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Distance rationalizability of scoring rules

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  • Can, B.

    (Microeconomics & Public Economics)

Abstract

Collective decision making problems can be seen as finding an outcome that is "closest" to a concept of "consensus". [1] introduced "Closeness to Unanimity Procedure" as a first example to this approach and showed that the Borda rule is the closest to unanimity under swap distance (a.k.a the [2] distance). [3] shows that the Dodgson rule is the closest to Condorcet under swap distance. [4, 5] generalized this concept as distance-rationalizability, where being close is measured via various distance functions and with many concepts of consensus, e.g., unanimity, Condorcet etc. In this paper, we show that all non-degenerate scoring rules can be distance-rationalized as "Closeness to Unanimity" procedures under a class of weighted distance functions introduced in [6]. Therefore, the results herein generalizes [1] and builds a connection between scoring rules and a generalization of the Kemeny distance, i.e. weighted distances.

Suggested Citation

  • Can, B., 2013. "Distance rationalizability of scoring rules," Research Memorandum 068, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013068
    DOI: 10.26481/umagsb.2013068
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    References listed on IDEAS

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    1. Tommi Meskanen & Hannu Nurmi, 2008. "Closeness Counts in Social Choice," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 15, pages 289-306, Springer.
    2. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    3. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2012. "Rationalizations of Condorcet-consistent rules via distances of hamming type," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 891-905, October.
    4. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(1), pages 161-169.
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    Cited by:

    1. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.

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    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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