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Improved Bounds for Single-Nomination Impartial Selection

Author

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  • Javier Cembrano

    (Department of Algorithms and Complexity, Max Planck Institute for Informatics, 66123 Saarbrücken, Germany; and Institute of Mathematics, Technische Universität Berlin, 10623 Berlin, Germany)

  • Felix Fischer

    (School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom)

  • Max Klimm

    (Institute of Mathematics, Technische Universität Berlin, 10623 Berlin, Germany)

Abstract

A randomized selection mechanism returns a probability distribution over individuals based on mutual nominations among them; it is impartial if the selection probability of each individual is independent of the nominations they cast and α -optimal if the expected number of nominations received by the selected individual is always at least α times that received by any individual. When individuals can cast multiple nominations, the permutation mechanism is 1 / 2 -optimal, and this is the best possible. We show that the permutation mechanism does not provide the best possible factor in the natural situation when individuals cast exactly one nomination. Specifically, we provide a tight analysis of the permutation mechanism showing that it is 2 / 3 -optimal in this case, and we design a new mechanism that is α -optimal for α > 2 / 3 . We further prove that no impartial mechanism can be better than 76 / 105 -optimal.

Suggested Citation

  • Javier Cembrano & Felix Fischer & Max Klimm, 2026. "Improved Bounds for Single-Nomination Impartial Selection," Mathematics of Operations Research, INFORMS, vol. 51(2), pages 1486-1513, May.
    • Handle: RePEc:inm:ormoor:v:51:y:2026:i:2:p:1486-1513
    DOI: 10.1287/moor.2024.0431
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