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Robust Winner Determination in Positional Scoring Rules with Uncertain Weights

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  • Paolo Viappiani

    (DECISION - LIP6 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

Abstract

Scoring rules constitute a particularly popular technique for aggregating a set of rank-ings. However, setting the weights associated to rank positions is a crucial task, as different instantiations of the weights can often lead to different winners. In this work we adopt minimax regret as a robust criterion for determining the winner in the presence of uncertainty over the weights. Focusing on two general settings (non-increasing weights and convex sequences of non-increasing weights) we provide a characterization of the minimax regret rule in terms of cumulative ranks, allowing a quick computation of the winner. We then analyze the properties of using minimax regret as a social choice function. Finally we provide some test cases of rank aggregation using the proposed method.

Suggested Citation

  • Paolo Viappiani, 2020. "Robust Winner Determination in Positional Scoring Rules with Uncertain Weights," Post-Print hal-02373399, HAL.
    • Handle: RePEc:hal:journl:hal-02373399
    DOI: 10.1007/s11238-019-09734-3
    Note: View the original document on HAL open archive server: https://hal.sorbonne-universite.fr/hal-02373399v1
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    References listed on IDEAS

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    3. 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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