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Democracy Undone. Systematic Minority Advantage in Competitive Vote Markets
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Democracy Undone. Systematic Minority Advantage in Competitive Vote Markets

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  • Casella, Alessandra
  • Turban, Sébastien

Abstract

We study the competitive equilibrium of a market for votes where voters can trade votes for a numeraire before making a decision via majority rule. The choice is binary and the number of supporters of either alternative is known. We identify a sufficient condition guaranteeing the existence of an ex ante equilibrium. In equilibrium, only the most intense voter on each side demands votes and each demand enough votes to alone control a majority. The probability of a minority victory is independent of the size of the minority and converges to one half, for any minority size, when the electorate is arbitrarily large. In a large electorate, the numerical advantage of the majority becomes irrelevant: democracy is undone by the market.

Suggested Citation

  • Casella, Alessandra & Turban, Sébastien, 2012. "Democracy Undone. Systematic Minority Advantage in Competitive Vote Markets," CEPR Discussion Papers 9242, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:9242
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    1. Myerson, Roger B., 1993. "Incentives to Cultivate Favored Minorities Under Alternative Electoral Systems," American Political Science Review, Cambridge University Press, vol. 87(4), pages 856-869, December.
    2. Riker, William H. & Brams, Steven J., 1973. "The Paradox of Vote Trading," American Political Science Review, Cambridge University Press, vol. 67(4), pages 1235-1247, December.
    3. Hortala-Vallve, Rafael & Llorente-Saguer, Aniol, 2010. "A simple mechanism for resolving conflict," Games and Economic Behavior, Elsevier, vol. 70(2), pages 375-391, November.
    4. Casella, Alessandra & Turban, Sébastien, 2014. "Democracy undone. Systematic minority advantage in competitive vote markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 47-70.
    5. Casella, Alessandra & Gelman, Andrew & Palfrey, Thomas R., 2006. "An experimental study of storable votes," Games and Economic Behavior, Elsevier, vol. 57(1), pages 123-154, October.
    6. Alessandra Casella & Thomas Palfrey & Raymond Riezman, 2013. "Minorities and Storable Votes," World Scientific Book Chapters, in: Raymond Riezman (ed.), International Trade Agreements and Political Economy, chapter 15, pages 247-282, World Scientific Publishing Co. Pte. Ltd..
    7. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    8. Dirk Engelmann & Veronika Grimm, 2012. "Mechanisms for Efficient Voting with Private Information about Preferences," Economic Journal, Royal Economic Society, vol. 122(563), pages 1010-1041, September.
    9. Mount, Kenneth & Reiter, Stanley, 1974. "The informational size of message spaces," Journal of Economic Theory, Elsevier, vol. 8(2), pages 161-192, June.
    10. George J. Mailath & Andrew Postlewaite, 1990. "Asymmetric Information Bargaining Problems with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 351-367.
    11. Haefele, Edwin T, 1971. "A Utility Theory of Representative Government," American Economic Review, American Economic Association, vol. 61(3), pages 350-367, June.
    12. Alessandra Casella & Aniol Llorente-Saguer & Thomas R. Palfrey, 2012. "Competitive Equilibrium in Markets for Votes," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 593-658.
    13. Rafael Hortala-Vallve, 2012. "Qualitative voting," Journal of Theoretical Politics, , vol. 24(4), pages 526-554, October.
    14. Levine, David K. & Palfrey, Thomas R., 2007. "The Paradox of Voter Participation? A Laboratory Study," American Political Science Review, Cambridge University Press, vol. 101(1), pages 143-158, February.
    15. Dekel, Eddie & Jackson, Matthew O. & Wolinsky, Asher, 2009. "Vote Buying: Legislatures and Lobbying," Quarterly Journal of Political Science, now publishers, vol. 4(2), pages 103-128, July.
    16. Klaus Kultti & Hannu Salonen, 2005. "Market for Votes," Homo Oeconomicus, Institute of SocioEconomics, vol. 23, pages 323-332.
    17. Iaryczower, Matias & Oliveros, Santiago, 2016. "Power brokers: Middlemen in legislative bargaining," Journal of Economic Theory, Elsevier, vol. 162(C), pages 209-236.
    18. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    19. Wilson, Robert, 1969. "An Axiomatic Model of Logrolling," American Economic Review, American Economic Association, vol. 59(3), pages 331-341, June.
    20. Peter Bernholz, 1974. "Logrolling, Arrow‐Paradox And Decision Rules ‐A Generalization ," Kyklos, Wiley Blackwell, vol. 27(1), pages 49-62, January.
    21. Green, Jerry, 1980. "On the Theory of Effective Demand," Economic Journal, Royal Economic Society, vol. 90(358), pages 341-353, June.
    22. Eddie Dekel & Matthew O. Jackson & Asher Wolinsky, 2008. "Vote Buying: General Elections," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 351-380, April.
    23. Schwartz, Thomas, 1977. "Collective Choice, Separation of Issues and Vote Trading," American Political Science Review, Cambridge University Press, vol. 71(3), pages 999-1010, September.
