IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v62y2016i4d10.1007_s00199-015-0930-7.html
   My bibliography  Save this article

Characterizing the resolute part of monotonic social choice correspondences

Author

Listed:
  • Fasil Alemante

    (The College of William and Mary)

  • Donald E. Campbell

    (The College of William and Mary)

  • Jerry S. Kelly

    (Syracuse University)

Abstract

The resolute domain of a social choice correspondence is the set of profiles at which only one alternative is selected. The Condorcet, plurality, approval voting, and maximin correspondences—restricted to their respective resolute domains—satisfy anonymity, neutrality, and a strong monotonicity condition, but are not characterized by those three conditions. We present examples illustrating this and provide additional conditions that do suffice for characterization.

Suggested Citation

  • Fasil Alemante & Donald E. Campbell & Jerry S. Kelly, 2016. "Characterizing the resolute part of monotonic social choice correspondences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 765-783, October.
    • Handle: RePEc:spr:joecth:v:62:y:2016:i:4:d:10.1007_s00199-015-0930-7
    DOI: 10.1007/s00199-015-0930-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-015-0930-7
    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/s00199-015-0930-7?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. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, vol. 42(2), pages 382-386, August.
    2. Carmen Herrero, 1996. "Capabilities and utilities," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 69-88, December.
    3. Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, July.
    4. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.
    5. Powers, R.C., 2010. "Maskin monotonic aggregation rules and partial anonymity," Economics Letters, Elsevier, vol. 106(1), pages 12-14, January.
    6. Samejima, Yusuke, 2005. "Strategic candidacy, monotonicity, and strategy-proofness," Economics Letters, Elsevier, vol. 88(2), pages 190-195, August.
    7. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
    8. Quesada, Antonio, 2010. "Monotonicity + efficiency + continuity = majority," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 149-153, September.
    9. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    10. Jain, Satish K., 1988. "Characterization of monotonicity and neutrality for binary Paretian social decision rules," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 307-312, June.
    11. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    12. Yasuhito Tanaka, 2001. "Generalized monotonicity and strategy-proofness: A note," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-6.
    13. Dipjyoti Majumdar & Arunava Sen, 2006. "Top-Pair and Top-Triple Monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 175-187, August.
    14. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    15. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
    16. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745.
    17. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 575-583, March.
    18. Satish Jain, 1996. "Structure of neutral and monotonic binary social decision rules with quasi-transitive individual preferences," Journal of Economics, Springer, vol. 64(2), pages 195-212, June.
    19. Kutlu, Levent, 2007. "Superdictatorial domains for monotonic social choice functions," Economics Letters, Elsevier, vol. 97(2), pages 151-154, November.
    20. Guha, Ashok, 1972. "Neutrality, Monotonicity, and the Right of Veto," Econometrica, Econometric Society, vol. 40(5), pages 821-826, September.
    21. Mark A. Chen, 2000. "Individual monotonicity and the leximin solution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 353-365.
    22. Barberà, Salvador & Moreno, Bernardo, 2011. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Games and Economic Behavior, Elsevier, vol. 73(2), pages 345-359.
    23. Takamiya, Koji, 2007. "Domains of social choice functions on which coalition strategy-proofness and Maskin monotonicity are equivalent," Economics Letters, Elsevier, vol. 95(3), pages 348-354, June.
    24. 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.
    25. Sylvain J. Durand, 2001. "A note on monotonicity in iterated choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 129-134.
    26. M. Sanver & William Zwicker, 2009. "One-way monotonicity as a form of strategy-proofness," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 553-574, November.
    27. Perry, Jonathan & Powers, Robert C., 2010. "Anonymity, monotonicity, and quota pair systems," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 57-60, July.
    28. Yasuhito Tanaka, 2001. "Generalized monotonicity and strategy-proofness for non-resolute social choice correspondences," Economics Bulletin, AccessEcon, vol. 4(12), pages 1-8.
    29. Mizukami, Hideki & Wakayama, Takuma, 2009. "The relation between non-bossiness and monotonicity," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 256-264, September.
    30. Blau, Julian H, 1976. "Neutrality, Monotonicity, and the Right of Veto: A Comment," Econometrica, Econometric Society, vol. 44(3), pages 603-603, May.
    31. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 461-471, June.
    32. Kutlu, Levent, 2009. "A dictatorial domain for monotone social choice functions," Economics Letters, Elsevier, vol. 105(1), pages 14-16, October.
    33. Yi, Jianxin, 2007. "Monotonicity, implementation and generalized strategy-proofness," Economics Letters, Elsevier, vol. 97(2), pages 124-127, November.
    34. Sethuraman, Jay & Teo, Chung-Piaw & Vohra, Rakesh V., 2006. "Anonymous monotonic social welfare functions," Journal of Economic Theory, Elsevier, vol. 128(1), pages 232-254, May.
    35. Manimay Sengupta, 1980. "Monotonicity, Independence of Irrelevant Alternatives and Strategy-Proofness of Social Decision Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 393-407.
    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. Kelly, Jerry S. & Qi, Shaofang, 2019. "Balancedness of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 59-67.
    2. Deirdre Haskell & Jeremiah Hurley & Junying Zhao, 2023. "The Possibility of Anonymous Social Orderings Using Curvature of Indifference Hypersurfaces," Department of Economics Working Papers 2023-06, McMaster University.
    3. Stergios Athanasoglou & Somouaoga Bonkoungou & Lars Ehlers, 2023. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Working Papers 519, University of Milano-Bicocca, Department of Economics.

    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. Kelly, Jerry S. & Qi, Shaofang, 2016. "Characterizing plurality rule on a fixed population," Economics Letters, Elsevier, vol. 146(C), pages 39-41.
    2. Walter Bossert & Kotaro Suzumura, 2020. "Positionalist voting rules: a general definition and axiomatic characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 85-116, June.
    3. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
    4. Cato, Susumu, 2011. "Maskin monotonicity and infinite individuals," Economics Letters, Elsevier, vol. 110(1), pages 56-59, January.
    5. Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
    6. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    7. Sato, Shin, 2016. "Informational requirements of social choice rules to avoid the Condorcet loser: A characterization of the plurality with a runoff," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 11-19.
    8. 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.
    9. Charles Blackorby & Walter Bossert & David Donaldson, 2005. "Multi-profile welfarism: A generalization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(2), pages 253-267, April.
    10. Clemens Puppe & Attila Tasnádi, 2008. "Nash implementable domains for the Borda count," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 367-392, October.
    11. Z. Emel Öztürk, 2020. "Consistency of scoring rules: a reinvestigation of composition-consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 801-831, September.
    12. 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.
    13. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    14. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    15. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    16. Walter Bossert & Kotaro Suzumura, 2017. "The greatest unhappiness of the least number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 637-655, December.
    17. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    18. Z. Emel Ozturk, 2017. "A composition-consistency characterization of the plurality rule," Working Papers 2017_04, Business School - Economics, University of Glasgow.
    19. Umut Keskin & M. Remzi Sanver & H. Berkay Tosunlu, 2021. "Recovering non-monotonicity problems of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(1), pages 125-141, January.
    20. Sato, Shin, 2009. "Informational requirements of social choice rules," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 188-198, March.

    More about this item

    Keywords

    Social choice correspondence; Social choice function; Resolute domain; Anonymity; Neutrality; Monotonicity; Upper invariance; Lower invariance; Condorcet; Plurality voting; Approval voting; Maximin;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • 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:spr:joecth:v:62:y:2016:i:4:d:10.1007_s00199-015-0930-7. 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.