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Metrizable preferences over preferences

Author

Listed:
  • Gilbert Laffond

    (Istanbul Bilgi University, Murat Sertel Center - Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University)

  • Jean Lainé

    (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - Cnam - Conservatoire National des Arts et Métiers [Cnam], Murat Sertel Center - Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University)

  • M. Remzi Sanver

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

A hyper-preference is a weak order over all linear orders defined over a finite set A of alternatives. An extension rule associates with each linear order p over A a hyper-preference. The well-known Kemeny extension rule ranks all linear orders over A according to their Kemeny distance to p. More generally, an extension rule is metrizable iff it extends p to a hyper-preference consistent with a distance criterion. We characterize the class of metrizable extension rules by means of two properties, namely self-consistency and acyclicity across orders. Moreover, we provide a characterization of neutral and metrizable extension rules, based on a simpler formulation of acyclicity across orders. Furthermore, we establish the logical incompatibility between neutrality, metrizability and strictness. However, we show that these three conditions are pairwise logically compatible.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Gilbert Laffond & Jean Lainé & M. Remzi Sanver, 2020. "Metrizable preferences over preferences," Post-Print hal-03271221, HAL.
    • Handle: RePEc:hal:journl:hal-03271221
    DOI: 10.1007/s00355-019-01235-0
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    Cited by:

    1. Athanasoglou, Stergios & Bonkoungou, Somouaoga & Ehlers, Lars, 2025. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Games and Economic Behavior, Elsevier, vol. 152(C), pages 216-240.

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