IDEAS home Printed from https://ideas.repec.org/p/spo/wpmain/infohdl2441-10273.html
   My bibliography  Save this paper

The Probability of Condorcet Cycles and Super-Majority Rules

Author

Listed:
  • Yves Balasko

    (Department of Economics and Related Studies)

  • Hervé Crès

Abstract

Majority voting aggregates individual preference profiles into a binary relation on the set of alternatives. Condorcet cycles are cycles of the aggregated binary relation. We show that the relative volume of the subset of the (n!−1)-simplex that represents profile distributions such that the aggregated preferences display Condorcet cycles is a decreasing function of the super majority levelτbounded by the expressionThis expression shows that Condorcet cycles become rare events for super majority rules larger than 53%.

Suggested Citation

  • Yves Balasko & Hervé Crès, 1997. "The Probability of Condorcet Cycles and Super-Majority Rules," Sciences Po publications info:hdl:2441/10273, Sciences Po.
    • Handle: RePEc:spo:wpmain:info:hdl:2441/10273
    as

    Download full text from publisher

    File URL: https://spire.sciencespo.fr/hdl:/2441/10273/resources/1997-balasko-cres-the-probability-of-condorcet-cycles-and-super-majority-rules.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kramer, Gerald H, 1973. "On a Class of Equilibrium Conditions for Majority Rule," Econometrica, Econometric Society, vol. 41(2), pages 285-297, March.
    2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    3. Gordon Tullock, 1967. "The General Irrelevance of the General Impossibility Theorem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(2), pages 256-270.
    4. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    5. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    6. DeMeyer, Frank & Plott, Charles R, 1970. "The Probability of a Cyclical Majority," Econometrica, Econometric Society, vol. 38(2), pages 345-354, March.
    7. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
    8. Kelly, Jerry S, 1974. "Voting Anomalies, the Number of Voters, and the Number of Alternatives," Econometrica, Econometric Society, vol. 42(2), pages 239-251, March.
    9. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
    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. Ngoie, Ruffin-Benoit M., 2012. "Choix social et partage équitable : Une analyse mathématique a posteriori des élections législatives et présidentielles de 2006 et 2011 en RDC [Social choice and fair sharing: An a posteriori mathe," MPRA Paper 64915, University Library of Munich, Germany.
    2. Mich Tvede & Hervé Crés, 2005. "Voting in assemblies of shareholders and incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 887-906, November.
    3. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Consistent collective decisions under majorities based on difference of votes," Theory and Decision, Springer, vol. 80(3), pages 473-494, March.
    4. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support," Group Decision and Negotiation, Springer, vol. 25(5), pages 967-994, September.
    5. Estelle Cantillon & Antonio Rangel, 2002. "A graphical analysis of some basic results in social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 587-611.
    6. Tovey, Craig A., 1997. "Probabilities of Preferences and Cycles with Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 271-279, August.
    7. repec:hal:spmain:info:hdl:2441/10283 is not listed on IDEAS
    8. Truchon, Michel, 1999. "La démocratie : oui, mais laquelle?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(1), pages 189-214, mars-juin.
    9. Roger D. Congleton, 2016. "Gordon Tullock’s implicit analytical history of government," Constitutional Political Economy, Springer, vol. 27(2), pages 179-193, June.
    10. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2023. "Decentralized revenue sharing from broadcasting sports," Public Choice, Springer, vol. 194(1), pages 27-44, January.
    11. Ram Sewak Dubey & Giorgio Laguzzi, 2022. "How rare are the properties of binary relations?," Papers 2202.05229, arXiv.org.
    12. Vicki Knoblauch, 2014. "Preference, topology and measure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 507-514, August.
    13. Eivind Stensholt, 2013. "What shall we do with the cyclic profile?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 229-262, January.
    14. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers halshs-01241996, HAL.
    15. Roger Congleton, 2012. "The constitutional political economy of Gordon Tullock," Public Choice, Springer, vol. 152(1), pages 131-146, July.
    16. Vicki Knoblauch, 2015. "Two preference metrics provide settings for the study of properties of binary relations," Theory and Decision, Springer, vol. 79(4), pages 615-625, December.
    17. repec:hal:wpspec:info:hdl:2441/10283 is not listed on IDEAS
    18. repec:spo:wpecon:info:hdl:2441/10283 is not listed on IDEAS
    19. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

