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The probability of ties with scoring methods: Some results

Author

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  • Thierry Marchant

    (Department of Data Analysis, Ghent University, H. Dunantlaan 1, 9000 Ghent, Belgium)

Abstract

The main flaw of the Condorcet method is that a Condorcet winner does not always exist (when there is a top cycle). Moreover, in some cases, all candidates are contained in one cycle and, therefore, a society or committee using the Condorcet method risks to face a severe indeterminacy. An indeterminacy can also happen when using other methods: for example the Borda method, plurality voting or any scoring method; but the origin of the indeterminacy is completely different. It happens when all candidates are tied. We study the probability that all candidates are tied when using a scoring method. We show that it is equivalent to some random walk problems. Some analytical and numerical results show that, under the assumptions underlying our study, the probability is very small and decreases when the number of voters or candidates increases.

Suggested Citation

  • Thierry Marchant, 2001. "The probability of ties with scoring methods: Some results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 709-735.
    • Handle: RePEc:spr:sochwe:v:18:y:2001:i:4:p:709-735
    Note: Received: 18 December 1998/Accepted: 17 March 2000
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    Citations

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    Cited by:

    1. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    2. Lirong Xia, 2020. "How Likely Are Large Elections Tied?," Papers 2011.03791, arXiv.org, revised Jul 2021.
    3. Takahiro Suzuki & Masahide Horita, 2023. "A Society Can Always Decide How to Decide: A Proof," Group Decision and Negotiation, Springer, vol. 32(5), pages 987-1023, October.
    4. Niclas Boehmer & Robert Bredereck & Piotr Faliszewski & Rolf Niedermeier, 2022. "A Quantitative and Qualitative Analysis of the Robustness of (Real-World) Election Winners," Papers 2208.13760, arXiv.org.
    5. 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.

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