IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v21y2013i3p590-611.html
   My bibliography  Save this article

Unanimity and the Anscombe’s paradox

Author

Listed:
  • G. Laffond
  • J. Lainé

Abstract

We establish a new sufficient condition for avoiding a generalized Anscombe’s paradox. In a situation where votes describe positions regarding finitely many yes-or-no issues, the Anscombe’s α-paradox holds if more than α% of the voters disagree on a majority of issues with the outcome of issue-wise majority voting. We define the level of unanimity of a set of votes as the number of issues minus the maximal Hamming distance between two votes. We compute for the case of large electorates the exact level of unanimity above which the Anscombe’s α-paradox never holds, whatever the distribution of individuals among votes. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • G. Laffond & J. Lainé, 2013. "Unanimity and the Anscombe’s paradox," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 590-611, October.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:3:p:590-611
    DOI: 10.1007/s11750-011-0192-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11750-011-0192-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11750-011-0192-x?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 855-867, October.
    2. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    3. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    4. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, October.
    5. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    6. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, July.
    7. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
    8. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    9. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, October.
    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. Nicolas Gabriel Andjiga & Issofa Moyouwou & Monge Kleber Kamdem Ouambo, 2017. "Avoiding Majority Dissatisfaction on a Series of Majority Decisions," Group Decision and Negotiation, Springer, vol. 26(3), pages 453-471, May.
    2. Gilbert Laffond & Jean Lainé, 2014. "Triple-consistent social choice and the majority rule," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 784-799, July.
    3. Hayrullah Dindar & Gilbert Laffond & Jean Laine, 2017. "The strong referendum paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(4), pages 1707-1731, July.
    4. Hayrullah Dindar & Gilbert Laffond & Jean Lainé, 2021. "Referendum Paradox for Party-List Proportional Representation," Group Decision and Negotiation, Springer, vol. 30(1), pages 191-220, February.

    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. Steven Brams & Michael Hansen & Michael Orrison, 2006. "Dead Heat: The 2006 Public Choice Society Election," Public Choice, Springer, vol. 128(3), pages 361-366, September.
    2. Nicolas Gabriel Andjiga & Issofa Moyouwou & Monge Kleber Kamdem Ouambo, 2017. "Avoiding Majority Dissatisfaction on a Series of Majority Decisions," Group Decision and Negotiation, Springer, vol. 26(3), pages 453-471, May.
    3. Florenz Plassmann & T. Tideman, 2014. "How frequently do different voting rules encounter voting paradoxes in three-candidate elections?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 31-75, January.
    4. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    5. Tanguiane, Andranick S., 2022. "Analysis of the 2021 Bundestag elections. 4/4. The third vote application," Working Paper Series in Economics 154, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    6. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    7. Shmuel Nitzan, 2010. "Demystifying the ‘metric approach to social compromise with the unanimity criterion’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 25-28, June.
    8. Shin Sato, 2012. "On strategy-proof social choice under categorization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 455-471, March.
    9. Colignatus, Thomas, 2013. "The performance of four possible rules for selecting the Prime Minister after the Dutch Parliamentary elections of September 2012," MPRA Paper 44158, University Library of Munich, Germany, revised 02 Feb 2013.
    10. Peter Emerson, 2013. "The original Borda count and partial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 353-358, February.
    11. Andranik Tangian, 2021. "MCDM Application of the Third Vote," Group Decision and Negotiation, Springer, vol. 30(4), pages 775-787, August.
    12. Hartvigsen, David, 2006. "Vote trading in public elections," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 31-48, July.
    13. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.
    14. Antoinette Baujard, 2006. "L'estimation des préférences individuelles en vue de la décision publique.. Problèmes, paradoxes, enjeux," Economie & Prévision, La Documentation Française, vol. 0(4), pages 51-63.
    15. Herrade Igersheim, 2006. "Invoking a Cartesian Product Structure on Social States: New Resolutions of Sen's and Gibbard's Impossibility Theorems," UFAE and IAE Working Papers 659.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    16. Hanna Bury & Dariusz Wagner, 2009. "Group judgement with ties. A position-based approach," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 9-26.
    17. Diana Cheng & Peter Coughlin, 2017. "Using equations from power indices to analyze figure skating teams," Public Choice, Springer, vol. 170(3), pages 231-251, March.
    18. Antoinette Baujard, 2006. "Une critique opérationnelle du welfarisme dans la prise de décision publique," Post-Print halshs-00155130, HAL.
    19. Cook, Wade D. & Kress, Moshe & Seiford, Lawrence M., 1997. "A general framework for distance-based consensus in ordinal ranking models," European Journal of Operational Research, Elsevier, vol. 96(2), pages 392-397, January.
    20. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.

    More about this item

    Keywords

    Anscombe; Voting paradox; Majority rule; Unanimity; Issue-wise voting; 91B12;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:topjnl:v:21:y:2013:i:3:p:590-611. 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.