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An impossibility theorem concerning positive involvement in voting

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  • Holliday, Wesley H.

Abstract

In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet methods, namely that the choice of winners depends only on the ordering of majority margins by size.

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  • Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    • Handle: RePEc:eee:ecolet:v:236:y:2024:i:c:s0165176524000727
    DOI: 10.1016/j.econlet.2024.111589
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    References listed on IDEAS

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    1. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    2. Yifeng Ding & Wesley H. Holliday & Eric Pacuit, 2022. "An Axiomatic Characterization of Split Cycle," Papers 2210.12503, arXiv.org, revised Jun 2024.
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    8. Wesley H. Holliday & Eric Pacuit, 2020. "Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers," Papers 2004.02350, arXiv.org, revised Nov 2023.
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    12. Wesley H. Holliday & Eric Pacuit, 2023. "Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers," Public Choice, Springer, vol. 197(1), pages 1-62, October.
    13. Wesley H. Holliday & Eric Pacuit, 2021. "Measuring Violations of Positive Involvement in Voting," Papers 2106.11502, arXiv.org.
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    19. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.
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    Cited by:

    1. Felix Brandt & Chris Dong & Dominik Peters, 2024. "Condorcet-Consistent Choice Among Three Candidates," Papers 2411.19857, arXiv.org.

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