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Borda rule as an almost first-order stochastic dominance rule

Author

Listed:
  • Mostapha Diss

    (CRESE, Univ. Bourgogne Franche-Comté)

  • Eric Kamwa

    (LC2S, Univ. des Antilles)

  • Muhammad Mahajne

    (GATE, Univ Lyon)

Abstract

In single-winner elections and individuals expressing linear orderings, an alternative has first-order stochastic dominance if the cumulative standing for this alternative at each rank is higher than that of the other alternatives. It is well known that this criterion may fail in ranking the competing alternatives since the first-order stochastic dominance winner may not exist in some situations. Making an adaptation of a centrality measure from network theory, we introduce in this note a rule, called the almost first-order stochastic dominance rule, which selects the alternative having first-order stochastic dominance if such an alternative exists, otherwise it selects the alternative which is close to achieve first-order stochastic dominance. It turns out that this rule is equivalent to the well-studied Borda rule. This result highlights an unknown property of the Borda rule.

Suggested Citation

  • Mostapha Diss & Eric Kamwa & Muhammad Mahajne, 2020. "Borda rule as an almost first-order stochastic dominance rule," Working Papers 2020-05, CRESE.
  • Handle: RePEc:crb:wpaper:2020-05
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    References listed on IDEAS

    as
    1. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    2. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    3. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    4. Stein, William E. & Mizzi, Philip J. & Pfaffenberger, Roger C., 1994. "A stochastic dominance analysis of ranked voting systems with scoring," European Journal of Operational Research, Elsevier, vol. 74(1), pages 78-85, April.
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    More about this item

    Keywords

    Network; centrality; centrality measures; rankings; first-order stochastic dominance; scoring rules; Borda’s rule.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • 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
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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