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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] - HESAM - HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université, 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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    References listed on IDEAS

    as
    1. Haeringer, Guillaume & Hałaburda, Hanna, 2016. "Monotone strategyproofness," Games and Economic Behavior, Elsevier, vol. 98(C), pages 68-77.
    2. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    3. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    4. Tommi Meskanen & Hannu Nurmi, 2006. "Distance from Consensus: A Theme and Variations," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 117-132, Springer.
    5. B. Monjardet, 1997. "Concordance between two linear orders: The Spearman and Kendall coefficients revisited," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 269-295, September.
    6. Jean Lainé & Ali Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 157-182, January.
    7. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    8. Herrade Igersheim, 2007. "Du paradoxe libéral-parétien à un concept de métaclassement des préférences," Recherches économiques de Louvain, De Boeck Université, vol. 73(2), pages 173-192.
    9. Ronald D. Armstrong & Wade D. Cook & Lawrence M. Seiford, 1982. "Priority Ranking and Consensus Formation: The Case of Ties," Management Science, INFORMS, vol. 28(6), pages 638-645, June.
    10. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    11. Claudio Borroni & Michele Zenga, 2007. "A test of concordance based on Gini’s mean difference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 289-308, November.
    12. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    13. Shin Sato, 2015. "Bounded response and the equivalence of nonmanipulability and independence of irrelevant alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 133-149, January.
    14. Athanasoglou, Stergios, 2016. "Strategyproof and efficient preference aggregation with Kemeny-based criteria," Games and Economic Behavior, Elsevier, vol. 95(C), pages 156-167.
    15. Jean Lainé & Ali Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 157-182, January.
    16. Bossert, Walter & Sprumont, Yves, 2014. "Strategy-proof preference aggregation: Possibilities and characterizations," Games and Economic Behavior, Elsevier, vol. 85(C), pages 109-126.
    17. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    18. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    19. Can, B. & Storcken, A.J.A., 2015. "Comparing orders, rankings, queues, tournaments and lists," Research Memorandum 020, Maastricht University, Graduate School of Business and Economics (GSBE).
    20. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
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