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Voting as a Lottery

Voting is a lottery in which an individual who is uncertain about how the others vote wins if she belongs to the majority or loses if she falls into the minority. The risk of losing can be reduced by increasing the majority threshold. This however has the negative effect of also lowering the chance to win. We find that an individual prefers higher majority thresholds when she is more risk averse, less powerful,or less optimistic about the chance that others will vote like her. Defacto, raising the majority threshold is a form of protection against the higher risk of being tyrannized by an unfavorable majority. We include these preferences for majority thresholds in a Nash bargaining game that describes constitutional negotiations over voting rules. Individuals that largely avert the risk of being tyrannized behave reluctantly during negotiations, and succeed in getting higher protection through a threshold raise.

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Paper provided by ISLA, Centre for research on Latin American Studies and Transition Economies, Universita' Bocconi, Milano, Italy in its series ISLA Working Papers with number 28.

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Length: 35 pages
Date of creation: May 2007
Date of revision:
Handle: RePEc:slp:islawp:islawp28
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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. Philippe Aghion & Alberto Alesina & Francesco Trebbi, 2004. "Endogenous Political Institutions," The Quarterly Journal of Economics, MIT Press, vol. 119(2), pages 565-611, May.
  3. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-97, June.
  4. Barbera, Salvador & Matthew O. Jackson, 2004. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Working Papers 1196, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Paul Schure & Francesco Passerelli & David Scoones, 2007. "When the Powerful Drag Their Feet," Department Discussion Papers 0703, Department of Economics, University of Victoria.
  6. Buchanan, James M & Faith, Roger L, 1980. "Subjective Elements in Rawlsian Contractual Agreement on Distributional Rules," Economic Inquiry, Western Economic Association International, vol. 18(1), pages 23-38, January.
  7. Matthias Messner & Mattias K. Polborn, 2004. "Voting on Majority Rules," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 115-132.
  8. Mariotti, Marco, 1998. "Extending Nash's Axioms to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 22(2), pages 377-383, February.
  9. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  10. Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer, vol. 15(3), pages 413-421.
  11. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, 09.
  12. Buchanan, James M & Faith, Roger L, 1981. "Entrepreneurship and the Internalization of Externalities," Journal of Law and Economics, University of Chicago Press, vol. 24(1), pages 95-111, April.
  13. Thomas Zorn & Dolores Martin, 1986. "Optimism and pessimism in political and market institutions," Public Choice, Springer, vol. 49(2), pages 165-178, January.
  14. Harrington, Joseph E, Jr, 1990. " The Role of Risk Preferences in Bargaining When Acceptance of a Proposal Requires Less than Unanimous Approval," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 135-54, June.
  15. Benoit, Jean-Pierre & Kornhauser, Lewis A., 2002. "Game-theoretic analysis of legal rules and institutions," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 60, pages 2229-2269 Elsevier.
  16. Vincenzo Denicolò & Marco Mariotti, 2000. "Nash Bargaining Theory, Nonconvex Problems and Social Welfare Orderings," Theory and Decision, Springer, vol. 48(4), pages 351-358, June.
  17. Mariotti, Marco, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 733-41, July.
  18. Roger B. Myerson & Daniel Diermeier, 1999. "Bicameralism and Its Consequences for the Internal Organization of Legislatures," American Economic Review, American Economic Association, vol. 89(5), pages 1182-1196, December.
  19. James M. Snyder Jr. & Michael M. Ting & Stephen Ansolabehere, 2005. "Legislative Bargaining under Weighted Voting," American Economic Review, American Economic Association, vol. 95(4), pages 981-1004, September.
  20. repec:cup:cbooks:9780521894753 is not listed on IDEAS
  21. Enriqueta Aragonés & Andrew Postlewaite, 1999. "Ambiguity in election games," Economics Working Papers 364, Department of Economics and Business, Universitat Pompeu Fabra.
  22. Mueller, Dennis C, 1973. "Constitutional Democracy and Social Welfare," The Quarterly Journal of Economics, MIT Press, vol. 87(1), pages 60-80, February.
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