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Positional Scoring Rules with Uncertain Weights

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Scalable Uncertainty Management (SUM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11142))

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Abstract

Positional scoring rules are frequently used for aggregating rankings (for example in social choice and in sports). These rules are highly sensitive to the weights associated to positions: depending on the weights, a different winner may be selected. In this paper we explicitly consider the role of weight uncertainty in both the case of monotone decreasing weights and of convex decreasing weights. First we discuss the problem of finding possible winners (candidates that may win for a feasible instantiation of the weights) based on previous works that established a connection with the notion of stochastic dominance. Second, we adopt decision-theoretic methods (minimax regret, maximum advantage, expected value) to pick a winner based on the weight uncertainty and we provide a characterization of these methods. Finally, we show some applications of our methodology in real datasets.

Work supported by the ANR project Cocorico-CoDec (ANR-14-CE24-0007-01).

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Notes

  1. 1.

    This hypothesis is removed in Goldsmith et al. [5] where the authors allow preferences for intermediate positions.

  2. 2.

    There is some redundancy in the constraints: it is enough to assume convexity and \(w_{m-1}\ge 0\) to ensure that the sequence is not increasing.

  3. 3.

    Several authors, including [3], have proposed to take a similar optimistic approach, although the way the feasible set is defined makes the resulting rules quite different.

  4. 4.

    Proofs are available from the author upon request.

  5. 5.

    Obtained from the PREFLIB data repository (http://www.preflib.org/).

  6. 6.

    To handle the case of ties (when a method returns multiple winners) we compute disagreement as the cardinality of the symmetric set difference normalized by the cardinality of the union.

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Authors and Affiliations

  1. Sorbonne Université, UMR7606 CNRS, LIP6, 4 pl. Jussieu, 75005, Paris, France

    Paolo Viappiani

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  1. Paolo Viappiani
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Correspondence to Paolo Viappiani .

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Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  3. Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

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Viappiani, P. (2018). Positional Scoring Rules with Uncertain Weights. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_21

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  • DOI: https://doi.org/10.1007/978-3-030-00461-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00460-6

  • Online ISBN: 978-3-030-00461-3

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