmateco.2011.05.003

**Fleurbaey-Michel conjecture on equitable weak Paretian social welfare order.** / Dubey, Ram.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fleurbaey-Michel conjecture on equitable weak Paretian social welfare order

AU - Dubey, Ram

PY - 2011/8/1

Y1 - 2011/8/1

N2 - The paper examines the problem of explicit description of a social welfare order over infinite utility streams, which respects anonymity and weak Pareto axioms. It provides a complete characterization of the domains of one period utilities, for which it is possible to explicitly describe a weak Paretian social welfare order satisfying the anonymity axiom. For domains containing any set of order type similar to the set of positive and negative integers, every equitable social welfare order satisfying the weak Pareto axiom is non-constructive. The paper resolves a conjecture by Fleurbaey and Michel (2003) that there exists no explicit (that is, avoiding the axiom of choice or similar contrivances) description of an ordering which satisfies weak Pareto and indifference to finite permutations. It also provides an interesting connection between the existence of social welfare function and the constructive nature of social welfare order by showing that the domain restrictions for the two are identical.

AB - The paper examines the problem of explicit description of a social welfare order over infinite utility streams, which respects anonymity and weak Pareto axioms. It provides a complete characterization of the domains of one period utilities, for which it is possible to explicitly describe a weak Paretian social welfare order satisfying the anonymity axiom. For domains containing any set of order type similar to the set of positive and negative integers, every equitable social welfare order satisfying the weak Pareto axiom is non-constructive. The paper resolves a conjecture by Fleurbaey and Michel (2003) that there exists no explicit (that is, avoiding the axiom of choice or similar contrivances) description of an ordering which satisfies weak Pareto and indifference to finite permutations. It also provides an interesting connection between the existence of social welfare function and the constructive nature of social welfare order by showing that the domain restrictions for the two are identical.

KW - Anonymity

KW - Non-Ramsey set

KW - Order type

KW - Social welfare order

KW - Weak Pareto

UR - http://www.scopus.com/inward/record.url?scp=83055188283&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2011.05.003

DO - 10.1016/j.jmateco.2011.05.003

M3 - Article

AN - SCOPUS:83055188283

VL - 47

SP - 434

EP - 439

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 4-5

ER -