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Robust winner determination in positional scoring rules with uncertain weights

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  • Paolo Viappiani

    (Sorbonne Université)

Abstract

Scoring rules constitute a particularly popular technique for aggregating a set of rankings. However, setting the weights associated with 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," Theory and Decision, Springer, vol. 88(3), pages 323-367, April.
    • Handle: RePEc:kap:theord:v:88:y:2020:i:3:d:10.1007_s11238-019-09734-3
    DOI: 10.1007/s11238-019-09734-3
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    References listed on IDEAS

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    Cited by:

    1. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Post-Print hal-04440153, HAL.
    2. Llamazares, Bonifacio, 2024. "Ranking voting systems and surrogate weights: Explicit formulas for centroid weights," European Journal of Operational Research, Elsevier, vol. 317(3), pages 967-976.

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