IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4762.html
   My bibliography  Save this article

On rank dominance of tie-breaking rules

Author

Listed:
  • Allman, Maxwell

    (Department Management Science and Engineering, Stanford University)

  • Ashlagi, Itai

    (Department Management Science and Engineering, Stanford University)

  • Nikzad, Afshin

    (Department of Economics, University of Southern California)

Abstract

Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of re- sources with heterogeneous qualities, where the agents’ preferences are generated from a multinomial-logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents’ preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie-breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.

Suggested Citation

  • Allman, Maxwell & Ashlagi, Itai & Nikzad, Afshin, 2023. "On rank dominance of tie-breaking rules," Theoretical Economics, Econometric Society, vol. 18(2), May.
    • Handle: RePEc:the:publsh:4762
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20230707/36533/1098
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Atila Abdulkadiro?lu & Yeon-Koo Che & Yosuke Yasuda, 2015. "Expanding "Choice" in School Choice," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 1-42, February.
    3. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    4. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    5. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
    6. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    7. Itai Ashlagi & Peng Shi, 2014. "Improving Community Cohesion in School Choice via Correlated-Lottery Implementation," Operations Research, INFORMS, vol. 62(6), pages 1247-1264, December.
    8. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    9. Itai Feigenbaum & Yash Kanoria & Irene Lo & Jay Sethuraman, 2020. "Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations," Management Science, INFORMS, vol. 66(11), pages 5341-5361, November.
    10. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    11. Ashlagi, Itai & Nikzad, Afshin & Romm, Assaf, 2019. "Assigning more students to their top choices: A comparison of tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 115(C), pages 167-187.
    12. Nikhil Agarwal & Paulo Somaini, 2018. "Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism," Econometrica, Econometric Society, vol. 86(2), pages 391-444, March.
    13. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Han, Xiang, 2024. "On the efficiency and fairness of deferred acceptance with single tie-breaking," Journal of Economic Theory, Elsevier, vol. 218(C).
    2. Kenny Peng & Nikhil Garg, 2023. "Monoculture in Matching Markets," Papers 2312.09841, arXiv.org.

    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. Dur, Umut & Pathak, Parag A. & Sönmez, Tayfun, 2020. "Explicit vs. statistical targeting in affirmative action: Theory and evidence from Chicago's exam schools," Journal of Economic Theory, Elsevier, vol. 187(C).
    2. Umut Dur & Parag A. Pathak & Tayfun Sönmez, 2016. "Explicit vs. Statistical Preferential Treatment in Affirmative Action: Theory and Evidence from Chicago's Exam Schools," NBER Working Papers 22109, National Bureau of Economic Research, Inc.
    3. Atila Abdulkadiroğlu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation," Econometrica, Econometric Society, vol. 85, pages 1373-1432, September.
    4. Hatfield, John William & Kojima, Fuhito & Narita, Yusuke, 2016. "Improving schools through school choice: A market design approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 186-211.
    5. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
    6. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    7. Ashlagi, Itai & Nikzad, Afshin & Romm, Assaf, 2019. "Assigning more students to their top choices: A comparison of tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 115(C), pages 167-187.
    8. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    9. Ágoston, Kolos Csaba & Biró, Péter & Kováts, Endre & Jankó, Zsuzsanna, 2022. "College admissions with ties and common quotas: Integer programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 722-734.
    10. Itai Feigenbaum & Yash Kanoria & Irene Lo & Jay Sethuraman, 2020. "Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations," Management Science, INFORMS, vol. 66(11), pages 5341-5361, November.
    11. Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
    12. Alvin E. Roth, 2009. "What Have We Learned from Market Design?," Innovation Policy and the Economy, University of Chicago Press, vol. 9(1), pages 79-112.
    13. Hafalir, Isa E. & Kojima, Fuhito & Yenmez, M. Bumin, 2022. "Interdistrict school choice: A theory of student assignment," Journal of Economic Theory, Elsevier, vol. 201(C).
    14. Ágoston, Kolos Csaba & Biró, Péter & Szántó, Richárd, 2018. "Stable project allocation under distributional constraints," Operations Research Perspectives, Elsevier, vol. 5(C), pages 59-68.
    15. Yeon-Koo Che & Olivier Tercieux, 2019. "Efficiency and Stability in Large Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 2301-2342.
    16. Mehmet Ekmekci & M. Bumin Yenmez, "undated". "Integrating Schools for Centralized Admissions," GSIA Working Papers 2014-E20, Carnegie Mellon University, Tepper School of Business.
    17. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    18. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    19. Echenique, Federico & Miralles, Antonio & Zhang, Jun, 2021. "Fairness and efficiency for allocations with participation constraints," Journal of Economic Theory, Elsevier, vol. 195(C).
    20. Federico Echenique & Antonio Miralles & Jun Zhang, 2018. "Fairness and Efficiency for Probabilistic Allocations with Endowments," Working Papers 1055, Barcelona School of Economics.

    More about this item

    Keywords

    Matching; deferred acceptance; tiebreaking;
    All these keywords.

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:the:publsh:4762. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.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.