IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03271221.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    2. Haeringer, Guillaume & Hałaburda, Hanna, 2016. "Monotone strategyproofness," Games and Economic Behavior, Elsevier, vol. 98(C), pages 68-77.
    3. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    4. 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.
    5. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    6. Athanasoglou, Stergios, 2016. "Strategyproof and efficient preference aggregation with Kemeny-based criteria," Games and Economic Behavior, Elsevier, vol. 95(C), pages 156-167.
    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. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Bossert, Walter & Sprumont, Yves, 2014. "Strategy-proof preference aggregation: Possibilities and characterizations," Games and Economic Behavior, Elsevier, vol. 85(C), pages 109-126.
    13. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    14. 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..
    15. 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.
    16. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    17. 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.
    18. 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).
    19. 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.
    20. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stergios, Athanasoglou, 2017. "An investigation of weak-veto rules in preference aggregation," Working Papers 363, University of Milano-Bicocca, Department of Economics, revised 18 Feb 2017.
    2. Burak Can & Peter Csoka & Emre Ergin, 2017. "How to choose a non-manipulable delegation?," CERS-IE WORKING PAPERS 1713, Institute of Economics, Centre for Economic and Regional Studies.
    3. 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.
    4. J González-Pachón & C Romero, 2006. "An analytical framework for aggregating multiattribute utility functions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1241-1247, October.
    5. Kikuchi, Kazuya, 2016. "Comparing preference orders: Asymptotic independence," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 1-5.
    6. Burak Can & Péter Csóka & Emre Ergin, 2021. "How to choose a fair delegation?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1339-1373, November.
    7. Can, Burak & Csóka, Péter & Ergin, Emre, 2017. "How to choose a delegation for a peace conference?," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    8. Bhattacharya, Mihir & Gravel, Nicolas, 2021. "Is the preference of the majority representative ?," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 87-94.
    9. Csóka, Péter & Kondor, Gábor, 2019. "Delegációk igazságos kiválasztása társadalmi választások elméletével [Choosing a fair delegation by social choice theory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 771-787.
    10. Van der Linden, Martin, 2017. "Impossibilities for strategy-proof committee selection mechanisms with vetoers," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 111-121.
    11. Stergios Athanasoglou & Somouaoga Bonkoungou & Lars Ehlers, 2023. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Working Papers 519, University of Milano-Bicocca, Department of Economics.
    12. Ilya Segal, 2004. "The Communication Requirements of of Social Choice Rules and Supporting Budget Sets," Economics Working Papers 0039, Institute for Advanced Study, School of Social Science.
    13. Athanasoglou, Stergios, 2019. "Solidarity and efficiency in preference aggregation: A tale of two rules," Games and Economic Behavior, Elsevier, vol. 118(C), pages 126-140.
    14. Saptarshi Mukherjee & Hans Peters, 2022. "Self-implementation of social choice correspondences in Nash equilibrium," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 1009-1028, November.
    15. Yucheng Dong & Yao Li & Ying He & Xia Chen, 2021. "Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 273-295, December.
    16. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    17. Ben Amor, Sarah & Martel, Jean-Marc, 2014. "A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1165-1169.
    18. Kotaro Suzumura, 2002. "Introduction to social choice and welfare," Temi di discussione (Economic working papers) 442, Bank of Italy, Economic Research and International Relations Area.
    19. Athanasoglou, Stergios, 2016. "Strategyproof and efficient preference aggregation with Kemeny-based criteria," Games and Economic Behavior, Elsevier, vol. 95(C), pages 156-167.
    20. Segal, Ilya, 2007. "The communication requirements of social choice rules and supporting budget sets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 341-378, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-03271221. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.