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Voters’ preference diversity, concepts of agreement and Condorcet’s paradox

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  • William Gehrlein
  • Dominique Lepelley
  • Issofa Moyouwou

Abstract

Gehrlein et al. (Math Soc Sci 66:352–365, 2013 ) have shown that an increase of the voters’ preference diversity, as measured by the number $$k$$ k of preference types in a voting situation, implies a decrease in the probability of having a Condorcet Winner. The results offered in this paper indicate that this relationship is far from being so clear when we consider instead the proximity of voting situations to having $$k$$ k distinct preference types. This measure of agreement is compared to other measures of group mutual coherence previously analyzed in Gehrlein (Condorcet’s paradox, Springer Publishing, Berlin, 2006 ). It turns out that our results are completely consistent with the theory introduced by List (Good Soc 11:72–79, 2002 ) that is based on an important distinction between two different concepts of agreement. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • William Gehrlein & Dominique Lepelley & Issofa Moyouwou, 2015. "Voters’ preference diversity, concepts of agreement and Condorcet’s paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2345-2368, November.
    • Handle: RePEc:spr:qualqt:v:49:y:2015:i:6:p:2345-2368
    DOI: 10.1007/s11135-014-0117-5
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    1. 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.
    2. 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.
    3. Dryzek, John S. & List, Christian, 2003. "Social Choice Theory and Deliberative Democracy: A Reconciliation," British Journal of Political Science, Cambridge University Press, vol. 33(1), pages 1-28, January.
    4. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
    5. William Gehrlein & Florenz Plassmann, 2014. "A comparison of theoretical and empirical evaluations of the Borda Compromise," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 747-772, October.
    6. William Gehrlein, 2005. "Probabilities of election outcomes with two parameters: The relative impact of unifying and polarizing candidates," Review of Economic Design, Springer;Society for Economic Design, vol. 9(4), pages 317-336, December.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    5. Dominique Lepelley & Issofa Moyouwou & Hatem Smaoui, 2018. "Monotonicity paradoxes in three-candidate elections using scoring elimination rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 1-33, January.
    6. 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.
    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. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    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. 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.
    11. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.
    12. William Gehrlein & Michel Breton & Dominique Lepelley, 2017. "The likelihood of a Condorcet winner in the logrolling setting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 315-327, August.
    13. 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.
    14. Stefania Capecchi & Domenico Piccolo, 2017. "Dealing with heterogeneity in ordinal responses," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(5), pages 2375-2393, September.
    15. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    16. 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.
    17. 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.
    18. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.

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