IDEAS home Printed from https://ideas.repec.org/p/crb/wpaper/2020-06.html
   My bibliography  Save this paper

Majority properties of positional social preference correspondences

Author

Listed:
  • Mostapha Diss

    (CRESE, Univ. Bourgogne Franche-Comté)

  • Michele Gori

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze)

Abstract

We characterize the positional social preference correspondences (spc) satisfying the qualified majority property for any given majority threshold. We also characterize the positional spcs satisfying the minimal majority property. We next evaluate the probability that the Borda, the Plurality and the Antiplurality spcs fulfil the two aforementioned properties under two assumptions on individuals’ preferences in the presence of three and four alternatives for various sizes of the society. Our results show that the Borda spc is the positional spc which better behaves in relation with the qualified majority principle and the minimal majority principle. Finally, we propose some remarks on the concept of Condorcet consistency for social choice correspondences.

Suggested Citation

  • Mostapha Diss & Michele Gori, 2020. "Majority properties of positional social preference correspondences," Working Papers 2020-06, CRESE.
    • Handle: RePEc:crb:wpaper:2020-06
    as

    Download full text from publisher

    File URL: https://crese.univ-fcomte.fr/uploads/wp/WP-2020-06.pdf
    File Function: First version, 2020
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    2. Michele Gori, 2014. "Selecting anonymous, neutral and reversal symmetric minimal majority rules," Working Papers - Mathematical Economics 2014-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    3. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2015. "The q-majority efficiency of positional rules," Post-Print hal-00914907, HAL.
    4. 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.
    5. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    6. Bubboloni, Daniela & Gori, Michele, 2015. "Symmetric majority rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 73-86.
    7. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, December.
    8. Abdelhalim El Ouafdi & Issofa Moyouwou & Hatem Smaoui, 2021. "IAC Probability Calculations in Voting Theory: Progress Report," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 399-416, Springer.
    9. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
    10. 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.
    11. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    12. 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.
    13. Mathieu Martin & Sebastien Courtin & Bertrand Tchantcho, 2015. "Positional rules and q-Condorcet consistency," Post-Print hal-02979994, HAL.
    14. Mostapha Diss & Vincent Merlin (ed.), 2021. "Evaluating Voting Systems with Probability Models," Studies in Choice and Welfare, Springer, number 978-3-030-48598-6, December.
    15. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    16. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    17. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "Probabilities of electoral outcomes: from three-candidate to four-candidate elections," Theory and Decision, Springer, vol. 88(2), pages 205-229, March.
    18. 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.
    19. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, December.
    20. Mathieu Martin & Sebastien Courtin & Issofa Moyouwou, 2015. "The q-Condorcet efficiency of the positional rules," Post-Print hal-02979993, HAL.
    21. Can, Burak & Storcken, Ton, 2013. "Update monotone preference rules," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 136-149.
    22. Winfried Bruns & Bogdan Ichim & Christof Söger, 2019. "Computations of volumes and Ehrhart series in four candidates elections," Annals of Operations Research, Springer, vol. 280(1), pages 241-265, September.
    23. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    24. J. Craven, 1971. "Majority Voting and Social Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 265-267.
    25. Sébastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2015. "Positional rules and q-Condorcet consistency," Post-Print hal-00914900, HAL.
    26. Sébastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2015. "Positional rules and q-Condorcet consistency," Review of Economic Design, Springer;Society for Economic Design, vol. 19(3), pages 229-245, September.
    27. William V. Gehrlein, 2006. "Condorcet’s Paradox," Theory and Decision Library C, Springer, number 978-3-540-33799-7, March.
    28. Alexander I. Barvinok, 1994. "A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 769-779, November.
    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. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    2. 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.
    3. 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.
    4. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2022. "Inconsistent weighting in weighted voting games," Public Choice, Springer, vol. 191(1), pages 75-103, April.
    5. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "Probabilities of electoral outcomes: from three-candidate to four-candidate elections," Theory and Decision, Springer, vol. 88(2), pages 205-229, March.
    6. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.
    7. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    8. 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.
    9. Eric Kamwa, 2021. "To what extent does the model of processing sincereincomplete rankings affect the likelihood of the truncation paradox?," Working Papers hal-02879390, HAL.
    10. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers halshs-01817943, HAL.
    11. Ahmad Awde & Mostapha Diss & Eric Kamwa & Julien Yves Rolland & Abdelmonaim Tlidi, 2023. "Social Unacceptability for Simple Voting Procedures," Studies in Choice and Welfare, in: Sascha Kurz & Nicola Maaser & Alexander Mayer (ed.), Advances in Collective Decision Making, pages 25-42, Springer.
    12. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    13. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    14. Ahmad Awde & Mostapha Diss & Eric Kamwa & Julien Yves Rolland & Abdelmonaim Tlidi, 2022. "Social unacceptability for simple voting procedures," Working Papers hal-03614587, HAL.
    15. Eric Kamwa & Issofa Moyouwou, 2019. "Susceptibility to Manipulation by Sincere Truncation : the Case of Scoring Rules and Scoring Runoff Systems," Working Papers hal-02185965, HAL.
    16. Winfried Bruns & Bogdan Ichim & Christof Söger, 2019. "Computations of volumes and Ehrhart series in four candidates elections," Annals of Operations Research, Springer, vol. 280(1), pages 241-265, September.
    17. Diss, Mostapha & Tsvelikhovskiy, Boris, 2021. "Manipulable outcomes within the class of scoring voting rules," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 11-18.
    18. Eric Kamwa & Issofa Moyouwou, 2021. "Susceptibility to Manipulation by Sincere Truncation: The Case of Scoring Rules and Scoring Runoff Systems," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 275-295, Springer.
    19. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    20. 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.

    More about this item

    Keywords

    social preference correspondence; social choice correspondence; positional rule; qualified majority; probability; Condorcet consistency.;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:crb:wpaper:2020-06. 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: Lauent Kondratuk (email available below). General contact details of provider: https://edirc.repec.org/data/crufcfr.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.