    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. repec:hal:spmain:info:hdl:2441/10273 is not listed on IDEAS
    2. Hervé Crès, 2001. "Aggregation of coarse preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 507-525.
    3. Yves Balasko & Hervé Crès, 1997. "The Probability of Condorcet Cycles and Super-Majority Rules," Post-Print hal-03458336, HAL.
    4. repec:hal:spmain:info:hdl:2441/10286 is not listed on IDEAS
    5. repec:hal:wpspec:info:hdl:2441/10286 is not listed on IDEAS
    6. Hervé Crès, 2000. "Aggregation of Coarse Preferences," SciencePo Working papers Main hal-01064879, HAL.
    7. repec:spo:wpecon:info:hdl:2441/10286 is not listed on IDEAS
    8. Hervé Crès, 2000. "Aggregation of Coarse Preferences," SciencePo Working papers hal-01064879, HAL.
    9. repec:hal:spmain:info:hdl:2441/10284 is not listed on IDEAS
    10. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    11. Hervé Crès, 2000. "Majority Stable Production Equilibria: A Multivariate Mean Shareholders Theorem," Working Papers hal-00598173, HAL.
    12. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    13. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09iepsg269m is not listed on IDEAS
    14. Hervé Crès & Mich Tvede, 2001. "Proxy fights in incomplete markets: when majority voting and sidepayments are equivalent," Sciences Po publications 726/2001, Sciences Po.
    15. William Gehrlein, 2002. "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences ," Theory and Decision, Springer, vol. 52(2), pages 171-199, March.
    16. Hervé Crès & M. Utku Ünver, 2010. "Ideology and Existence of 50%-Majority Equilibria in Multidimensional Spatial Voting Models," Journal of Theoretical Politics, , vol. 22(4), pages 431-444, October.
    17. Regenwetter, Michel & Marley, A. A. J. & Grofman, Bernard, 2002. "A general concept of majority rule," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 405-428, July.
    18. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    19. Grandmont, Jean-Michel, 1992. "Transformations of the commodity space, behavioral heterogeneity, and the aggregation problem," Journal of Economic Theory, Elsevier, vol. 57(1), pages 1-35.
    20. Tanner, Thomas Cole, 1994. "The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space," ISU General Staff Papers 1994010108000018174, Iowa State University, Department of Economics.
    21. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    22. repec:spo:wpecon:info:hdl:2441/10284 is not listed on IDEAS
    23. repec:hal:spmain:info:hdl:2441/10282 is not listed on IDEAS
    24. repec:hal:wpspec:info:hdl:2441/10284 is not listed on IDEAS
    25. Roberts, Kevin, 2015. "Dynamic voting in clubs," Research in Economics, Elsevier, vol. 69(3), pages 320-335.
    26. Hervé Crès & Mich Tvede, 2005. "Portfolio Diversification and Internalization of Production Externalities through Majority Voting," Working Papers hal-00587205, HAL.
    27. Crès, Hervé & Utku Ünver, M., 2017. "Toward a 50%-majority equilibrium when voters are symmetrically distributed," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 145-149.
    28. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    29. repec:spo:wpecon:info:hdl:2441/10281 is not listed on IDEAS
    30. repec:hal:spmain:info:hdl:2441/10277 is not listed on IDEAS
    31. repec:spo:wpecon:info:hdl:2441/10277 is not listed on IDEAS
    32. repec:hal:wpspec:info:hdl:2441/10277 is not listed on IDEAS
    33. repec:hal:spmain:info:hdl:2441/10281 is not listed on IDEAS
    34. repec:hal:wpspec:info:hdl:2441/10281 is not listed on IDEAS
    35. Riste Gjorgjiev & Dimitrios Xefteris, 2015. "Transitive supermajority rule relations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 299-312, October.

    More about this item

    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:spo:wpmain:info:hdl:2441/10273. 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: Spire @ Sciences Po Library (email available below). General contact details of provider: https://edirc.repec.org/data/ecspofr.html .

    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.