IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00759869.html
   My bibliography  Save this paper

Borda's Paradox with weighted scoring rules

Author

Listed:
  • Mostapha Diss

    () (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon)

  • William V. Gehrlein

Abstract

Representations are obtained for the probabilities that a Strict Borda Paradox and a Strong Borda Paradox are observed for large electorates with three candidates under the standard assumptions of Impartial Culture and Impartial Anonymous Culture. These representations are obtained for general weighted scoring rules (WSRs), and the probabilities are found to be maximized for voting rules like plurality rule and negative plurality rule. It is found that these paradox probabilities are not reduced for every scoring rule with the introduction of some degree of dependence among voters' preferences with IAC. It is concluded that actual observances of a Strict Borda Paradox should be extremely rare, and that while observances of a Strong Borda Paradox should also be rare, they might occasionally be witnessed.

Suggested Citation

  • Mostapha Diss & William V. Gehrlein, 2012. "Borda's Paradox with weighted scoring rules," Post-Print halshs-00759869, HAL.
  • Handle: RePEc:hal:journl:halshs-00759869
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00759869
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tataru, Maria & Merlin, Vincent, 1997. "On the relationship of the Condorcet winner and positional voting rules," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 81-90, August.
    2. Van Newenhizen, Jill, 1992. "The Borda Method Is Most Likely to Respect the Condorcet Principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 69-83, January.
    3. Gehrlein, William V., 2004. "The effectiveness of weighted scoring rules when pairwise majority rule cycles exist," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 69-85, January.
    4. Thom Bezembinder, 1996. "The plurality majority converse under single peakedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 365-380.
    5. Davide Cervone & William Gehrlein & William Zwicker, 2005. "Which Scoring Rule Maximizes Condorcet Efficiency Under Iac?," Theory and Decision, Springer, vol. 58(2), pages 145-185, March.
    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 & Eric Kamwa & Abdelmonaim Tlidi, 2018. "A Note on the Likelihood of the Absolute Majority Paradoxes," Economics Bulletin, AccessEcon, vol. 38(4), pages 1727-1734.
    2. Eric Kamwa, 2018. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Working Papers hal-01786590, HAL.
    3. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    4. Gehrlein, William V. & Lepelley, Dominique & Moyouwou, Issofa, 2016. "A note on Approval Voting and electing the Condorcet loser," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 115-122.
    5. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    6. Eric Kamwa, 2019. "Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser," Theory and Decision, Springer, vol. 87(3), pages 299-320, October.
    7. 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.
    8. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    9. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    10. 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.
    11. Eric Kamwa & Fabrice Valognes, 2017. "Scoring Rules and Preference Restrictions: The Strong Borda Paradox Revisited," Revue d'économie politique, Dalloz, vol. 127(3), pages 375-395.
    12. 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.
    13. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    14. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    15. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers hal-01757761, HAL.
    16. 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.
    17. 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.
    18. McIntee, Tomas J. & Saari, Donald G., 2017. "Likelihood of voting outcomes with generalized IAC probabilities," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 1-10.
    19. 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. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    2. Eric Kamwa, 2018. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Working Papers hal-01786590, HAL.
    3. Kamwa, Eric & Merlin, Vincent, 2015. "Scoring rules over subsets of alternatives: Consistency and paradoxes," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 130-138.
    4. 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.
    5. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
    6. William Gehrlein & Dominique Lepelley, 2010. "On the probability of observing Borda’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 1-23, June.
    7. Regenwetter, Michel & Grofman, Bernard & Marley, A. A. J., 2002. "On the model dependence of majority preference relations reconstructed from ballot or survey data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 451-466, July.
    8. 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.
    9. Gehrlein, William V. & Moyouwou, Issofa & Lepelley, Dominique, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 352-365.
    10. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    11. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    12. 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.
    13. Zachary F. Lansdowne, 1996. "Ordinal ranking methods for multicriterion decision making," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 613-627, August.
    14. 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.
    15. 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.
    16. Eric Kamwa & Vincent Merlin, 2018. "The Likelihood of the Consistency of Collective Rankings under Preferences Aggregation with Four Alternatives using Scoring Rules: A General Formula and the Optimal Decision Rule," Working Papers hal-01757742, HAL.
    17. 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.
    18. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "A Note on the Likelihood of the Absolute Majority Paradoxes," Economics Bulletin, AccessEcon, vol. 38(4), pages 1727-1734.
    19. Martin, Mathieu & Merlin, Vincent, 2002. "The stability set as a social choice correspondence," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 91-113, September.
    20. William V. Gehrlein & Dominique Lepelley & Florenz Plassmann, 2016. "Should voters be required to rank candidates in an election?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 707-747, April.

    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:hal:journl:halshs-00759869. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.