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Scoring rules, ballot truncation, and the truncation paradox

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  • Eric Kamwa

    (Université des Antilles)

Abstract

A voting rule that permits some voters to favor a candidate by revealing only the initial segment of their sincere rankings is said to be vulnerable to the truncation paradox. In this paper, we consider four models for counting truncated ballots, optimistic, pessimistic (the most common), averaged, and round-down. Under the impartial anonymous culture assumption, the choice of model generally has a real impact on truncation-paradox vulnerability, but exceptions exist. When the election is decided by a one-shot scoring rule, the optimistic model is invulnerable to the truncation paradox, but all other models are vulnerable. We identify new voting rules immune to the truncation paradox, such as the Modified Borda Count. To obtain a more complete picture of the impact of processing model, we assess the likelihood of the truncation paradox in three-candidate elections with large electorates, focusing not only on one-shot scoring rules but also scoring rules with one-by-one or below-average elimination. Our assessment confirms that the processing model for truncated ballots may really matter.

Suggested Citation

  • Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    • Handle: RePEc:kap:pubcho:v:192:y:2022:i:1:d:10.1007_s11127-022-00972-8
    DOI: 10.1007/s11127-022-00972-8
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    Cited by:

    1. Kiran Tomlinson & Johan Ugander & Jon Kleinberg, 2022. "Ballot Length in Instant Runoff Voting," Papers 2207.08958, arXiv.org, revised Dec 2022.
    2. Maciel, Marcelo Veloso, 2024. "Was Bolsonaro’s 2018 electoral victory an institutional accident?," European Journal of Political Economy, Elsevier, vol. 83(C).
    3. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    4. Mallory Dickerson & Erin Martin & David McCune, 2023. "An Empirical Analysis of the Effect of Ballot Truncation on Ranked-Choice Electoral Outcomes," Papers 2306.05966, arXiv.org.
    5. Salvatore Barbaro, 2024. "Electoral Methods and Political Polarization," Working Papers 2411, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    6. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.

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    More about this item

    Keywords

    Truncation; Rankings; Scoring model; Probability; Paradox; Impartial and anonymous culture;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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