IDEAS home Printed from https://ideas.repec.org/p/ema/worpap/2012-36.html
   My bibliography  Save this paper

Positional rules and q-Condorcet consistency

Author

Listed:
  • Sébastien Courtin

    (THEMA, Universite de Cergy-Pontoise)

  • Mathieu Martin

    (THEMA, Universite de Cergy-Pontoise)

  • Bertrand Tchantcho

    (THEMA, Universite de Cergy-Pontoise
    University of Yaounde I)

Abstract

A well-known result in Social Choice theory is the following: every scoring rule (positional rules) violates Condorcet consistency. A rule is Condorcet consistent when it selects the alternative that is preferred to every other alternative by a majority of individuals. In this paper, we investigate some limits of this negative result. We expose the relationship between a weaker version of the Condorcet consistency principle and the scoring rules. Our main objective is then to study the condition on the quota that ensure that positional rules (simple and sequential) satisfy this principle.

Suggested Citation

  • Sébastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2012. "Positional rules and q-Condorcet consistency," THEMA Working Papers 2012-36, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2012-36
    as

    Download full text from publisher

    File URL: http://thema.u-cergy.fr/IMG/documents/2012-36.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dominique Lepelley, 1996. "Constant scoring rules, Condorcet criteria and single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 491-500.
    2. Sebastien Courtin & Mathieu Martin & Issofa Moyouwou, 2013. "The q-Condorcet efficiency of positional rules," Working Papers hal-00914907, HAL.
    3. Eyal Baharad & Shmuel Nitzan, 2003. "The Borda rule, Condorcet consistency and Condorcet stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 685-688, October.
    4. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    5. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    6. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2013. "The q-Condorcet efficiency of positional rules," THEMA Working Papers 2013-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Donald Saari, 2006. "Which is better: the Condorcet or Borda winner?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 107-129, January.
    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. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    2. Sebastien Courtin & Mathieu Martin & Issofa Moyouwou, 2013. "The q-Condorcet efficiency of positional rules," Working Papers hal-00914907, HAL.
    3. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2015. "The $$q$$ q -majority efficiency of positional rules," Theory and Decision, Springer, vol. 79(1), pages 31-49, July.
    4. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.
    5. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2015. "The q-majority efficiency of positional rules," Post-Print hal-00914907, HAL.
    6. Aleksei Y. Kondratev & Alexander S. Nesterov, 2020. "Measuring majority power and veto power of voting rules," Public Choice, Springer, vol. 183(1), pages 187-210, April.
    7. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2013. "The q-Condorcet efficiency of positional rules," THEMA Working Papers 2013-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    9. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2019. "Condorcet efficiency of general weighted scoring rules under IAC: indifference and abstention," Working Papers hal-02196387, HAL.

    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. Sebastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2013. "Positional rules and q- Condorcet consistency," Working Papers hal-00914900, HAL.
    2. Sébastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2015. "Positional rules and q-Condorcet consistency," Post-Print hal-00914900, HAL.
    3. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    4. Hannu Nurmi & Hannu Salonen, 2008. "More Borda Count Variations for Project Assesment," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(2), pages 109-122, September.
    5. Eyal Baharad & Shmuel Nitzan, 2016. "Is majority consistency possible?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 287-299, February.
    6. Bock, Hans-Hermann & Day, William H. E. & McMorris, F. R., 1998. "Consensus rules for committee elections," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 219-232, May.
    7. Burak Can & Peter Csoka & Emre Ergin, 2017. "How to choose a non-manipulable delegation?," CERS-IE WORKING PAPERS 1713, Institute of Economics, Centre for Economic and Regional Studies.
    8. Núñez, Matías & Sanver, M. Remzi, 2017. "Revisiting the connection between the no-show paradox and monotonicity," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 9-17.
    9. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
    10. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    11. Antonin Macé, 2017. "Voting with evaluations: characterizations of evaluative voting and range voting," Working Papers halshs-01222200, HAL.
    12. Csóka, Péter & Kondor, Gábor, 2019. "Delegációk igazságos kiválasztása társadalmi választások elméletével [Choosing a fair delegation by social choice theory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 771-787.
    13. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    14. Joaquín Pérez & José L. Jimeno & Estefanía García, 2015. "No Show Paradox and the Golden Number in Generalized Condorcet Voting Methods," Group Decision and Negotiation, Springer, vol. 24(3), pages 497-513, May.
    15. Kelly, Jerry S. & Qi, Shaofang, 2019. "Balancedness of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 59-67.
    16. 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.
    17. Lederer, Patrick, 2024. "Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule," Journal of Economic Theory, Elsevier, vol. 218(C).
    18. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    19. Brady, Richard L. & Chambers, Christopher P., 2015. "Spatial implementation," Games and Economic Behavior, Elsevier, vol. 94(C), pages 200-205.
    20. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.

    More about this item

    Keywords

    Positional rules (Simple and Sequential) . Condorcet Consistency . q-majority;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ema:worpap:2012-36. 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: Stefania Marcassa (email available below). General contact details of provider: https://edirc.repec.org/data/themafr.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.