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Linear voting Rules

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  • Grüner, Hans Peter
  • Tröger, Thomas

Abstract

How should a society choose between two social alternatives if participation in the decision process is voluntary and costly and monetary transfers are not feasible? Considering symmetric voters with private valuations, we show that it is utilitarian-optimal to use a linear voting rule: votes get alternative-dependent weights, and a default obtains if the weighted sum of votes stays below some threshold. Standard quorum rules are not optimal. We develop a perturbation method to characterize equilibria in the case of small participation costs and show that leaving participation voluntary increases welfare for linear rules that are optimal under compulsory participation.

Suggested Citation

  • Grüner, Hans Peter & Tröger, Thomas, 2016. "Linear voting Rules," CEPR Discussion Papers 11127, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:11127
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    1. François Maniquet & Massimo Morelli, 2015. "Approval quorums dominate participation quorums," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 1-27, June.
    2. Patricia Charléty & Marie-Cécile Fagart & Saïd Souam, 2017. "Quorum Rules and Shareholder Power," EconomiX Working Papers 2017-35, University of Paris Nanterre, EconomiX.
    3. Sayantan Ghosal & Ben Lockwood, 2009. "Costly voting when both information and preferences differ: is turnout too high or too low?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 25-50, June.
    4. 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.
    5. Paulo P. Côrte-Real & Paulo T. Pereira, 2004. "The voter who wasn’t there: Referenda, representation and abstention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 349-369, April.
    6. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    7. Helios Herrera & Andrea Mattozzi, 2010. "Quorum and Turnout in Referenda," Journal of the European Economic Association, MIT Press, vol. 8(4), pages 838-871, June.
    8. Vijay Krishna & John Morgan, 2015. "Majority Rule and Utilitarian Welfare," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 339-375, November.
    9. Kwiek, Maksymilian, 2014. "Efficient voting with penalties," Discussion Paper Series In Economics And Econometrics 1419, Economics Division, School of Social Sciences, University of Southampton.
    10. Aguiar-Conraria, Luís & Magalhães, Pedro C., 2010. "How quorum rules distort referendum outcomes: Evidence from a pivotal voter model," European Journal of Political Economy, Elsevier, vol. 26(4), pages 541-557, December.
    11. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    12. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    13. Xiaoyong Cao & Guofu Tan & Guoqiang Tian & Okan Yilankaya, 2018. "Equilibria in second-price auctions with private participation costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 231-249, March.
    14. Timothy Feddersen & Alvaro Sandroni, 2006. "A Theory of Participation in Elections," American Economic Review, American Economic Association, vol. 96(4), pages 1271-1282, September.
    15. Celik Gorkem & Yilankaya Okan, 2009. "Optimal Auctions with Simultaneous and Costly Participation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-33, July.
    16. Kwiek, Maksymilian, 2017. "Efficient voting with penalties," Games and Economic Behavior, Elsevier, vol. 104(C), pages 468-485.
    17. Melis Kartal, 2015. "A Comparative Welfare Analysis of Electoral Systems with Endogenous Turnout," Economic Journal, Royal Economic Society, vol. 125(587), pages 1369-1392, September.
    18. Chakravarty, Surajeet & Kaplan, Todd R. & Myles, Gareth, 2018. "When costly voting is beneficial," Journal of Public Economics, Elsevier, vol. 167(C), pages 33-42.
    19. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-424, June.
    20. Krasa, Stefan & Polborn, Mattias K., 2009. "Is mandatory voting better than voluntary voting?," Games and Economic Behavior, Elsevier, vol. 66(1), pages 275-291, May.
    21. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 688-717.
    22. Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
    23. Nöldeke, Georg & Peña, Jorge, 2016. "The symmetric equilibria of symmetric voter participation games with complete information," Games and Economic Behavior, Elsevier, vol. 99(C), pages 71-81.
    24. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    25. Jacob Goeree & Jens Großer, 2007. "Welfare Reducing Polls," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 51-68, April.
    26. Taylor, Curtis R. & Yildirim, Huseyin, 2010. "A unified analysis of rational voting with private values and group-specific costs," Games and Economic Behavior, Elsevier, vol. 70(2), pages 457-471, November.
    27. Kos, Nenad, 2012. "Communication and efficiency in auctions," Games and Economic Behavior, Elsevier, vol. 75(1), pages 233-249.
    28. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    29. Chakravarty, Surajeet & Kaplan, Todd R & Myles, Gareth, 2010. "The Benefits of Costly Voting," MPRA Paper 21372, University Library of Munich, Germany.
    30. Ledyard, John O. & Palfrey, Thomas R., 2002. "The approximation of efficient public good mechanisms by simple voting schemes," Journal of Public Economics, Elsevier, vol. 83(2), pages 153-171, February.
    31. Felix J. Bierbrauer & Martin F. Hellwig, 2016. "Robustly Coalition-Proof Incentive Mechanisms for Public Good Provision are Voting Mechanisms and Vice Versa," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1440-1464.
    32. Bognar, Katalin & Börgers, Tilman & Meyer-ter-Vehn, Moritz, 2010. "An optimal Voting System when Voting is costly," MPRA Paper 29123, University Library of Munich, Germany.
    33. Helios Herrera & Massimo Morelli & Thomas Palfrey, 2014. "Turnout and Power Sharing," Economic Journal, Royal Economic Society, vol. 124(574), pages 131-162, February.
    34. Palfrey, Thomas R. & Rosenthal, Howard, 1985. "Voter Participation and Strategic Uncertainty," American Political Science Review, Cambridge University Press, vol. 79(1), pages 62-78, March.
    35. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
    36. Annick Laruelle & Federico Valenciano, 2011. "Majorities with a quorum," Journal of Theoretical Politics, , vol. 23(2), pages 241-259, April.
    37. Colin M. Campbell, 1999. "Large Electorates and Decisive Minorities," Journal of Political Economy, University of Chicago Press, vol. 107(6), pages 1199-1217, December.
    38. Bognar, Katalin & Börgers, Tilman & Meyer-ter-Vehn, Moritz, 2015. "An optimal voting procedure when voting is costly," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1056-1073.
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    More about this item

    Keywords

    Mechanisms design; Optimal voting rules; Costly voting; Compulsory voting; Quorum rules;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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