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Towards Copeland Optimization in Combinatorial Problems

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13292))

Abstract

Traditional approaches to fairness in operations research and social choice, such as the egalitarian/Rawlsian, the utilitarian or the proportional-fair rule implicitly assume that the voters’ utility functions are – to a certain degree – comparable. Otherwise, statements such as “maximize the worst-off voter’s utility” or “maximize the sum of utilities” are void. But what if the different valuations should truly not be compared or converted into each other? Voting theory only relies on ordinal information and can help to provide democratic rules to define winning solutions. Copeland’s method is a well-known generalization of the Condorcet criterion in social choice theory and asks for an outcome that has the best ratio of pairwise majority duel wins to losses. If we simply ask for a feasible solution to a combinatorial problem that maximizes the Copeland score, we are at risk to encounter intractability (due to having to explore all solutions) or suffer from (the lack of) irrelevant alternatives. We present first results from optimizing for a Copeland winner to a constraint problem formulated in MiniZinc in a local search fashion based on a changing solution pool. We investigate the effects of diversity constraints on the quality of the estimated Copeland score as well as the gap between the best reported Copeland scores to the actual Copeland scores.

This research has been sponsored by DAAD Research Internships in Science and Engineering (RISE).

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Notes

  1. 1.

    Our implementation indeed uses integer variables for utilities that need to be maximized but nothing prohibits more general “is-better” predicates.

  2. 2.

    Source code: https://github.com/s1db/Local-Search-Copeland-Method.

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Acknowledgments

We thank Guido Tack and Alexander Knapp for initial discussions that led to the idea of this paper.

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Authors and Affiliations

  1. University of Glasgow, Glasgow, Scotland

    Sidhant Bhavnani

  2. Technische Hochschule Ingolstadt, Ingolstadt, Germany

    Alexander Schiendorfer

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  1. Sidhant Bhavnani
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  2. Alexander Schiendorfer
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Correspondence to Alexander Schiendorfer .

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  1. UCLouvain, Louvain-la-Neuve, Belgium

    Pierre Schaus

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Bhavnani, S., Schiendorfer, A. (2022). Towards Copeland Optimization in Combinatorial Problems. In: Schaus, P. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2022. Lecture Notes in Computer Science, vol 13292. Springer, Cham. https://doi.org/10.1007/978-3-031-08011-1_4

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  • DOI: https://doi.org/10.1007/978-3-031-08011-1_4

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  • Online ISBN: 978-3-031-08011-1

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