IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v50y2018i1d10.1007_s00355-017-1075-3.html
   My bibliography  Save this article

Strategy-proofness of scoring allocation correspondences for indivisible goods

Author

Listed:
  • Nhan-Tam Nguyen

    (Heinrich-Heine-Universität Düsseldorf)

  • Dorothea Baumeister

    (Heinrich-Heine-Universität Düsseldorf)

  • Jörg Rothe

    (Heinrich-Heine-Universität Düsseldorf)

Abstract

We study strategy-proofness in a model of resource allocation due to Brams and King (Ration Soc 17:387–421, 2005) and Brams et al. (Theory Decis 55:147–180, 2003), further developed by Baumeister et al. (J Auton Agents Multi Agent Syst 31(3):628–655, 2017). We assume resources to be indivisible and nonshareable and that agents have responsive preferences over the power set of the resources, but only submit ordinal preferences over single resources to the social planner. Using scoring vectors, these ordinal preferences induce additive utility functions. We then focus on allocation correspondences that maximize utilitarian social welfare, and we use extension principles (from social choice theory, such as the Kelly and the Gärdenfors extension) for preferences to study manipulation of allocation correspondences. We characterize strategy-proofness of the utilitarian allocation correspondence: It is Gärdenfors/Kelly-strategy-proof if and only if the number of different values in the scoring vector is at most two or the number of occurrences of the greatest value in the scoring vector is larger than half the number of resources.

Suggested Citation

  • Nhan-Tam Nguyen & Dorothea Baumeister & Jörg Rothe, 2018. "Strategy-proofness of scoring allocation correspondences for indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 101-122, January.
    • Handle: RePEc:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1075-3
    DOI: 10.1007/s00355-017-1075-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-017-1075-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-017-1075-3?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. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Salvador Barberà & Lars Ehlers, 2011. "Free triples, large indifference classes and the majority rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 559-574, October.
    3. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    4. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    6. Steven Brams & Michael Jones & Christian Klamler, 2008. "Proportional pie-cutting," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 353-367, March.
    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. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    9. Steven J. Brams & Paul H. Edelman & Peter C. Fishburn, 2003. "Fair Division Of Indivisible Items," Theory and Decision, Springer, vol. 55(2), pages 147-180, September.
    10. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 505-515, September.
    11. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    12. David A. Kohler & R. Chandrasekaran, 1971. "A Class of Sequential Games," Operations Research, INFORMS, vol. 19(2), pages 270-277, April.
    13. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    14. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    15. Szilvia Pápai, 2001. "Strategyproof and Nonbossy Multiple Assignments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(3), pages 257-271, July.
    16. Dorothea Herreiner & Clemens Puppe, 2002. "A simple procedure for finding equitable allocations of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 415-430.
    17. Sato, Shin, 2009. "Strategy-proof social choice with exogenous indifference classes," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 48-57, January.
    18. Steven J. Brams & Daniel L. King, 2005. "Efficient Fair Division," Rationality and Society, , vol. 17(4), pages 387-421, November.
    19. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    20. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    21. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    22. Peter Cramton & Yoav Shoham & Richard Steinberg (ed.), 2006. "Combinatorial Auctions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033429, April.
    23. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    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. Rothe, Jörg & Schadrack, Hilmar & Schend, Lena, 2018. "Borda-induced hedonic games with friends, enemies, and neutral players," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 21-36.

    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. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    2. Eve Ramaekers, 2013. "Fair allocation of indivisible goods: the two-agent case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 359-380, July.
    3. Miralles, Antonio, 2012. "Cardinal Bayesian allocation mechanisms without transfers," Journal of Economic Theory, Elsevier, vol. 147(1), pages 179-206.
    4. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    5. 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.
    6. Monte, Daniel & Tumennasan, Norovsambuu, 2013. "Matching with quorums," Economics Letters, Elsevier, vol. 120(1), pages 14-17.
    7. Honda, Edward, 2021. "A modified deferred acceptance algorithm for conditionally lexicographic-substitutable preferences," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    8. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    9. Jacob Coreno & Ivan Balbuzanov, 2022. "Axiomatic Characterizations of Draft Rules," Papers 2204.08300, arXiv.org, revised May 2024.
    10. Eduardo M Azevedo & Eric Budish, 2019. "Strategy-proofness in the Large," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 81-116.
    11. Di Feng & Bettina Klaus, 2022. "Preference revelation games and strict cores of multiple‐type housing market problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 61-76, March.
    12. Hoda Atef Yekta & Robert Day, 2020. "Optimization-based Mechanisms for the Course Allocation Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 641-660, July.
    13. Papai, Szilvia, 2007. "Exchange in a general market with indivisible goods," Journal of Economic Theory, Elsevier, vol. 132(1), pages 208-235, January.
    14. Bettina Klaus & Alexandru Nichifor, 2020. "Serial dictatorship mechanisms with reservation prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 665-684, October.
    15. Madhav Raghavan, 2017. "Serial Priority in Project Allocation: A Characterisation," Cahiers de Recherches Economiques du Département d'économie 17.17, Université de Lausanne, Faculté des HEC, Département d’économie.
    16. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    17. Caspari, Gian, 2020. "Booster draft mechanism for multi-object assignment," ZEW Discussion Papers 20-074, ZEW - Leibniz Centre for European Economic Research.
    18. Franz Diebold & Haris Aziz & Martin Bichler & Florian Matthes & Alexander Schneider, 2014. "Course Allocation via Stable Matching," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 6(2), pages 97-110, April.
    19. Jörgen Kratz, 2017. "Overlapping multiple object assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 723-753, March.
    20. Manjunath, Vikram, 2012. "When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds," Games and Economic Behavior, Elsevier, vol. 74(2), pages 576-587.

    More about this item

    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:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1075-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.