IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v45y2015i4p793-804.html
   My bibliography  Save this article

Set-monotonicity implies Kelly-strategyproofness

Author

Listed:
  • Felix Brandt

Abstract

This paper studies the strategic manipulation of set-valued social choice functions according to Kelly’s preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred to all elements of the latter. It is shown that set-monotonicity—a new variant of Maskin-monotonicity—implies Kelly-strategyproofness in comprehensive subdomains of the linear domain. Interestingly, there are a handful of appealing Condorcet extensions—such as the top cycle, the minimal covering set, and the bipartisan set—that satisfy set-monotonicity even in the unrestricted linear domain, thereby answering questions raised independently by Barberà (J Econ Theory 15(2):266–278( 1977a )) and Kelly (Econometrica 45(2):439–446 ( 1977 )). Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:45:y:2015:i:4:p:793-804
    DOI: 10.1007/s00355-015-0881-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-015-0881-8
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00355-015-0881-8?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. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 185-192.
    2. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 569-580.
    3. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    4. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    5. Laslier, Jean-Francois, 1996. "Rank-based choice correspondences," Economics Letters, Elsevier, vol. 52(3), pages 279-286, September.
    6. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
    7. Barbera, Salvador, 1977. "The Manipulation of Social Choice Mechanisms That Do Not Leave "Too Much" to Chance," Econometrica, Econometric Society, vol. 45(7), pages 1573-1588, October.
    8. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    9. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    10. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    11. Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-640, May.
    12. Monjardet, B., 2008. "Statement of precedence and a comment on IIA terminology," Games and Economic Behavior, Elsevier, vol. 62(2), pages 736-738, March.
    13. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    14. 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.
    15. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    16. Klaus Nehring, 2000. "Monotonicity implies generalized strategy-proofness for correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 367-375.
    17. Bandyopadhyay, Taradas, 1983. "Multi-valued decision rules and coalitional non-manipulability : Two possibility theorems," Economics Letters, Elsevier, vol. 13(1), pages 37-44.
    18. Joaqui´n Pérez, 2001. "The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 601-616.
    19. Jean-FranÚois Laslier, 2000. "Aggregation of preferences with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 269-282.
    20. Shin Sato, 2008. "On strategy-proof social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 331-343, August.
    21. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    22. Felix Brandt & Maria Chudnovsky & Ilhee Kim & Gaku Liu & Sergey Norin & Alex Scott & Paul Seymour & Stephan Thomassé, 2013. "A counterexample to a conjecture of Schwartz," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 739-743, March.
    23. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    24. Bordes, Georges, 1983. "On the possibility of reasonable consistent majoritarian choice: Some positive results," Journal of Economic Theory, Elsevier, vol. 31(1), pages 122-132, October.
    25. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
    26. Bettina Klaus & Olivier Bochet, 2013. "The relation between monotonicity and strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 41-63, January.
    27. MacIntyre, I. & Pattanaik, Prasanta K., 1981. "Strategic voting under minimally binary group decision functions," Journal of Economic Theory, Elsevier, vol. 25(3), pages 338-352, December.
    28. Georges Bordes, 1976. "Consistency, Rationality and Collective Choice," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 451-457.
    29. John Duggan, 2013. "Uncovered sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 489-535, September.
    30. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    31. Barbera, Salvador, 1977. "Manipulation of social decision functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 266-278, August.
    32. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    33. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    34. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
    35. Bandyopadhyay, Taradas, 1983. "Manipulation of non-imposed, non-oligarchic, non-binary group decision rules," Economics Letters, Elsevier, vol. 11(1-2), pages 69-73.
    36. Masashi Umezawa, 2009. "Coalitionally strategy-proof social choice correspondences and the Pareto rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 151-158, June.
    37. Bandyopadhyay, Taradas, 1982. "Threats, counter-threats and strategic manipulation for non-binary group decision rules," Mathematical Social Sciences, Elsevier, vol. 2(2), pages 145-155, March.
