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One Person, Many Votes: Divided Majority and Information Aggregation

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  • Laurent Bouton
  • Micael Castanheira De Moura

Abstract

This paper shows that information imperfections and common values can solve coordination problems in multicandidate elections. We analyze an election in which (i) the majority is divided between two alternatives and (ii) the minority backs a third alternative, which the majority views as strictly inferior. Standard analyses assume voters have a fixed preference ordering over candidates. Coordination problems cannot be overcome in such a case, and it is possible that inferior candidates win. In our setup the majority is also divided as a result of information imperfections. The majority thus faces two problems: aggregating information and coordinating to defeat the minority candidate. We show that when the common value component is strong enough, approval voting produces full information and coordination equivalence: the equilibrium is unique and solves both problems. Thus, the need for information aggregation helps resolve the majority's coordination problem under approval voting. This is not the case under standard electoral systems.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/108675.

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Date of creation: 10 Jan 2012
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Publication status: Published in: Econometrica (2012) v.80 n° 1,p.43-87
Handle: RePEc:ulb:ulbeco:2013/108675

Note: This is a translation of: One Person, Many Votes: Divided Majority and Information Aggregation
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  1. GOERTZ, Johanna M. & MANIQUET, François, 2009. "On the informational efficiency of simple scoring rules," CORE Discussion Papers 2009026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Roger B. Myerson, 1998. "Comparison of Scoring Rules in Poisson Voting Games," Discussion Papers 1214, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Micael Castanheira De Moura, 2003. "Why vote for losers?," ULB Institutional Repository 2013/10005, ULB -- Universite Libre de Bruxelles.
  4. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
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  6. César Martinelli, 2002. "Simple plurality versus plurality runoff with privately informed voters," Social Choice and Welfare, Springer, vol. 19(4), pages 901-919.
  7. Sourav Bhattacharya, 2006. "Preference Monotonicity and Information Aggregation in Elections," Working Papers 325, University of Pittsburgh, Department of Economics, revised Dec 2008.
  8. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
  9. David S. Ahny & Santiago Oliveros, 2013. "Approval Voting and Scoring Rules with Common Values," Economics Discussion Papers 732, University of Essex, Department of Economics.
  10. 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.
  11. 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.
  12. Jean-François Laslier, 2004. "Strategic approval voting in a large electorate," IDEP Working Papers 0405, Institut d'economie publique (IDEP), Marseille, France.
  13. 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.
  14. Timothy Feddersen & Wolfgang Pesendorfer, 1994. "Voting Behavior and Information Aggregation in Elections with Private Information," Discussion Papers 1117, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  17. Piketty, Thomas, 2000. "Voting as Communicating," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 169-91, January.
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  19. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Timothy J. Feddersen & Wolfgang Pesendorfer, 1995. "The Swing Voter's Curse," Discussion Papers 1064, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. 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.
  22. 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.
  23. 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.
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  25. 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.
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Citations

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Cited by:
  1. Matias Nunez, 2013. "The Strategic Sincerity of Approval Voting," Post-Print hal-00917101, HAL.
  2. 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).
  3. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer, vol. 56(1), pages 157-189, May.
  4. David S. Ahny & Santiago Oliveros, 2013. "Approval Voting and Scoring Rules with Common Values," Economics Discussion Papers 732, University of Essex, Department of Economics.
  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. 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.
  7. Matias Nunez & Jean-Francois Laslier, 2013. "Preference Intensity Representation : Strategic Overstating in Large Elections," Post-Print hal-00917099, HAL.
  8. Bouton, Laurent & Gratton, Gabriele, 0. "Majority runoff elections: strategic voting and Duverger's hypothesis," Theoretical Economics, Econometric Society.
  9. Sebastien Courtin & Matias Nunez, 2013. "Dominance Solvable Approval Voting Games," Working Papers hal-00914890, HAL.
  10. 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.
  11. Laurent Bouton, 2013. "A Theory of Strategic Voting in Runoff Elections," American Economic Review, American Economic Association, vol. 103(4), pages 1248-88, June.
  12. 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.
  13. 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).

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