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Distance Rationalizability of Scoring Rules

In: Individual and Collective Choice and Social Welfare

Author

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

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    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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