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Distance Rationalizability of Scoring Rules

In: Individual and Collective Choice and Social Welfare

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  • Burak Can

    (Maastricht University)

Abstract

Collective decision making problems can be seen as finding an outcome that is “closest” to a concept of “consensus”. Nitzan (1981) introduced “Closeness to Unanimity Procedure” as a first example to this approach and showed that the Borda rule is the closest to unanimity under the Kemeny (1959) distance. Elkind et al. (2009) generalized this concept as distance-rationalizability, and showed that all scoring rules can be distance rationalized via a class of distance functions, which we call scoring distances. In this paper, we propose another class of distances, i.e., weighted distances, introduced in Can (2014). This class is a generalization of the Kemeny distance that rationalizes the generalization of the Borda rule, i.e., scoring rules. Hence the results here extend those in Nitzan (1981) and reveal the broader connection between Kemeny-like distances and Borda-like voting rules.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stcchp:978-3-662-46439-7_11
    DOI: 10.1007/978-3-662-46439-7_11
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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. 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.
    4. 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.
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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

    Keywords

    Distance rationalizability; Scoring rules; Voting; Weighted distances;
    All these keywords.

    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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