IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v282y2020i3p972-979.html
   My bibliography  Save this article

Weighted committee games

Author

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

Abstract

Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of different voting weights (shareholdings, party seats, etc.) under plurality, Borda, Copeland, and antiplurality rule. The number and geometry of weight equivalence classes differ widely across the rules. Decisions can be much more sensitive to weights in Borda committees than (anti-)plurality or Copeland ones.

Suggested Citation

  • Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2020. "Weighted committee games," European Journal of Operational Research, Elsevier, vol. 282(3), pages 972-979.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:3:p:972-979
    DOI: 10.1016/j.ejor.2019.10.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719308586
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.10.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lucia Buenrostro & Amrita Dhillon & Peter Vida, 2013. "Scoring rule voting games and dominance solvability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 329-352, February.
    2. Steven J. Brams & Peter C. Fishburn, 1996. "Minimal winning coalitions in weighted-majority voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(4), pages 397-417.
    3. Myerson, Roger B. & Weber, Robert J., 1993. "A Theory of Voting Equilibria," American Political Science Review, Cambridge University Press, vol. 87(1), pages 102-114, March.
    4. Sascha Kurz, 2012. "On minimum sum representations for weighted voting games," Annals of Operations Research, Springer, vol. 196(1), pages 361-369, July.
    5. Sascha Kurz & Nicola Maaser & Stefan Napel, 2017. "On the Democratic Weights of Nations," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1599-1634.
    6. Kurihara, Takashi, 2018. "A simple characterization of the anti-plurality rule," Economics Letters, Elsevier, vol. 168(C), pages 110-111.
    7. Machover, Moshé & Terrington, Simon D., 2014. "Mathematical structures of simple voting games," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 61-68.
    8. 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, February.
    9. 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.
    10. 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.
    11. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    12. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    13. Houy, Nicolas & Zwicker, William S., 2014. "The geometry of voting power: Weighted voting and hyper-ellipsoids," Games and Economic Behavior, Elsevier, vol. 84(C), pages 7-16.
    14. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    15. 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.
    16. Monroy, Luisa & Fernández, Francisco R., 2011. "The Shapley-Shubik index for multi-criteria simple games," European Journal of Operational Research, Elsevier, vol. 209(2), pages 122-128, March.
    17. Josep Freixas & Marc Freixas & Sascha Kurz, 2017. "On the characterization of weighted simple games," Theory and Decision, Springer, vol. 83(4), pages 469-498, December.
    18. 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.
    19. Freixas, Josep & Kaniovski, Serguei, 2014. "The minimum sum representation as an index of voting power," European Journal of Operational Research, Elsevier, vol. 233(3), pages 739-748.
    20. 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.
    21. Owen, Guillermo, 1975. "Evaluation of a Presidential Election Game," American Political Science Review, Cambridge University Press, vol. 69(3), pages 947-953, September.
    22. Moulin, H, 1982. "Voting with Proportional Veto Power," Econometrica, Econometric Society, vol. 50(1), pages 145-162, January.
    23. Felsenthal, Dan S. & Maoz, Zeev & Rapoport, Amnon, 1993. "An Empirical Evaluation of Six Voting Procedures: Do They Really Make Any Difference?," British Journal of Political Science, Cambridge University Press, vol. 23(1), pages 1-27, January.
    24. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-1288, June.
    25. 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.
    26. 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.
    27. 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.
    28. Jean-François Laslier, 2011. "And the loser is... Plurality Voting," Working Papers hal-00609810, HAL.
    29. 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.
    30. Cheung, Wai-Shun & Ng, Tuen-Wai, 2014. "A three-dimensional voting system in Hong Kong," European Journal of Operational Research, Elsevier, vol. 236(1), pages 292-297.
    31. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    32. 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.
    33. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    34. Hervé Moulin, 1981. "The Proportional Veto Principle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 407-416.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mahajan, Aseem & Pongou, Roland & Tondji, Jean-Baptiste, 2023. "Supermajority politics: Equilibrium range, policy diversity, utilitarian welfare, and political compromise," European Journal of Operational Research, Elsevier, vol. 307(2), pages 963-974.
    2. Alexander Mayer & Stefan Napel, 2021. "Weighted Scoring Committees," Games, MDPI, vol. 12(4), pages 1-17, December.
    3. Michela Chessa & Vito Fragnelli, 2022. "The Italian referendum: what can we get from game theory?," Annals of Operations Research, Springer, vol. 318(2), pages 849-869, November.
    4. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    5. Josep Freixas & Montserrat Pons, 2021. "On anonymous and weighted voting systems," Theory and Decision, Springer, vol. 91(4), pages 477-491, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(C).
    2. Courtin, Sébastien & Nganmeni, Zéphirin & Tchantcho, Bertrand, 2017. "Dichotomous multi-type games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 9-17.
    3. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2017. "Dichotomous multi-type games with a coalition structure," Post-Print halshs-01545772, HAL.
    4. Josep Freixas & Montserrat Pons, 2022. "A critical analysis on the notion of power," Annals of Operations Research, Springer, vol. 318(2), pages 911-933, November.
    5. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    6. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    7. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
    8. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    9. Freixas, Josep & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
    10. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    11. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    12. Luisa Monroy & Francisco Fernández, 2014. "Banzhaf index for multiple voting systems. An application to the European Union," Annals of Operations Research, Springer, vol. 215(1), pages 215-230, April.
    13. Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.
    14. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.
    15. Guemmegne, Juliette T. & Pongou, Roland, 2014. "A policy-based rationalization of collective rules: Dimensionality, specialized houses, and decentralized authority," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 182-193.
    16. Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    17. Josep Freixas & Montserrat Pons, 2021. "An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval," Group Decision and Negotiation, Springer, vol. 30(2), pages 447-462, April.
    18. Le Breton, Michel & Lepelley, Dominique & Macé, Antonin & Merlin, Vincent, 2017. "Le mécanisme optimal de vote au sein du conseil des représentants d’un système fédéral," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 203-248, Mars-Juin.
    19. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    20. Sascha Kurz & Issofa Moyouwou & Hilaire Touyem, 2021. "Axiomatizations for the Shapley–Shubik power index for games with several levels of approval in the input and output," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 569-594, April.

    More about this item

    Keywords

    Group decisions and negotiations; Weighted voting; Simple games; Scoring rules; Majority rule;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:282:y:2020:i:3:p:972-979. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.