IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.11976.html
   My bibliography  Save this paper

Towards a Characterization of Random Serial Dictatorship

Author

Listed:
  • Felix Brandt
  • Matthias Greger
  • Ren'e Romen

Abstract

Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$, Bogomolnaia and Moulin (2001) have shown that RSD is characterized by these axioms. Extending this characterization to arbitrary $n$ is a long-standing open problem. By weakening ex post efficiency and strategyproofness, we reduce the question of whether RSD is characterized by these axioms for fixed $n$ to determining whether a matrix has rank $n^2 n!^n$. We provide computer-generated counterexamples to show that two other approaches for proving the characterization (using deterministic extreme points or restricted domains of preferences) are inadequate.

Suggested Citation

  • Felix Brandt & Matthias Greger & Ren'e Romen, 2023. "Towards a Characterization of Random Serial Dictatorship," Papers 2303.11976, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2303.11976
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.11976
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manea, Mihai, 2007. "Serial dictatorship and Pareto optimality," Games and Economic Behavior, Elsevier, vol. 61(2), pages 316-330, November.
    2. Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    3. 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.
    4. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    5. Aziz, Haris & Brandt, Felix & Brill, Markus, 2013. "The computational complexity of random serial dictatorship," Economics Letters, Elsevier, vol. 121(3), pages 341-345.
    6. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    7. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    8. Sophie Bade, 2020. "Random Serial Dictatorship: The One and Only," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 353-368, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    2. Christian Basteck, 2024. "An Axiomatization of the Random Priority Rule," Rationality and Competition Discussion Paper Series 502, CRC TRR 190 Rationality and Competition.
    3. 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.
    4. Harless, Patrick & Phan, William, 2022. "Efficient mixtures of priority rules for assigning objects," Games and Economic Behavior, Elsevier, vol. 132(C), pages 73-89.
    5. Basteck, Christian, 2024. "An axiomatization of the random priority rule," Discussion Papers, Research Unit: Market Behavior SP II 2024-201, WZB Berlin Social Science Center.
    6. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    7. Felix Brandt & Patrick Lederer, 2024. "Weak Strategyproofness in Randomized Social Choice," Papers 2412.11977, arXiv.org.
    8. 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.
    9. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    10. Imamura, Kenzo & Kawase, Yasushi, 2024. "Efficient matching under general constraints," Games and Economic Behavior, Elsevier, vol. 145(C), pages 197-207.
    11. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    12. Biró, Péter & Klijn, Flip & Pápai, Szilvia, 2022. "Serial Rules in a Multi-Unit Shapley-Scarf Market," Games and Economic Behavior, Elsevier, vol. 136(C), pages 428-453.
    13. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    14. Monte, Daniel & Tumennasan, Norovsambuu, 2013. "Matching with quorums," Economics Letters, Elsevier, vol. 120(1), pages 14-17.
    15. 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.
    16. Lessan, Javad & Fu, Liping & Bachmann, Chris, 2020. "Towards user-centric, market-driven mobility management of road traffic using permit-based schemes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    17. Chatterji, Shurojit & Liu, Peng, 2020. "Random assignments of bundles," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 15-30.
    18. Karmokar, Madhuparna & Majumdar, Dipjyoti & Roy, Souvik, 2024. "Some further results on random OBIC rules," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 102-112.
    19. Bichler, Martin & Merting, Sören, 2018. "Truthfulness in advertising? Approximation mechanisms for knapsack bidders," European Journal of Operational Research, Elsevier, vol. 270(2), pages 775-783.
    20. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2303.11976. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.