Robust winner determination in positional scoring rules with uncertain weights
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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.
KeywordsScoring rules Rank aggregation Computational social choice Possible winners Minimax regret Convex sequences Robust optimization
This work was partially supported by the ANR project Cocorico-CoDec. The author thanks two anonymous reviewers for helpful comments. Moreover, the author would like to thank Jerome Lang for several comments on an early version of this paper, Stefano Moretti for pointing out some typos, and Patrice Perny for discussion on dominance relations and possible winners.
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