### Abstract

We study social ordering functions in exchange economies. We show that if a social ordering function satisfies certain Pareto, individual rationality, and local independence conditions, then (i) the set of top allocations of the chosen social ordering is contained in the set of Walrasian allocations and is typically non-empty, and (ii) all individually rational but non-Walrasian allocations are typically ranked indifferently. Thus, such a social ordering function is quite similar to the Walrasian correspondence, which can be regarded as the social ordering function whose associated indifference classes are the set of Walrasian allocations and the set of other allocations.

Original language | English |
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Pages (from-to) | 16-22 |

Number of pages | 7 |

Journal | Journal of Mathematical Economics |

Volume | 45 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2009 Jan 20 |

Externally published | Yes |

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### Keywords

- Arrow's impossibility theorem
- Individual rationality
- Local independence
- Price mechanism
- Social ordering function
- Walrasian social choice

### ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics