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Statistical evaluation of voting rules

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  • James Green-Armytage
  • T. Tideman
  • Rafael Cosman

Abstract

We generate synthetic elections using two sources of survey data, two spatial models, and two standard models from the voting literature, IAC and IC. For each election that we generate, we test whether each of 54 voting rules is (1) non-manipulable, and (2) efficient in the sense of maximizing summed utilities. We find that Hare and Condorcet–Hare are the most strategy-resistant non-dictatorial rules. Most rules have very similar efficiency scores, apart from a few poor performers such as random dictator, plurality and anti-plurality. Our results are highly robust across data-generating processes. In addition to presenting our numerical results, we explore analytically the effects of adding a Condorcet provision to a base rule and show that, for all but a few base rules, this modification cannot introduce a possibility of manipulation where none existed before. Our analysis provides support for the Condorcet–Hare rule, which has not been prominent in the literature. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    • Handle: RePEc:spr:sochwe:v:46:y:2016:i:1:p:183-212
    DOI: 10.1007/s00355-015-0909-0
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    1. Lepelley, Dominique & Valognes, Fabrice, 2003. "Voting Rules, Manipulability and Social Homogeneity," Public Choice, Springer, vol. 116(1-2), pages 165-184, July.
    2. David A. Smith, 1999. "Manipulability measures of common social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 639-661.
    3. Samuel Merrill Iii & Nicolaus Tideman, 1991. "The Relative Efficiency of Approval and Condorcet Voting Procedures," Rationality and Society, , vol. 3(1), pages 65-77, January.
    4. James Green-Armytage, 2014. "Strategic voting and nomination," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 111-138, January.
    5. Dan S. Felsenthal, 2012. "Review of Paradoxes Afflicting Procedures for Electing a Single Candidate," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 19-91, Springer.
    6. Geoffrey Pritchard & Mark Wilson, 2007. "Exact results on manipulability of positional voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 487-513, October.
    7. Sven Berg, 1985. "Paradox of voting under an urn model: The effect of homogeneity," Public Choice, Springer, vol. 47(2), pages 377-387, January.
    8. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    9. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "Borda rule, Copeland method and strategic manipulation," Post-Print halshs-00069522, HAL.
    10. Chamberlin, John R. & Cohen, Michael D., 1978. "Toward Applicable Social Choice Theory: A Comparison of Social Choice Functions under Spatial Model Assumptions," American Political Science Review, Cambridge University Press, vol. 72(4), pages 1341-1356, December.
    11. Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "original papers : Borda rule, Copeland method and strategic manipulation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 213-228.
    12. Jose Apesteguia & Miguel A. Ballester & Rosa Ferrer, 2011. "On the Justice of Decision Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 1-16.
    13. Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 485-509, June.
    14. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    15. Bordley, Robert F., 1983. "A Pragmatic Method for Evaluating Election Schemes through Simulation," American Political Science Review, Cambridge University Press, vol. 77(1), pages 123-141, March.
    16. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    17. Ilia Tsetlin & Michel Regenwetter & Bernard Grofman, 2003. "The impartial culture maximizes the probability of majority cycles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 387-398, December.
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    Cited by:

    1. Conal Duddy, 2017. "Geometry of run-off elections," Public Choice, Springer, vol. 173(3), pages 267-288, December.
    2. James Green-Armytage, 2023. "A Dodgson-Hare synthesis," Constitutional Political Economy, Springer, vol. 34(3), pages 458-470, September.
    3. Benoît R. Kloeckner, 2022. "Cycles in synchronous iterative voting: general robustness and examples in Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 423-466, August.
    4. Lirong Xia, 2022. "The Impact of a Coalition: Assessing the Likelihood of Voter Influence in Large Elections," Papers 2202.06411, arXiv.org, revised Jun 2023.
    5. Chang Geun Song, 2023. "What difference does a voting rule make?," Constitutional Political Economy, Springer, vol. 34(3), pages 275-285, September.
    6. James Green-Armytage & T. Nicolaus Tideman, 2020. "Selecting the runoff pair," Public Choice, Springer, vol. 182(1), pages 119-137, January.
    7. Aleksei Y. Kondratev & Alexander S. Nesterov, 2020. "Measuring majority power and veto power of voting rules," Public Choice, Springer, vol. 183(1), pages 187-210, April.
    8. Sara Wolk & Jameson Quinn & Marcus Ogren, 2023. "STAR Voting, equality of voice, and voter satisfaction: considerations for voting method reform," Constitutional Political Economy, Springer, vol. 34(3), pages 310-334, September.
    9. Amir Babak Aazami & Hubert Lewis Bray, 2023. "Classification of preferential ballot voting methods," Constitutional Political Economy, Springer, vol. 34(4), pages 510-523, December.
    10. Dan S. Felsenthal & Hannu Nurmi, 2018. "Monotonicity Violations by Borda’s Elimination and Nanson’s Rules: A Comparison," Group Decision and Negotiation, Springer, vol. 27(4), pages 637-664, August.
    11. David McCune & Jennifer Wilson, 2023. "Ranked-choice voting and the spoiler effect," Public Choice, Springer, vol. 196(1), pages 19-50, July.
    12. Dougherty, Keith L. & Heckelman, Jac C., 2020. "The probability of violating Arrow’s conditions," European Journal of Political Economy, Elsevier, vol. 65(C).
    13. Robbie Robinette, 2023. "Implications of strategic position choices by candidates," Constitutional Political Economy, Springer, vol. 34(3), pages 445-457, September.
    14. Karthik H. Shankar, 2022. "Normed Negative Voting to Depolarize Politics," Group Decision and Negotiation, Springer, vol. 31(6), pages 1097-1120, December.
    15. Adam Graham-Squire & David McCune, 2023. "An Examination of Ranked Choice Voting in the United States, 2004-2022," Papers 2301.12075, arXiv.org, revised Mar 2023.
    16. Postl, Peter, 2017. "Évaluation et comparaison des règles de vote derrière le voile de l’ignorance : Tour d'horizon sélectif et analyse des règles de scores à deux paramètres," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 249-290, Mars-Juin.
    17. Richard B. Darlington, 2023. "The case for minimax-TD," Constitutional Political Economy, Springer, vol. 34(3), pages 410-420, September.
    18. Richard F. Potthoff, 2019. "Three Bizarre Presidential-Election Scenarios: The Perils of Simplism," Social Sciences, MDPI, vol. 8(5), pages 1-23, April.

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