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A re-characterization of the Kemeny distance

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  • Can, Burak
  • Storcken, Ton

Abstract

The well-known swap distance (Kemeny, 1959; Kendall, 1938 and Hamming, 1950) is analyzed. On weak preferences, this function was characterized by Kemeny (1959) with five conditions; metric, betweenness, neutrality, reducibility, and normalization. We show that the same result can be achieved without the reducibility condition, which shows the Kemeny distance is much less demanding than it seems. We provide a new and logically independent characterization of the Kemeny distance and provide some insight to further analyze distance functions on preferences.

Suggested Citation

  • Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    • Handle: RePEc:eee:mateco:v:79:y:2018:i:c:p:112-116
    DOI: 10.1016/j.jmateco.2018.04.007
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    1. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
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    Cited by:

    1. Gilbert Laffond & Jean Lainé & M. Remzi Sanver, 2020. "Metrizable preferences over preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 177-191, June.
    2. Burak Can, 2015. "Distance Rationalizability of Scoring Rules," Studies in Choice and Welfare, in: Constanze Binder & Giulio Codognato & Miriam Teschl & Yongsheng Xu (ed.), Individual and Collective Choice and Social Welfare, edition 127, pages 171-178, Springer.
    3. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2017. "Cost of transformation: a measure on matchings," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    4. Hiroki Nishimura & Efe A. Ok, 2022. "A class of dissimilarity semimetrics for preference relations," Papers 2203.04418, arXiv.org.
    5. Bhattacharya, Mihir & Gravel, Nicolas, 2021. "Is the preference of the majority representative ?," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 87-94.
    6. 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).
    7. Kikuchi, Kazuya, 2016. "Comparing preference orders: Asymptotic independence," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 1-5.
    8. 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.
    9. Saeideh Babashahi & Paul Hansen & Ronald Peeters, 2023. "External validity of multi-criteria preference data obtained from non-random sampling: measuring cohesiveness within and between groups," Annals of Operations Research, Springer, vol. 325(2), pages 939-949, June.
    10. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    11. Dinko Dimitrov & Emiliya A. Lazarova & Shao-Chin Sung, 2016. "Inducing stability in hedonic games," University of East Anglia School of Economics Working Paper Series 2016-09, School of Economics, University of East Anglia, Norwich, UK..
    12. Walter Bossert & Burak Can & Conchita D'Ambrosio, 2018. "A Head‐count Measure of Rank Mobility and its Directional Decomposition," Economica, London School of Economics and Political Science, vol. 85(340), pages 793-807, October.
    13. Irina Georgescu & Jani Kinnunen, 2015. "Distances of Fuzzy Choice Functions," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 249-265.
    14. Uuganbaatar Ninjbat, 2018. "Impossibility theorems with countably many individuals," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 9(3), pages 333-350, August.
    15. László Csató, 2017. "On the ranking of a Swiss system chess team tournament," Annals of Operations Research, Springer, vol. 254(1), pages 17-36, July.
    16. 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.
    17. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    18. Walter Bossert & Burak Can & Conchita D’Ambrosio, 2016. "Measuring rank mobility with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 917-931, April.
    19. 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.
    20. Ali Ihsan Ozkes, 2013. "Preferential Polarization Measures," Working Papers hal-00875949, HAL.
    21. Burak Can & Mohsen Pourpouneh & Ton Storcken, 2021. "An axiomatic characterization of the Slater rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 835-853, May.
    22. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.
    23. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.
    24. 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).

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    More about this item

    Keywords

    Kemeny distance; Swap distance; Inversion metric; Preferences;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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