IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-14-01048.html
   My bibliography  Save this article

Condorcet's Paradox and the Median Voter Theorem for Randomized Social Choice

Author

Listed:
  • Haris Aziz

    (NICTA and UNSW)

Abstract

Condorcet's paradox is one of the most prominent results in social choice theory. It says that there may not exist any alternative that a net majority prefers over every other alternative. When outcomes need not be deterministic alternatives, we show that a similar paradox still exists even if preferences are dichotomous. Thus relaxing the requirement of discrete alternatives does not help in circumventing Condorcet's paradox. On the other hand, we show that a fractional/randomized version of Black's Median Voter Theorem still holds for single-peaked preferences.

Suggested Citation

  • Haris Aziz, 2015. "Condorcet's Paradox and the Median Voter Theorem for Randomized Social Choice," Economics Bulletin, AccessEcon, vol. 35(1), pages 745-749.
    • Handle: RePEc:ebl:ecbull:eb-14-01048
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2015/Volume35/EB-15-V35-I1-P78.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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).
    2. Brandl, Florian & Brandt, Felix, 0. "A natural adaptive process for collective decision-making," Theoretical Economics, Econometric Society.
    3. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    4. Tom Demeulemeester & Dries Goossens & Ben Hermans & Roel Leus, 2023. "Fair integer programming under dichotomous and cardinal preferences," Papers 2306.13383, arXiv.org, revised Apr 2024.
    5. Florian Brandl & Felix Brandt, 2021. "A Natural Adaptive Process for Collective Decision-Making," Papers 2103.14351, arXiv.org, revised Mar 2024.
    6. 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.
    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. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2022. "Efficiency in Random Resource Allocation and Social Choice," Papers 2203.06353, arXiv.org, revised Aug 2022.
    9. 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.
    10. Peter Fishburn & Steven Brams, 1984. "Manipulability of voting by sincere truncation of preferences," Public Choice, Springer, vol. 44(3), pages 397-410, January.
    11. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    12. Yaron Azrieli & Christopher P. Chambers & Paul J. Healy, 2020. "Incentives in experiments with objective lotteries," Experimental Economics, Springer;Economic Science Association, vol. 23(1), pages 1-29, March.
    13. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2024. "Optimal Budget Aggregation with Single-Peaked Preferences," Papers 2402.15904, arXiv.org.
    14. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    15. Picot, Jérémy & Sen, Arunava, 2012. "An extreme point characterization of random strategy-proof social choice functions: The two alternative case," Economics Letters, Elsevier, vol. 115(1), pages 49-52.
    16. McLennan, Andrew, 2011. "Manipulation in elections with uncertain preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 370-375.
    17. Felix Brandt & Patrick Lederer & Warut Suksompong, 2022. "Incentives in Social Decision Schemes with Pairwise Comparison Preferences," Papers 2204.12436, arXiv.org, revised Nov 2022.
    18. Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    19. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    20. Eun Jeong Heo & Vikram Manjunath, 2017. "Implementation in stochastic dominance Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 5-30, January.

    More about this item

    Keywords

    Social choice theory; Condorcet's Paradox; Median Voter Theorem; Social decision function;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    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:ebl:ecbull:eb-14-01048. 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: John P. Conley (email available below). General contact details of provider: .

    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.