IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v202y2022ics0022053122000370.html
   My bibliography  Save this article

Strategyproof social choice when preferences and outcomes may contain ties

Author

Listed:
  • Brandt, Felix
  • Saile, Christian
  • Stricker, Christian

Abstract

The Gibbard-Satterthwaite theorem implies that all anonymous, Pareto-optimal, and single-valued social choice functions can be strategically manipulated. In this paper, we investigate whether there exist social choice correspondences (SCCs), that satisfy these conditions under various assumptions about how single alternatives are eventually selected from the choice set. These assumptions include even-chance lotteries as well as resolute choice functions and linear tie-breaking orderings unknown to the agents. We show that (i) all anonymous Pareto-optimal SCCs where ties are broken according to some linear tie-breaking ordering or by means of even-chance lotteries are manipulable, and that (ii) all pairwise Pareto-optimal SCCs are manipulable for any deterministic tie-breaking rule. These results are proved by reducing the statements to finite—yet very large—formulas in propositional logic, which are then shown to be unsatisfiable by a computer.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jetheo:v:202:y:2022:i:c:s0022053122000370
    DOI: 10.1016/j.jet.2022.105447
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053122000370
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2022.105447?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. 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.
    2. 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.
    3. 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.
    4. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 185-192.
    5. 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.
    6. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
    7. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.
    8. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    9. 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.
    10. Bandyopadhyay, Taradas, 1983. "Coalitional manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 29(2), pages 359-363, April.
    11. 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.
    12. 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.
    13. Nesterov, Alexander S., 2017. "Fairness and efficiency in strategy-proof object allocation mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 145-168.
    14. 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.
    15. 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.
    16. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    17. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    18. 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.
    19. 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.
    20. Bandyopadhyay, Taradas, 1983. "Manipulation of non-imposed, non-oligarchic, non-binary group decision rules," Economics Letters, Elsevier, vol. 11(1-2), pages 69-73.
    21. 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.
    22. 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.
    23. 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.
    24. Felix Brandt & Martin Bullinger & Patrick Lederer, 2021. "On the Indecisiveness of Kelly-Strategyproof Social Choice Functions," Papers 2102.00499, arXiv.org, revised Mar 2022.
    25. Shin Sato, 2014. "A fundamental structure of strategy-proof social choice correspondences with restricted preferences over alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 831-851, April.
    26. Zwicker, William S., 1991. "The voters' paradox, spin, and the Borda count," Mathematical Social Sciences, Elsevier, vol. 22(3), pages 187-227, December.
    27. 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.
    28. 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.
    29. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    30. Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
    31. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    32. P. C. Fishburn, 1984. "Probabilistic Social Choice Based on Simple Voting Comparisons," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 683-692.
    33. 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.
    34. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    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. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    2. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    3. Th'eo Delemazure & Tom Demeulemeester & Manuel Eberl & Jonas Israel & Patrick Lederer, 2022. "Strategyproofness and Proportionality in Party-Approval Multiwinner Elections," Papers 2211.13567, arXiv.org.
    4. Fujun Hou, 2024. "A new social welfare function with a number of desirable properties," Papers 2403.16373, 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. 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.
    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. Brandt, Felix & Lederer, Patrick & Suksompong, Warut, 2023. "Incentives in social decision schemes with pairwise comparison preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 266-291.
    6. 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.
    7. Eraslan, H.Hulya & McLennan, Andrew, 2004. "Strategic candidacy for multivalued voting procedures," Journal of Economic Theory, Elsevier, vol. 117(1), pages 29-54, July.
    8. 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.
    9. Felix Brandt & Patrick Lederer, 2021. "Characterizing the Top Cycle via Strategyproofness," Papers 2108.04622, arXiv.org, revised Jun 2023.
    10. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    11. 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.
    12. 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.
    13. 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.
    14. Shin Sato, 2014. "A fundamental structure of strategy-proof social choice correspondences with restricted preferences over alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 831-851, April.
    15. 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.
    16. Demeze-Jouatsa, Ghislain-Herman, 2022. "Ambiguous Social Choice Functions," Center for Mathematical Economics Working Papers 660, Center for Mathematical Economics, Bielefeld University.
    17. Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
    18. 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.
    19. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    20. Brandl, Florian & Brandt, Felix, 2024. "A natural adaptive process for collective decision-making," Theoretical Economics, Econometric Society, vol. 19(2), May.

    More about this item

    Keywords

    Gibbard-Satterthwaite theorem; Social choice theory; Strategyproofness; Pareto optimality;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:jetheo:v:202:y:2022:i:c:s0022053122000370. 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/622869 .

    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.