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Measuring Violations of Positive Involvement in Voting

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  • Wesley H. Holliday

    (University of California, Berkeley)

  • Eric Pacuit

    (University of Maryland)

Abstract

In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected.

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  • Wesley H. Holliday & Eric Pacuit, 2021. "Measuring Violations of Positive Involvement in Voting," Papers 2106.11502, arXiv.org.
    • Handle: RePEc:arx:papers:2106.11502
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    References listed on IDEAS

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    1. Emerson Niou, 1987. "A note on Nanson's rule," Public Choice, Springer, vol. 54(2), pages 191-193, January.
    2. Dan S. Felsenthal & Hannu Nurmi, 2016. "Two types of participation failure under nine voting methods in variable electorates," Public Choice, Springer, vol. 168(1), pages 115-135, July.
    3. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    4. Dan Felsenthal & Nicolaus Tideman, 2013. "Varieties of failure of monotonicity and participation under five voting methods," Theory and Decision, Springer, vol. 75(1), pages 59-77, July.
    5. Sven Berg, 1985. "Paradox of voting under an urn model: The effect of homogeneity," Public Choice, Springer, vol. 47(2), pages 377-387, January.
    6. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    7. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    8. 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.
    9. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    10. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(3), pages 478-490.
    11. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    12. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, July.
    13. Dowding, Keith & Van Hees, Martin, 2008. "In Praise of Manipulation," British Journal of Political Science, Cambridge University Press, vol. 38(1), pages 1-15, January.
    14. 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.
    15. José Jimeno & Joaquín Pérez & Estefanía García, 2009. "An extension of the Moulin No Show Paradox for voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 343-359, September.
    16. Dan S. Felsenthal & Hannu Nurmi, 2017. "Monotonicity Failures Afflicting Procedures for Electing a Single Candidate," SpringerBriefs in Economics, Springer, number 978-3-319-51061-3, April.
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    Cited by:

    1. 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.
    2. Wesley H. Holliday & Eric Pacuit, 2021. "Axioms for defeat in democratic elections," Journal of Theoretical Politics, , vol. 33(4), pages 475-524, October.
    3. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).

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