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An impossibility theorem concerning positive involvement in voting

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  • Wesley H. Holliday

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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  • Wesley H. Holliday, 2024. "An impossibility theorem concerning positive involvement in voting," Papers 2401.05657, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2401.05657
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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. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
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    5. Markus Schulze, 2011. "A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 267-303, February.
    6. Raúl Pérez-Fernández & Bernard De Baets, 2018. "The supercovering relation, the pairwise winner, and more missing links between Borda and Condorcet," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 329-352, February.
    7. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
    8. 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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