IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2502.13850.html
   My bibliography  Save this paper

The probability of satisfying axioms: a non-binary perspective on economic design

Author

Listed:
  • Pierre Bardier

Abstract

We provide a formal framework accounting for a widespread idea in the theory of economic design: analytically established incompatibilities between given axioms should be qualified by the likelihood of their violation. We define the degree to which rules satisfy an axiom, as well as several axioms, on the basis of a probability measure over the inputs of the rules. Armed with this notion of degree, we propose and characterize i) a criterion to evaluate and compare rules given a set of axioms, allowing the importance of each combination of axioms to differ, and ii) a criterion to measure the compatibility between given axioms, building on a analogy with cooperative game theory.

Suggested Citation

  • Pierre Bardier, 2025. "The probability of satisfying axioms: a non-binary perspective on economic design," Papers 2502.13850, arXiv.org.
    • Handle: RePEc:arx:papers:2502.13850
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2502.13850
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, September.
    2. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
    3. Christopher P Chambers & Federico Echenique, 2025. "Decision theory and the "almost implies near" phenomenon," Papers 2502.07126, arXiv.org, revised Jul 2025.
    4. Mostapha Diss & Eric Kamwa, 2020. "Simulations in Models of Preference Aggregation," Post-Print hal-02424936, HAL.
    5. Hervé Moulin, 2019. "Fair Division in the Internet Age," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 407-441, August.
    6. Atila Abdulkadiroğlu & Aram Grigoryan, 2021. "Priority-based Assignment with Reserves and Quotas," NBER Working Papers 28689, National Bureau of Economic Research, Inc.
    7. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, March.
    8. Barberà, Salvador & Gerber, Anke, 2017. "Sequential voting and agenda manipulation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    9. repec:spr:thdchp:978-3-319-30690-2_2 is not listed on IDEAS
    10. Echenique, Federico & Miyashita, Masaki & Nakamura, Yuta & Pomatto, Luciano & Vinson, Jamie, 2022. "Twofold multiprior preferences and failures of contingent reasoning," Journal of Economic Theory, Elsevier, vol. 202(C).
    11. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    12. Schummer, James, 2004. "Almost-dominant strategy implementation: exchange economies," Games and Economic Behavior, Elsevier, vol. 48(1), pages 154-170, July.
    13. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    14. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    15. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    16. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    17. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    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. Bonifacio, Agustín G., 2024. "Trade-off between manipulability and dictatorial power: A proof of the Gibbard–Satterthwaite Theorem," Mathematical Social Sciences, Elsevier, vol. 130(C), pages 1-3.
    2. DECERF, Benoit & VAN DER LINDEN, Martin, 2016. "A criterion to compare mechanisms when solutions are not unique, with applications to constrained school choice," LIDAM Discussion Papers CORE 2016033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    4. Cato, Susumu, 2011. "Maskin monotonicity and infinite individuals," Economics Letters, Elsevier, vol. 110(1), pages 56-59, January.
    5. Martin Van der Linden, 2019. "Deferred acceptance is minimally manipulable," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 609-645, June.
    6. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    7. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    8. Hans Gersbach & Oriol Tejada, 2024. "Semi-flexible majority rules for public good provision," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(3), pages 677-715, November.
    9. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2018. "Strategy-proof location of public facilities," Games and Economic Behavior, Elsevier, vol. 112(C), pages 21-48.
    10. Haeringer, Guillaume & Hałaburda, Hanna, 2016. "Monotone strategyproofness," Games and Economic Behavior, Elsevier, vol. 98(C), pages 68-77.
    11. Salvatore Barbaro & Anna Specht, 2021. "Simple-majority rule and the size of the Bundestag," Working Papers 2105, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    12. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.
    13. Shengwu Li, 2024. "Designing Simple Mechanisms," Journal of Economic Perspectives, American Economic Association, vol. 38(4), pages 175-192, Fall.
    14. Bettina Klaus & Panos Protopapas, 2020. "On strategy-proofness and single-peakedness: median-voting over intervals," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1059-1080, December.
    15. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Boston College Working Papers in Economics 639, Boston College Department of Economics.
    16. Birendra K. Rai1 & Chiu Ki So & Aaron Nicholas, 2011. "Mathematical Economics: A Reader," Monash Economics Working Papers 02-11, Monash University, Department of Economics.
    17. Pongou,Roland & Sidie,Ghislain Junior, 2024. "Voting when Rankings Matter : Truthful Equilibria, Efficiency, and Abstention," Policy Research Working Paper Series 10837, The World Bank.
    18. Bonkoungou, Somouaoga & Nesterov, Alexander, 2023. "Incentives in matching markets: counting and comparing manipulating agents," Theoretical Economics, Econometric Society, vol. 18(3), July.
    19. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    20. Donald Campbell & Jerry Kelly, 2009. "Gains from manipulating social choice rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 349-371, September.

    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:2502.13850. 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.