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One Person, Many Votes: Divided Majority and Information Aggregation

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  • Laurent Bouton
  • Micael Castanheira

Abstract

This paper compares the properties of three electoral systems when voters have imperfect information. Imperfect information blurs voter decisions and may divorce the electoral outcome from the true preferences of the electorate. The challenge for electoral design is therefore to translate the (sometimes contradictory) elements of information dispersed in the electorate into the most efficient aggregate outcome. We propose a novel model of multi-candidate elections in Poisson games, and show that Approval Voting produces a unique equilibrium that is fully efficient: the candidate who wins the election is the one preferred by a majority of the electorate under full information. By contrast, traditional systems such as Plurality and Runoff elections cannot cope satisfactorily with information imperfections.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 80 (2012)
Issue (Month): 1 (01)
Pages: 43-87

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Handle: RePEc:ecm:emetrp:v:80:y:2012:i:1:p:43-87

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  1. Goertz, Johanna M.M. & Maniquet, François, 2011. "On the informational efficiency of simple scoring rules," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1464-1480, July.
  2. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Feddersen, Timothy J & Pesendorfer, Wolfgang, 1996. "The Swing Voter's Curse," American Economic Review, American Economic Association, vol. 86(3), pages 408-24, June.
  4. Timothy Feddersen & Wolfgang Pesendorfer, 1996. "Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts," Discussion Papers 1170, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Jean-François Laslier, 2004. "Strategic approval voting in a large electorate," IDEP Working Papers 0405, Institut d'economie publique (IDEP), Marseille, France.
  6. Torun Dewan & David P. Myatt, 2006. "Leading the Party:Coordination, Direction, and Communication," STICERD - Political Economy and Public Policy Paper Series 22, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Francesco Sinopoli & Bhaskar Dutta & Jean-François Laslier, 2006. "Approval voting: three examples," International Journal of Game Theory, Springer, vol. 35(1), pages 27-38, December.
  8. Micael Castanheira, . "Why Vote for Losers?," Working Papers 125, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  9. Roger B. Myerson, 1994. "Extended Poisson Games and the Condorcet Jury Theorem," Discussion Papers 1103, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections With Private Information," Levine's Working Paper Archive 1560, David K. Levine.
  11. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
  12. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-88, June.
  13. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
  14. Laurent Bouton & Micael Castanheira De Moura, 2009. "The Condorcet-Duverger Trade-Off: swing voters and voting equilibria," ULB Institutional Repository 2013/159859, ULB -- Universite Libre de Bruxelles.
  15. David S. Ahny & Santiago Oliveros, 2013. "Approval Voting and Scoring Rules with Common Values," Economics Discussion Papers 732, University of Essex, Department of Economics.
  16. Piketty, Thomas, 2000. "Voting as Communicating," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 169-91, January.
  17. Sourav Bhattacharya, 2006. "Preference Monotonicity and Information Aggregation in Elections," Working Papers 325, University of Pittsburgh, Department of Economics, revised Dec 2008.
  18. David P. Myatt, 2007. "On the Theory of Strategic Voting -super-1," Review of Economic Studies, Oxford University Press, vol. 74(1), pages 255-281.
  19. Roger B. Myerson, 1997. "Large Poisson Games," Discussion Papers 1189, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Kim, Jaehoon & Fey, Mark, 2007. "The swing voter's curse with adversarial preferences," Journal of Economic Theory, Elsevier, vol. 135(1), pages 236-252, July.
  21. Roger B. Myerson & Robert J. Weber, 1988. "A Theory of Voting Equilibria," Discussion Papers 782, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  22. Cesar Martinelli, 2000. "Simple Plurality versus Plurality Runoff with Privately Informed Voters," Working Papers 0004, Centro de Investigacion Economica, ITAM.
  23. Steven Brams & Peter Fishburn, 2005. "Going from theory to practice: the mixed success of approval voting," Social Choice and Welfare, Springer, vol. 25(2), pages 457-474, December.
  24. Martin J. Osborne & Matthew A. Turner, 2010. "Cost Benefit Analyses versus Referenda," Journal of Political Economy, University of Chicago Press, vol. 118(1), pages 156-187, 02.
  25. Matias Nuñez, 2010. "Condorcet Consistency of Approval Voting: a Counter Example in Large Poisson Games," Journal of Theoretical Politics, , vol. 22(1), pages 64-84, January.
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Citations

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Cited by:
  1. Matias Nunez & Jean-Francois Laslier, 2013. "Preference Intensity Representation : Strategic Overstating in Large Elections," Post-Print hal-00917099, HAL.
  2. GOERTZ, Johanna & MANIQUET, François, 2013. "Large elections with multiple alternatives: a Condorcet Jury Theorem and inefficient equilibria," CORE Discussion Papers 2013023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. MANIQUET, François & MORELLI, Massimo & ,, 2013. "Approval quorums dominate participation quorums," CORE Discussion Papers 2013054, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Francesco De Sinopoli & Claudia Meroni & Carlos Pimienta, 2014. "Strategic Stability in Poisson Games," Discussion Papers 2014-09, School of Economics, The University of New South Wales.
  5. Laurent Bouton & Micael Castanheira & Aniol Llorente-Saguer, 2012. "Divided Majority and Information Aggregation: Theory and Experiment," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2012_20, Max Planck Institute for Research on Collective Goods.
  6. David S. Ahny & Santiago Oliveros, 2013. "Approval Voting and Scoring Rules with Common Values," Economics Discussion Papers 732, University of Essex, Department of Economics.
  7. Laurent Bouton & Gabriele Gratton, 2013. "Majority Runoff Elections: Strategic Voting and Duverger's Hypothesis," Discussion Papers 2013-23, School of Economics, The University of New South Wales.
  8. Sébastien Courtin & Matias Nunez, 2013. "A Map of Approval Voting Equilibria Outcomes," THEMA Working Papers 2013-31, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  9. Sébastien Courtin & Matias Nùnez, 2013. "Dominance Solvable Approval Voting Games," THEMA Working Papers 2013-27, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  10. Laurent Bouton, 2012. "A Theory of Strategic Voting in Runoff Elections," Boston University - Department of Economics - Working Papers Series WP2012-001, Boston University - Department of Economics.
  11. Matias Nunez, 2013. "The Strategic Sincerity of Approval Voting," Post-Print hal-00917101, HAL.
  12. Martin Gregor, 2013. "The Optimal Ballot Structure for Double-Member Districts," CERGE-EI Working Papers wp493, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  13. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer, vol. 56(1), pages 157-189, May.

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