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Borda’s Paradox with weighted scoring rules

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  • Mostapha Diss

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  • William 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.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:38:y:2012:i:1:p:121-136
    DOI: 10.1007/s00355-010-0522-1
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    File URL: http://hdl.handle.net/10.1007/s00355-010-0522-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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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    Cited by:

    1. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    2. 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.
    3. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    4. 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.
    5. repec:eee:matsoc:v:89:y:2017:i:c:p:70-82 is not listed on IDEAS
    6. repec:eee:matsoc:v:87:y:2017:i:c:p:1-10 is not listed on IDEAS

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