IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20140019.html
   My bibliography  Save this paper

Solving the Inverse Power Problem in Two-Tier Voting Settings

Author

Listed:
  • Matthias Weber

    (CREED, University of Amsterdam)

Abstract

There are many situations in which different groups make collective decisions by committee voting, where each group is represented by a single person. Theoretical concepts suggest how the voting systems in such committees should be designed, but these abstract rules can usually not be implemented perfectly. To find voting systems that approximate these rules the so called inverse power problem needs to be solved. I introduce a new method to address this problem in two-tier voting settings using the coefficient of variation. This method can easily be applied to a wide variety of settings and rules. After deriving the new method, I illustrate why it is to be preferred over more traditional methods.

Suggested Citation

  • Matthias Weber, 2014. "Solving the Inverse Power Problem in Two-Tier Voting Settings," Tinbergen Institute Discussion Papers 14-019/I, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20140019
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/14019.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    2. Sascha Kurz & Stefan Napel, 2014. "Heuristic and exact solutions to the inverse power index problem for small voting bodies," Annals of Operations Research, Springer, vol. 215(1), pages 137-163, April.
    3. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    4. Laruelle, Annick & Widgren, Mika, 1998. "Is the Allocation of Voting Power among EU States Fair?," Public Choice, Springer, vol. 94(3-4), pages 317-339, March.
    5. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    6. Baldwin, Richard & Widgrén, Mika, 2004. "Winners and Losers Under Various Dual Majority Rules for the EU Council of Ministers," CEPR Discussion Papers 4450, C.E.P.R. Discussion Papers.
    7. Dan S Felsenthal & Moshé Machover, 2004. "Analysis of QM rules in the draft constitution for Europe proposed by the European Convention, 2003," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 1-20, August.
    8. František Turnovec, 2009. "Fairness and squareness: fair decision making rules in the EU Council?," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 4, pages 110-124.
    9. Stefan Napel & Mika Widgrén, 2006. "The Inter-Institutional Distribution of Power in EU Codecision," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 129-154, August.
    10. Nicola Maaser & Stefan Napel, 2007. "Equal representation in two-tier voting systems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 401-420, April.
    11. Laruelle, Annick & Valenciano, Federico, 2002. "Inequality among EU citizens in the EU's Council decision procedure," European Journal of Political Economy, Elsevier, vol. 18(3), pages 475-498, September.
    12. Claus Beisbart & Luc Bovens & Stephan Hartmann, 2005. "A Utilitarian Assessment of Alternative Decision Rules in the Council of Ministers," European Union Politics, , vol. 6(4), pages 395-418, December.
    13. Annick Laruelle & Federico Valenciano, 2010. "Egalitarianism and utilitarianism in committees of representatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 221-243, July.
    14. Frantisek Turnovec, 2009. "Fairness and squareness: fair decision making rules in the eu council?," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 110-124.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    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. Matthias Weber, 2014. "Choosing Voting Systems behind the Veil of Ignorance: A Two-Tier Voting Experiment," Tinbergen Institute Discussion Papers 14-042/I, Tinbergen Institute.
    2. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    3. Di Giannatale, Paolo & Passarelli, Francesco, 2013. "Voting chances instead of voting weights," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 164-173.
    4. 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.
    5. Weber, Matthias, 2016. "Two-tier voting: Measuring inequality and specifying the inverse power problem," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 40-45.
    6. Stefan Napel & Mika Widgrén, 2011. "Strategic versus non-strategic voting power in the EU Council of Ministers: the consultation procedure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 511-541, September.
    7. Zaporozhets, Vera, 2015. "Power Distribution in French River Basin Committees," TSE Working Papers 15-558, Toulouse School of Economics (TSE).
    8. 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.
    9. Mika Widgrén, 2008. "The Impact of Council's Internal Decision-Making Rules on the Future EU," Discussion Papers 26, Aboa Centre for Economics.
    10. Widgrén, Mika, 2008. "The Impact of Council Voting Rules on EU Decision-Making," Discussion Papers 1162, The Research Institute of the Finnish Economy.
    11. Kauppi, Heikki & Widgrén, Mika, 2008. "Do Benevolent Aspects Have Room in Explaining EU Budget Receipts?," CEPR Discussion Papers 6778, C.E.P.R. Discussion Papers.
    12. Matthew Gould & Matthew D. Rablen, 2019. "Are World Leaders Loss Averse?," CESifo Working Paper Series 7763, CESifo.
    13. Kauppi, Heikki & Widgrén, Mika, 2008. "Do Benevolent Aspects Have Room Explaining EU Bydget Receipts?," Discussion Papers 1161, The Research Institute of the Finnish Economy.
    14. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    15. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    16. Matthew Gould & Matthew D. Rablen, 2013. "Equitable Representation in the Councils of the United Nations: Theory and Application," CEDI Discussion Paper Series 13-07, Centre for Economic Development and Institutions(CEDI), Brunel University.
    17. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    18. Stefan Napel & Mika Widgrén, 2006. "The Inter-Institutional Distribution of Power in EU Codecision," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 129-154, August.
    19. Nicola Maaser & Alexander Mayer, 2016. "Codecision in context: implications for the balance of power in the EU," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 213-237, January.
    20. N. Maaser, 2017. "Simple vs. Sophisticated Rules for the Allocation of Voting Weights," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(1), pages 67-78, April.

    More about this item

    Keywords

    inverse power problem; indirect voting power; two-tier voting; Penrose’s Square Root Rule;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tin:wpaper:20140019. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.