IDEAS home Printed from https://ideas.repec.org/a/spr/reecde/v17y2013i3p239-248.html
   My bibliography  Save this article

On the structure of voting systems between two alternatives

Author

Listed:
  • Bonifacio Llamazares

Abstract

Voting systems between two alternatives have been widely studied in the literature of Social Choice. One of the results given by Fishburn (The theory of social choice. Princeton University Press, Princeton, 1973 ) allows us to characterize anonymous, neutral and monotonic voting systems by means of functions satisfying adequate conditions. From among all kinds of functions, the class of affine functions is highly interesting because from them it is possible to obtain the voting systems most used in practice. In this paper we analyze the structure of the set of these functions and we show that this set is convex and its extreme points are the functions that generate the following voting systems: simple majority, absolute majority, unanimous majority and Pareto majority. Moreover, we suggest a simple method for choosing a voting system when two alternatives are under consideration. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Bonifacio Llamazares, 2013. "On the structure of voting systems between two alternatives," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 239-248, September.
    • Handle: RePEc:spr:reecde:v:17:y:2013:i:3:p:239-248
    DOI: 10.1007/s10058-013-0146-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10058-013-0146-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10058-013-0146-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 search for a different version of it.

    References listed on IDEAS

    as
    1. Houy, Nicolas, 2007. "Some further characterizations for the forgotten voting rules," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 111-121, January.
    2. Fishburn, P. C., 1983. "A new characterization of simple majority," Economics Letters, Elsevier, vol. 13(1), pages 31-35.
    3. Remzi Sanver, M., 2006. "Nash implementation of the majority rule," Economics Letters, Elsevier, vol. 91(3), pages 369-372, June.
    4. Quesada, Antonio, 2011. "Parallel axiomatizations of majority and unanimity," Economics Letters, Elsevier, vol. 111(2), pages 151-154, May.
    5. Quesada, Antonio, 2010. "Monotonicity + efficiency + continuity = majority," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 149-153, September.
    6. Nicolas Houy, 2007. "A new characterization of absolute qualified majority voting," Economics Bulletin, AccessEcon, vol. 4(4), pages 1-8.
    7. Asan, Goksel & Sanver, M. Remzi, 2002. "Another characterization of the majority rule," Economics Letters, Elsevier, vol. 75(3), pages 409-413, May.
    8. Xu, Yongsheng & Zhong, Zhen, 2010. "Single profile of preferences with variable societies: A characterization of simple majority rule," Economics Letters, Elsevier, vol. 107(2), pages 119-121, May.
    9. Asan, Goksel & Sanver, M. Remzi, 2006. "Maskin monotonic aggregation rules," Economics Letters, Elsevier, vol. 91(2), pages 179-183, May.
    10. Miroiu, Adrian, 2004. "Characterizing majority rule: from profiles to societies," Economics Letters, Elsevier, vol. 85(3), pages 359-363, December.
    11. Woeginger, Gerhard J., 2005. "More on the majority rule: Profiles, societies, and responsiveness," Economics Letters, Elsevier, vol. 88(1), pages 7-11, July.
    12. Antonio Quesada, 2013. "The majority rule with a chairman," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 679-691, March.
    13. J. Woeginger, Gerhard, 2003. "A new characterization of the majority rule," Economics Letters, Elsevier, vol. 81(1), pages 89-94, October.
    14. J. Craven, 1971. "Majority Voting and Social Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 265-267.
    15. Llamazares, Bonifacio, 2006. "The forgotten decision rules: Majority rules based on difference of votes," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 311-326, May.
    16. M. Sanver, 2009. "Characterizations of majoritarianism: a unified approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 159-171, June.
    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. Cailloux, Olivier & Hervouin, Matthieu & Ozkes, Ali I. & Sanver, M. Remzi, 2024. "Classification aggregation without unanimity," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 6-9.
    2. King, Sarah Schulz & Powers, Robert C., 2018. "Beyond neutrality: Extended difference of votes rules," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 146-152.
    3. Bandhu, Sarvesh & Lahiri, Abhinaba & Pramanik, Anup, 2020. "A characterization of status quo rules in the binary social choice model," Economics Letters, Elsevier, vol. 191(C).
    4. Patrick Harless, 2015. "Reaching consensus: solidarity and strategic properties in binary social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 97-121, June.

    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. Quesada, Antonio, 2011. "Parallel axiomatizations of majority and unanimity," Economics Letters, Elsevier, vol. 111(2), pages 151-154, May.
    2. José Carlos R. Alcantud, 2020. "Simple Majorities with Voice but No Vote," Group Decision and Negotiation, Springer, vol. 29(5), pages 803-822, October.
    3. Alcantud, José Carlos R., 2019. "Yet another characterization of the majority rule," Economics Letters, Elsevier, vol. 177(C), pages 52-55.
    4. Ozkes, Ali Ihsan & Sanver, M. Remzi, 2017. "Absolute qualified majoritarianism: How does the threshold matter?," Economics Letters, Elsevier, vol. 153(C), pages 20-22.
    5. Antonio Quesada, 2012. "A short step between democracy and dictatorship," Theory and Decision, Springer, vol. 72(2), pages 149-166, February.
    6. Quesada, Antonio, 2010. "Monotonicity + efficiency + continuity = majority," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 149-153, September.
    7. Antonio Quesada, 2013. "The Majority Rule with Arbitrators," Group Decision and Negotiation, Springer, vol. 22(2), pages 321-330, March.
    8. Antonio Quesada, 2013. "The majority rule with a chairman," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 679-691, March.
    9. José Luis Garcí a-Lapresta & Bonifacio Llamazares, 2010. "Preference Intensities and Majority Decisions Based on Difference of Support Between Alternatives," Group Decision and Negotiation, Springer, vol. 19(6), pages 527-542, November.
    10. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
    11. M. Sanver, 2009. "Characterizations of majoritarianism: a unified approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 159-171, June.
    12. 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.
    13. Mateusz Krukowski, 2023. "Majority rule as a unique voting method in elections with multiple candidates," Papers 2310.12983, arXiv.org.
    14. Daniela Bubboloni & Michele Gori, 2014. "Anonymous and neutral majority rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 377-401, August.
    15. Adrian Miroiu, 2021. "Majority Voting and Higher-Order Societies," Group Decision and Negotiation, Springer, vol. 30(5), pages 983-999, October.
    16. Xu, Yongsheng & Zhong, Zhen, 2010. "Single profile of preferences with variable societies: A characterization of simple majority rule," Economics Letters, Elsevier, vol. 107(2), pages 119-121, May.
    17. Llamazares, Bonifacio, 2006. "The forgotten decision rules: Majority rules based on difference of votes," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 311-326, May.
    18. repec:ebl:ecbull:v:4:y:2007:i:4:p:1-8 is not listed on IDEAS
    19. Quesada, Antonio, 2009. "Decision by majority and the right to vote," MPRA Paper 19400, University Library of Munich, Germany.
    20. Bandhu, Sarvesh & Lahiri, Abhinaba & Pramanik, Anup, 2020. "A characterization of status quo rules in the binary social choice model," Economics Letters, Elsevier, vol. 191(C).
    21. Matías Núñez & Giacomo Valletta, 2015. "The informational basis of scoring rules," Review of Economic Design, Springer;Society for Economic Design, vol. 19(4), pages 279-297, December.

    More about this item

    Keywords

    Voting systems; Simple majority; Absolute majority ; Unanimous majority; Pareto majority; D71;
    All these keywords.

    JEL classification:

    • 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:reecde:v:17:y:2013:i:3:p:239-248. 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.