IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/28364.html
   My bibliography  Save this paper

Influence Vs. Utility in the Evaluation of Voting Rules: A New Look at the Penrose Formula

Author

Listed:
  • Le Breton, Michel
  • Van Der Straeten, Karine

Abstract

In this paper, we clarify the relationship between influence/power measurement and utility measurement, the most popular two social objective criteria used when evaluating voting mechanisms. For one particular probabilistic model describing the preferences of the electorate, the so-called Impartial Culture (IC) model used by Banzhaf, the Penrose formula show that the two objectives coincide. The IC probabilistic model assumes that voter preferences are independent. In this article, we prove a general version of the Penrose formula, allowing for correlations in the electorate. We show that in that case, the two social objectives no longer coincide, and qualitative conclusions can be very different.

Suggested Citation

  • Le Breton, Michel & Van Der Straeten, Karine, 2014. "Influence Vs. Utility in the Evaluation of Voting Rules: A New Look at the Penrose Formula," TSE Working Papers 14-511, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:28364
    as

    Download full text from publisher

    File URL: http://www.tse-fr.eu/sites/default/files/medias/doc/wp/pe/wp_tse_511.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Felsenthal, Dan S. & Machover, Moshe, 1999. "Minimizing the mean majority deficit: The second square-root rule," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 25-37, January.
    2. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    3. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2004. "The probability of conflicts in a U.S. presidential type election," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 227-257, January.
    4. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    5. 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.
    6. Chamberlain, Gary & Rothschild, Michael, 1981. "A note on the probability of casting a decisive vote," Journal of Economic Theory, Elsevier, vol. 25(1), pages 152-162, August.
    7. 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.
    8. Claus Beisbart & Luc Bovens, 2013. "Minimizing the threat of a positive majority deficit in two-tier voting systems with equipopulous units," Public Choice, Springer, vol. 154(1), pages 75-94, January.
    9. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
    10. 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.
    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. 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.
    2. Olivier Mouzon & Thibault Laurent & Michel Breton & Dominique Lepelley, 2019. "Exploring the effects of national and regional popular vote Interstate compact on a toy symmetric version of the Electoral College: an electoral engineering perspective," Public Choice, Springer, vol. 179(1), pages 51-95, April.
    3. Laurent, Thibault & Le Breton, Michel & Lepelley, Dominique & de Mouzon, Olivier, 2017. "Exploring the Effects on the Electoral College of National and Regional Popular Vote Interstate Compact: An Electoral Engineering Perspective," TSE Working Papers 17-861, Toulouse School of Economics (TSE), revised May 2018.
    4. 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.
    5. Michel Breton & Karine Straeten, 2015. "Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula," Public Choice, Springer, vol. 165(1), pages 103-122, October.
    6. Le Breton, Michel & Lepelley, Dominique & Smaoui, Hatem, 2012. "The Probability of Casting a Decisive Vote: From IC to IAC trhough Ehrhart's Polynomials and Strong Mixing," IDEI Working Papers 722, Institut d'Économie Industrielle (IDEI), Toulouse.
    7. 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.
    8. Imma Curiel, 2014. "A multifaceted analysis of the electoral system of the Republic of Suriname," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(4), pages 29-49.
    9. 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.
    10. Kazuya Kikuchi & Yukio Koriyama, 2019. "The Winner-Take-All Dilemma," ISER Discussion Paper 1059r, Institute of Social and Economic Research, Osaka University, revised Dec 2019.
    11. Claus Beisbart, 2010. "Groups can make a difference: voting power measures extended," Theory and Decision, Springer, vol. 69(3), pages 469-488, September.
    12. 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.
    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. Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.
    15. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
    16. Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Post-Print halshs-00142479, HAL.
    17. Edwards, Jeremy S.S. & Weichenrieder, Alfons J., 2009. "Control rights, pyramids, and the measurement of ownership concentration," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 489-508, October.
    18. 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.
    19. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali & Sarkar, Palash, 2004. "A characterization and some properties of the Banzhaf-Coleman-Dubey-Shapley sensitivity index," Games and Economic Behavior, Elsevier, vol. 49(1), pages 31-48, October.
    20. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.

    More about this item

    Keywords

    Power measurement; Voting; Random electorates;
    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:tse:wpaper:28364. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    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.