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Aggregation of Rankings: a Brief Review of Distance-Based Rules

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  • Michel Truchon

Abstract

Some researchers have addressed the problem of aggregating individual preferences or rankings by seeking a ranking that is closest to the individual rankings. Their methods differ according to the notion of distance that they use. The best known method of this sort is due to Kemeny. The first part of this paper offers a brief survey of some of these methods. Another way of approaching the aggregation of rankings is as a problem of optimal statistical inference, in which an expected loss is minimised. This approach requires a loss function, a concept closely related the notion of distance between rankings. The second part of this paper examines two classes of parametric functions and proposes one class for the optimal statistical inference problem.

Suggested Citation

  • Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    • Handle: RePEc:lvl:lacicr:0534
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    File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2005/CIRPEE05-34.pdf
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    References listed on IDEAS

    as
    1. Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
    2. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    3. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    4. Iqbal Ali & Wade D. Cook & Moshe Kress, 1986. "On the Minimum Violations Ranking of a Tournament," Management Science, INFORMS, vol. 32(6), pages 660-672, June.
    5. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
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    Cited by:

    1. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    2. Stephen Gordon & Michel Truchon, 2008. "Social choice, optimal inference and figure skating," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 265-284, February.
    3. Mostapha Diss & Eric Kamwa & Muhammad Mahajne, 2020. "Borda rule as an almost first-order stochastic dominance rule," Working Papers hal-04543260, HAL.

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    More about this item

    Keywords

    Vote aggregation; ranking rules; distance; loss function; maximum likelihood; optimal inference; Kemeny;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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