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Weighted distances between preferences

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  • Can, B.

    (Microeconomics & Public Economics)

Abstract

Individual disagreements are assumed to be reflected in the preferences. Distance functions, e.g., the well-known Kemeny (1959) metric, are used to measure these disagreements. However, a disagreement on how to rank the top two alternatives may be perceived more (or less) than a disagreement on how to rank the bottom two alternatives. We propose two conditions on functions which characterize a class of weighted semi-metric functions. This class of semi-metrics allows to quantify disagreements according to where they occur in preferences. It turns out one of these functions, “the path minimizing function”, is the only metric which generalizes the Kemeny metric.
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  • Can, B., 2012. "Weighted distances between preferences," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2012056
    DOI: 10.26481/umamet.2012056
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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. 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).
    3. Hiroki Nishimura & Efe A. Ok, 2022. "A class of dissimilarity semimetrics for preference relations," Papers 2203.04418, arXiv.org.
    4. Huremović, Kenan & Ozkes, Ali I., 2022. "Polarization in networks: Identification–alienation framework," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    5. Kikuchi, Kazuya, 2016. "Comparing preference orders: Asymptotic independence," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 1-5.
    6. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    7. Herings, P. Jean-Jacques & Meshalkin, Andrey & Predtetchinski, Arkadi, 2017. "A one-period memory folk theorem for multilateral bargaining games," Games and Economic Behavior, Elsevier, vol. 103(C), pages 185-198.
    8. 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.
    9. Jorge Alcalde-Unzu & Marc Vorsatz, 2016. "Do we agree? Measuring the cohesiveness of preferences," Theory and Decision, Springer, vol. 80(2), pages 313-339, February.
    10. Matteo Brunelli & Michele Fedrizzi, 2019. "A general formulation for some inconsistency indices of pairwise comparisons," Annals of Operations Research, Springer, vol. 274(1), pages 155-169, March.
    11. Burak Can & Mohsen Pourpouneh & Ton Storcken, 2022. "An axiomatic re-characterization of the Kemeny rule," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 447-467, September.
    12. Antonella Plaia & Simona Buscemi & Johannes Fürnkranz & Eneldo Loza Mencía, 2022. "Comparing Boosting and Bagging for Decision Trees of Rankings," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 78-99, March.
    13. Karpov, Alexander, 2016. "Preference diversity orderings," Working Papers 0610, University of Heidelberg, Department of Economics.
    14. João V. Ferreira & Erik Schokkaert & Benoît Tarroux, 2023. "How group deliberation affects individual distributional preferences: An experimental study," Working Papers 2301, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    15. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    16. Daniele Checchi & Gianni De Fraja & Stefano Verzillo, 2018. "Selections from ordered sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(4), pages 677-703, April.
    17. Gyimesi, András, 2021. "Hosszú távú versenyegyensúly egy csapatsportliga közgazdasági modelljében [Long-term competitive balance in an economic model of a team sports league]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 585-616.
    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).

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