    38. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    39. José Jimeno & Joaquín Pérez & Estefanía García, 2009. "An extension of the Moulin No Show Paradox for voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 343-359, September.
    40. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 75-93, January.
    41. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    42. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, 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. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    2. Matías Núñez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 421-441, February.
    3. Brandt, Felix & Geist, Christian & Peters, Dominik, 2017. "Optimal bounds for the no-show paradox via SAT solving," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 18-27.
    4. Hayrullah Dindar & Jean Lainé, 2023. "Vote swapping in irresolute two-tier voting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 221-262, August.
    5. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    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. Demeze-Jouatsa, Ghislain-Herman, 2022. "Ambiguous Social Choice Functions," Center for Mathematical Economics Working Papers 660, Center for Mathematical Economics, Bielefeld University.
    8. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    9. Felix Brandt & Markus Brill & Paul Harrenstein, 2018. "Extending tournament solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 193-222, August.
    10. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    11. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    12. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2018. "On the structure of stable tournament solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 483-507, March.
    13. Felix Brandt & Martin Bullinger & Patrick Lederer, 2021. "On the Indecisiveness of Kelly-Strategyproof Social Choice Functions," Papers 2102.00499, arXiv.org, revised Mar 2022.
    14. Florian Brandl & Felix Brandt & Christian Stricker, 2022. "An analytical and experimental comparison of maximal lottery schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 5-38, January.
    15. 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.
    16. Felix Brandt & Patrick Lederer, 2021. "Characterizing the Top Cycle via Strategyproofness," Papers 2108.04622, arXiv.org, revised Jun 2023.
    17. 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.
    18. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2020. "On the Structure of Stable Tournament Solutions," Papers 2004.01651, 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. 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.
    2. 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).
    3. Felix Brandt & Martin Bullinger & Patrick Lederer, 2021. "On the Indecisiveness of Kelly-Strategyproof Social Choice Functions," Papers 2102.00499, arXiv.org, revised Mar 2022.
    4. Hayrullah Dindar & Jean Lainé, 2023. "Vote swapping in irresolute two-tier voting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 221-262, August.
    5. Bochet, Olivier & Sakai, Toyotaka, 2007. "Strategic manipulations of multi-valued solutions in economies with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 53-68, January.
    6. Felix Brandt & Patrick Lederer, 2021. "Characterizing the Top Cycle via Strategyproofness," Papers 2108.04622, arXiv.org, revised Jun 2023.
    7. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    8. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    9. Wesley H. Holliday & Eric Pacuit, 2023. "Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers," Public Choice, Springer, vol. 197(1), pages 1-62, October.
    10. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    11. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    12. Eraslan, H.Hulya & McLennan, Andrew, 2004. "Strategic candidacy for multivalued voting procedures," Journal of Economic Theory, Elsevier, vol. 117(1), pages 29-54, July.
    13. Felix Brandt & Chris Dong, 2022. "On Locally Rationalizable Social Choice Functions," Papers 2204.05062, arXiv.org, revised Mar 2024.
    14. Masashi Umezawa, 2009. "Coalitionally strategy-proof social choice correspondences and the Pareto rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 151-158, June.
    15. Hiroki Saitoh, 2022. "Characterization of tie-breaking plurality rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 139-173, July.
    16. Cato, Susumu, 2011. "Maskin monotonicity and infinite individuals," Economics Letters, Elsevier, vol. 110(1), pages 56-59, January.
    17. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
    18. Lê Nguyên Hoang, 2017. "Strategy-proofness of the randomized Condorcet voting system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 679-701, March.
    19. Felix Brandt & Markus Brill & Felix Fischer & Paul Harrenstein, 2014. "Minimal retentive sets in tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 551-574, March.
    20. KayI, Çagatay & Ramaekers, Eve, 2010. "Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems," Games and Economic Behavior, Elsevier, vol. 68(1), pages 220-232, January.

    More about this item

    Keywords

    D71; C70;

    JEL classification:

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

    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:45:y:2015:i:4:p:793-804. 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.