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To what extent does the model of processing sincereincomplete rankings affect the likelihood of thetruncation paradox?

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  • Eric Kamwa

    () (LC2S - Laboratoire caribéen de sciences sociales - UA - Université des Antilles - CNRS - Centre National de la Recherche Scientifique)

Abstract

For a given voting rule, if voters can favor a preferred outcome by providing only a part of their sincere rankings on the competing candidates, rather than listing their entire preference rankings on all the competing candidates, this rule is said to be vulnerable to the truncation paradox. In this paper, we show that the way of dealing with the truncated ballot can really impact the occurrence of the paradox: this paradox never occurs with any one-shot scoring rules when truncated ballot a treated according the optimistic model. The optimistic model is, along with the pessimistic model and the averaged model, the three most common ways of dealing with truncated preferences. The few papers that assess the likelihood of the occurrence of this paradox implicitly assume the pessimistic model. In this paper, we assess the likelihood of the truncation paradox under the two other models for three-candidate elections and large electorates. We focus on whole families of one-shot scoring rules, iterative scoring rules both with one-by-one eliminations and with elimination by the average. This assessment confirms that the choice of model may really matter: under the optimistic model, all the one-shot scoring rules are immune to the truncation paradox, whereas it is is more likely to occur under the pessimistic model than under the averaged model; for each of the scoring runoff rules, we find that the likelihood of the truncation paradox is higher under the pessimistic model, and lower under the optimistic model. Our analysis is performed under the Impartial Anonymous Culture assumption.

Suggested Citation

  • Eric Kamwa, 2021. "To what extent does the model of processing sincereincomplete rankings affect the likelihood of thetruncation paradox?," Working Papers hal-02879390, HAL.
  • Handle: RePEc:hal:wpaper:hal-02879390
    Note: View the original document on HAL open archive server: https://hal.univ-antilles.fr/hal-02879390v2
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    References listed on IDEAS

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    1. 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.
    2. Diss, Mostapha & Louichi, Ahmed & Merlin, Vincent & Smaoui, Hatem, 2012. "An example of probability computations under the IAC assumption: The stability of scoring rules," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 57-66.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Florenz Plassmann & T. Tideman, 2014. "How frequently do different voting rules encounter voting paradoxes in three-candidate elections?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 31-75, January.
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    9. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607.
    10. Mostapha Diss & William V. Gehrlein, 2015. "The True Impact of Voting Rule Selection on Condorcet Efficiency," Economics Bulletin, AccessEcon, vol. 35(4), pages 2418-2426.
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    15. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
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    Keywords

    Truncation; Rankings; Scoring model; Probability; Paradox; Impartial and Anonymous Culture;
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