IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v95y2016icp168-177.html
   My bibliography  Save this article

Incentive properties for ordinal mechanisms

Author

Listed:
  • Cho, Wonki Jo

Abstract

We study three incentive properties for ordinal mechanisms: (i) strategy-proofness, which requires that no agent gain by misrepresenting his preferences; (ii) adjacent strategy-proofness, which requires that no agent gain by switching the rankings of two adjacent alternatives; and (iii) mistake monotonicity, which requires that the welfare of each agent weakly decrease as he reports increasingly bigger mistakes. Each of these properties has three versions, depending on whether preferences over sure alternatives are extended to preferences over lotteries by the stochastic dominance, downward lexicographic, or upward lexicographic extension. We identify conditions on the preference domain that guarantee the equivalence of these properties. The universal domain and the domains of single-dipped and single-peaked preferences satisfy our conditions.

Suggested Citation

  • Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    • Handle: RePEc:eee:gamebe:v:95:y:2016:i:c:p:168-177
    DOI: 10.1016/j.geb.2015.12.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825615001608
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2015.12.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    2. Bogomolnaia, Anna, 2015. "Random assignment: Redefining the serial rule," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 308-318.
    3. Alcalde, Jose, 2013. "Random Housing with Existing Tenants," QM&ET Working Papers 13-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    4. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    5. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    6. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    7. 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.
    8. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    9. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    10. 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.
    11. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    12. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    13. Alcalde, Jose & Silva-Reus, José Ángel, 2013. "Allocating via Priorities," QM&ET Working Papers 13-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    14. Saban, Daniela & Sethuraman, Jay, 2014. "A note on object allocation under lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 283-289.
    15. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    16. William Vickrey, 1960. "Utility, Strategy, and Social Decision Rules," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 74(4), pages 507-535.
    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. 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.
    2. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    3. Liu, Peng, 2020. "Local vs. global strategy-proofness: A new equivalence result for ordinal mechanisms," Economics Letters, Elsevier, vol. 189(C).
    4. Kumar, Ujjwal & Roy, Souvik & Sen, Arunava & Yadav, Sonal & Zeng, Huaxia, 2021. "Local global equivalence for unanimous social choice functions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 299-308.
    5. 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.
    6. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    7. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    8. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    9. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    10. Youngsub Chun & Kiyong Yun, 2020. "Upper-contour strategy-proofness in the probabilistic assignment problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 667-687, April.
    11. Harless, Patrick, 2016. "Solidarity in preference aggregation: Improving on a status quo," Games and Economic Behavior, Elsevier, vol. 95(C), pages 73-87.
    12. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    13. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    14. William Thomson, 2023. "Where should your daughter go to college? An axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 313-330, January.
    15. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Discussion Papers 20-06, Indian Statistical Institute, Delhi.
    16. 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.
    17. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    18. Altuntaş, Açelya & Phan, William & Tamura, Yuki, 2023. "Some characterizations of Generalized Top Trading Cycles," Games and Economic Behavior, Elsevier, vol. 141(C), pages 156-181.
    19. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    20. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    21. Muto, Nozomu & Sato, Shin, 2017. "An impossibility under bounded response of social choice functions," Games and Economic Behavior, Elsevier, vol. 106(C), pages 1-15.
    22. Cho, Wonki Jo & Doğan, Battal, 2016. "Equivalence of efficiency notions for ordinal assignment problems," Economics Letters, Elsevier, vol. 146(C), pages 8-12.
    23. Andrew McLennan & Shino Takayama & Yuki Tamura, 2024. "An Efficient, Computationally Tractable School Choice Mechanism," Discussion Papers Series 668, School of Economics, University of Queensland, Australia.

    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. Wonki Jo Cho, 2018. "Probabilistic assignment: an extension approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 137-162, June.
    2. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    3. Sulagna Dasgupta & Debasis Mishra, 2022. "Ordinal Bayesian incentive compatibility in random assignment model," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 651-664, December.
    4. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    5. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Papers 2009.13104, arXiv.org, revised May 2021.
    6. Liu, Peng, 2020. "Local vs. global strategy-proofness: A new equivalence result for ordinal mechanisms," Economics Letters, Elsevier, vol. 189(C).
    7. 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.
    8. Yajing Chen & Patrick Harless & Zhenhua Jiao, 2021. "The probabilistic rank random assignment rule and its axiomatic characterization," Papers 2104.09165, arXiv.org.
    9. Cho, Wonki Jo & Doğan, Battal, 2016. "Equivalence of efficiency notions for ordinal assignment problems," Economics Letters, Elsevier, vol. 146(C), pages 8-12.
    10. Che, Yeon-Koo & Kim, Jinwoo & Kojima, Fuhito, 2015. "Efficient assignment with interdependent values," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 54-86.
    11. Felix Brandt & Patrick Lederer & René Romen, 2024. "Relaxed notions of Condorcet-consistency and efficiency for strategyproof social decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 19-55, August.
    12. 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.
    13. 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.
    14. 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.
    15. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.
    16. 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.
    17. Marek Pycia & M. Utku Ünver, 2022. "Outside options in neutral allocation of discrete resources," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 581-604, December.
    18. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
    19. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    20. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).

    More about this item

    Keywords

    Ordinal mechanism; Strategy-proofness; Adjacent strategy-proofness; Mistake monotonicity;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:eee:gamebe:v:95:y:2016:i:c:p:168-177. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.