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The Borda Method Is Most Likely to Respect the Condorcet Principle

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  • Van Newenhizen, Jill

Abstract

We prove that in the class of weighted voting systems the Borda Count maximizes the probability that a Condorcet candidate is ranked first in a group election. A direct result is that the Borda Count maximizes the probability that a transitive, binary ranking of the candidates is preserved in a group election. A preliminary result, but one of independent interest, is that the Borda Count maximizes the probability that a majority outcome between any two candidates is reflected by the group election. All theorems are valid when there is a uniform probability distribution on the voter profiles and can be generalized to other "uniform-like" probability distributions. This work extends previous results of Fishburn and Gehrlein from three candidates to any number of candidates.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:2:y:1992:i:1:p:69-83
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    Citations

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    Cited by:

    1. 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.
    2. Stensholt, Eivind, 1999. "Beta distributions in a simplex and impartial anonymous cultures," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 45-57, January.
    3. Agnes Erzse & Teurai Rwafa-Ponela & Petronell Kruger & Feyisayo A. Wayas & Estelle Victoria Lambert & Clarisse Mapa-Tassou & Edwin Ngwa & Susan Goldstein & Louise Foley & Karen J. Hofman & Stephanie T, 2022. "A Mixed-Methods Participatory Intervention Design Process to Develop Intervention Options in Immediate Food and Built Environments to Support Healthy Eating and Active Living among Children and Adoles," IJERPH, MDPI, vol. 19(16), pages 1-12, August.
    4. Dominique Lepelley, 1994. "Condorcet efficiency of positional voting rules with single-peaked preferences," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 289-299, December.
    5. 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.
    6. 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.
    7. 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.
    8. Mostapha Diss & William Gehrlein, 2012. "Borda’s Paradox with weighted scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 121-136, January.
    9. Gehrlein, William V. & Lepelley, Dominique, 2001. "The Condorcet efficiency of Borda Rule with anonymous voters," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 39-50, January.
    10. 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.
    11. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 365-391, February.
    12. 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.
    13. Emilio De Santis & Fabio Spizzichino, 2023. "Construction of voting situations concordant with ranking patterns," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 129-156, June.
    14. 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.
    15. Marcel Richter & Kam-Chau Wong, 2008. "Preference densities and social choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 225-238, August.
    16. Sandro Ambuehl & B. Douglas Bernheim, 2021. "Interpreting the will of the people: social preferences over ordinal outcomes," ECON - Working Papers 395, Department of Economics - University of Zurich, revised Jan 2024.
    17. Keith L. Dougherty & Robi Ragan, 2024. "Borda count in a forward agenda," Public Choice, Springer, vol. 199(1), pages 27-44, April.
    18. Sandro Ambuehl & B. Douglas Bernheim, 2021. "Interpreting the Will of the People - A Positive Analysis of Ordinal Preference Aggregation," CESifo Working Paper Series 9317, CESifo.
    19. 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.

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