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The Borda rule, Condorcet consistency and Condorcet stability

Author

Listed:
  • Eyal Baharad
  • Shmuel Nitzan

Abstract

The Borda rule is known to be the least vulnerable scoring rule to Condorcet inconsistency, Saari (2000). Such inconsistency occurs when the Condorcet winner (the alternative which is preferred to any other alternative by a simple majority) is not selected by the Borda rule. This note exposes the relationship between the Borda rule and the Condorcet q-majority principle as well as the Condorcet q-majority voting rule. The main result establishes that the Borda rule is Condorcet q-majority consistent when where k is the number of alternatives. The second result establishes that is the minimal degree of majority decisiveness corresponding to the Borda rule under sincere voting. The same majority is required to ensure decisiveness under the Borda rule and to ensure that a q-rule (the generalized q-majority Condorcet rule) is a voting rule. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:22:y:2003:i:3:p:685-688
    DOI: 10.1007/s00199-002-0318-3
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    Citations

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    Cited by:

    1. Sebastien Courtin & Mathieu Martin & Issofa Moyouwou, 2013. "The q-Condorcet efficiency of positional rules," Working Papers hal-00914907, HAL.
    2. Eyal Baharad & Shmuel Nitzan, 2011. "Condorcet vs. Borda in light of a dual majoritarian approach," Theory and Decision, Springer, vol. 71(2), pages 151-162, August.
    3. Pablo Amorós, 2009. "Unequivocal majority and Maskin-monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 521-532, November.
    4. Sebastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2013. "Positional rules and q- Condorcet consistency," Working Papers hal-00914900, HAL.
    5. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    6. 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.
    7. Eyal Baharad & Shmuel Nitzan, 2007. "The Costs of Implementing the Majority Principle: The Golden Voting Rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 69-84, April.
    8. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2015. "The q-majority efficiency of positional rules," Post-Print hal-00914907, HAL.
    9. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    10. 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.
    11. Muhammad Mahajne & Oscar Volij, 2019. "Condorcet winners and social acceptability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 641-653, 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. 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.
    14. Sébastien Courtin & Mathieu Martin & Bertrand Tchantcho, 2015. "Positional rules and q-Condorcet consistency," Post-Print hal-00914900, 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. 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.
    18. 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.
    19. Akira Okada & Ryoji Sawa, 2016. "An evolutionary approach to social choice problems with q-quota rules," KIER Working Papers 936, Kyoto University, Institute of Economic Research.
    20. 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.

    More about this item

    Keywords

    Keywords and Phrases: The Borda rule; q-rules; Condorcet consistency; Condorcet stability; Majority decisiveness.; JEL Classification Numbers: D71; D72.;
    All these keywords.

    JEL classification:

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

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