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The computational complexity of random serial dictatorship

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  • Aziz, Haris
  • Brandt, Felix
  • Brill, Markus

Abstract

In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful in the special domain of random assignment where indifferences are unavoidable. While executing RSD is obviously feasible, we show that computing the resulting probabilities is #P-complete, and thus intractable, both in the context of voting and assignment.

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  • Aziz, Haris & Brandt, Felix & Brill, Markus, 2013. "The computational complexity of random serial dictatorship," Economics Letters, Elsevier, vol. 121(3), pages 341-345.
    • Handle: RePEc:eee:ecolet:v:121:y:2013:i:3:p:341-345
    DOI: 10.1016/j.econlet.2013.09.006
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    Citations

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    Cited by:

    1. Aziz, Haris & Luo, Pang & Rizkallah, Christine, 2017. "Incompatibility of efficiency and strategyproofness in the random assignment setting with indifferences," Economics Letters, Elsevier, vol. 160(C), pages 46-49.
    2. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    3. Felix Brandt & Matthias Greger & Ren'e Romen, 2023. "Towards a Characterization of Random Serial Dictatorship," Papers 2303.11976, arXiv.org, revised Jun 2023.
    4. Tom Demeulemeester & Dries Goossens & Ben Hermans & Roel Leus, 2023. "Fair integer programming under dichotomous and cardinal preferences," Papers 2306.13383, arXiv.org, revised Apr 2024.
    5. Aziz, Haris & Brandl, Florian & Brandt, Felix, 2015. "Universal Pareto dominance and welfare for plausible utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 123-133.
    6. Brandl, Florian & Brandt, Felix & Suksompong, Warut, 2016. "The impossibility of extending random dictatorship to weak preferences," Economics Letters, Elsevier, vol. 141(C), pages 44-47.
    7. Aziz, Haris & Mestre, Julián, 2014. "Parametrized algorithms for random serial dictatorship," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 1-6.
    8. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    9. Daniela Saban & Jay Sethuraman, 2015. "The Complexity of Computing the Random Priority Allocation Matrix," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1005-1014, October.
    10. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'économie 14.07, Université de Lausanne, Faculté des HEC, Département d’économie.
    11. Demeulemeester, Tom & Goossens, Dries & Hermans, Ben & Leus, Roel, 2023. "A pessimist’s approach to one-sided matching," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1087-1099.
    12. Harless, Patrick & Phan, William, 2022. "Efficient mixtures of priority rules for assigning objects," Games and Economic Behavior, Elsevier, vol. 132(C), pages 73-89.
    13. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    14. Martin Bichler & Soeren Merting, 2021. "Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3540-3559, October.
    15. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).

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    More about this item

    Keywords

    Social choice theory; Random serial dictatorship; Random priority; Computational complexity; Assignment problem;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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