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Influence in weighted committees

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  • Kurz, Sascha
  • Mayer, Alexander
  • Napel, Stefan

Abstract

Committee decisions on more than two alternatives much depend on the adopted aggregation rule, and so does the distribution of power among committee members. We quantify how different voting methods such as pairwise majority votes, plurality voting with or without a runoff, or Borda rule map asymmetric numbers of seats, shares, voting weights, etc. to influence on collective outcomes when individual preferences vary. Generalizations of the Penrose-Banzhaf and Shapley-Shubik power indices are proposed and applied to elections of the IMF Managing Director. Previous analysis of a priori power in binary voting is thus extended to universal social choice rules.

Suggested Citation

  • Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:eecrev:v:132:y:2021:i:c:s0014292120302646
    DOI: 10.1016/j.euroecorev.2020.103634
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    1. Jean-François Laslier, 2012. "And the Loser Is… Plurality Voting," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 327-351, Springer.
    2. Tchantcho, Bertrand & Lambo, Lawrence Diffo & Pongou, Roland & Engoulou, Bertrand Mbama, 2008. "Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories," Games and Economic Behavior, Elsevier, vol. 64(1), pages 335-350, September.
    3. C. H. Ueng & Vincent C. H. Chua & H. C. Huang, 2002. "A method for evaluating the behavior of power indices in weighted plurality games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 665-680.
    4. 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.
    5. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    6. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    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. Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
    9. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    10. Myerson, Roger B., 1999. "Theoretical comparisons of electoral systems," European Economic Review, Elsevier, vol. 43(4-6), pages 671-697, April.
    11. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 175-186.
    12. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    13. Alexander Tabarrok & Lee Spector, 1999. "Would the Borda Count Have Avoided the Civil War?," Journal of Theoretical Politics, , vol. 11(2), pages 261-288, April.
    14. Josep Freixas, 2005. "Banzhaf Measures for Games with Several Levels of Approval in the Input and Output," Annals of Operations Research, Springer, vol. 137(1), pages 45-66, July.
    15. 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.
    16. J. Alonso-Meijide & C. Bowles, 2005. "Generating Functions for Coalitional Power Indices: An Application to the IMF," Annals of Operations Research, Springer, vol. 137(1), pages 21-44, July.
    17. K. Ortmann, 1998. "Conservation of energy in value theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(3), pages 423-449, October.
    18. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    19. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    20. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    21. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2020. "Weighted committee games," European Journal of Operational Research, Elsevier, vol. 282(3), pages 972-979.
    22. Stefan Napel & Mika Widgren, 2004. "Power Measurement as Sensitivity Analysis," Journal of Theoretical Politics, , vol. 16(4), pages 517-538, October.
    23. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-1288, June.
    24. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    25. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    26. R. Amer & F. Carreras & A. Magaña, 1998. "Extension of values to games withmultiple alternatives," Annals of Operations Research, Springer, vol. 84(0), pages 63-78, December.
    27. Annick Laruelle & Federico Valenciano, 2012. "Quaternary dichotomous voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 431-454, March.
    28. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
    29. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Alexander Mayer & Stefan Napel, 2021. "Weighted Scoring Committees," Games, MDPI, vol. 12(4), pages 1-17, December.
    2. Kirsch, Werner & Toth, Gabor, 2022. "Collective bias models in two-tier voting systems and the democracy deficit," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 118-137.

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