    24. Jeffrey S. Rosenthal & Martin J. Osborne & Matthew A. Turner, 2000. "Meetings with Costly Participation," American Economic Review, American Economic Association, vol. 90(4), pages 927-943, September.
    25. Casella, Alessandra, 2005. "Storable votes," Games and Economic Behavior, Elsevier, vol. 51(2), pages 391-419, May.
    26. Jeffrey Weiss, 1988. "Is vote-selling desirable?," Public Choice, Springer, vol. 59(2), pages 177-194, November.
    27. Eddie Dekel & Matthew O. Jackson & Asher Wolinsky, 2004. "Vote Buying," Discussion Papers 1386, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
      • Eddie Dekel & Matthew O. Jackson & Asher Wolinsky, 2005. "Vote Buying," Others 0503006, University Library of Munich, Germany.
      • Jackson, Matthew O. & Dekel, Eddie & Wolinsky, Asher, 2005. "Vote buying," Working Papers 1215, California Institute of Technology, Division of the Humanities and Social Sciences.
    28. Bettina Klose & Dan Kovenock, 2015. "The all-pay auction with complete information and identity-dependent externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 1-19, May.
    29. Tobin, James, 1970. "On Limiting the Domain of Inequality," Journal of Law and Economics, University of Chicago Press, vol. 13(2), pages 263-277, October.
    30. Tullock, Gordon, 1970. "A Simple Algebraic Logrolling Model," American Economic Review, American Economic Association, vol. 60(3), pages 419-426, June.
    31. Peter Bernholz, 1973. "Logrolling, arrow paradox and cyclical majorities," Public Choice, Springer, vol. 15(1), pages 87-95, June.
    32. repec:esx:essedp:731 is not listed on IDEAS
    33. Koehler, David H., 1975. "Vote Trading and the Voting Paradox: A Proof of Logical Equivalence," American Political Science Review, Cambridge University Press, vol. 69(3), pages 954-960, September.
    34. Casella, Alessandra, 2012. "Storable Votes: Protecting the Minority Voice," OUP Catalogue, Oxford University Press, number 9780195309089, December.
    35. Casella, Alessandra & Palfrey, Thomas & Turban, Sébastien, 2014. "Vote trading with and without party leaders," Journal of Public Economics, Elsevier, vol. 112(C), pages 115-128.
    36. Manfred Gartner, 1976. "Endogenous bandwagon and underdog effects in a rational choice model," Public Choice, Springer, vol. 25(1), pages 83-89, March.
    37. Joseph Kadane, 1972. "On division of the question," Public Choice, Springer, vol. 13(1), pages 47-54, September.
    38. Philipson, Tomas J & Snyder, James M, Jr, 1996. "Equilibrium and Efficiency in an Organized Vote Market," Public Choice, Springer, vol. 89(3-4), pages 245-265, December.
    39. Groseclose, Tim & Snyder, James M., 1996. "Buying Supermajorities," American Political Science Review, Cambridge University Press, vol. 90(2), pages 303-315, June.
    40. Matthew O Jackson & Hugo F Sonnenschein, 2007. "Overcoming Incentive Constraints by Linking Decisions -super-1," Econometrica, Econometric Society, vol. 75(1), pages 241-257, January.
    41. Dennis C. Mueller, 1973. "Constitutional Democracy and Social Welfare," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(1), pages 60-80.
    42. Thomas Schwartz, 1981. "The universal-instability theorem," Public Choice, Springer, vol. 37(3), pages 487-501, January.
    43. Ilyana Kuziemko & Eric Werker, 2006. "How Much Is a Seat on the Security Council Worth? Foreign Aid and Bribery at the United Nations," Journal of Political Economy, University of Chicago Press, vol. 114(5), pages 905-930, October.
    44. Satz, Debra, 2010. "Why Some Things Should Not Be for Sale: The Moral Limits of Markets," OUP Catalogue, Oxford University Press, number 9780195311594, December.
    45. Beth Allen & James S. Jordan, 1998. "The existence of rational expectations equilibrium: a retrospective," Staff Report 252, Federal Reserve Bank of Minneapolis.
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    Cited by:

    1. Wagner, Alexander K. & Granic, Dura-Georg, 2017. "Tie-Breaking Power in Committees," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168187, Verein für Socialpolitik / German Economic Association.
    2. Casella, Alessandra & Turban, Sébastien, 2014. "Democracy undone. Systematic minority advantage in competitive vote markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 47-70.
    3. Alessandra Casella & Antonin Macé, 2021. "Does Vote Trading Improve Welfare?," Annual Review of Economics, Annual Reviews, vol. 13(1), pages 57-86, August.
    4. Dimitrios Xefteris & Nicholas Ziros, 2024. "The “invisible hand” of vote markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 153-165, February.
    5. Xefteris, Dimitrios & Ziros, Nicholas, 2018. "Strategic vote trading under complete information," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 52-58.
    6. Dimitrios Xefteris & Nicholas Ziros, 2017. "Strategic Vote Trading in Power Sharing Systems," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 76-94, May.
    7. Casella, Alessandra & Palfrey, Thomas & Turban, Sébastien, 2014. "Vote trading with and without party leaders," Journal of Public Economics, Elsevier, vol. 112(C), pages 115-128.
    8. Nikolas Tsakas & Dimitrios Xefteris & Nicholas Ziros, 2021. "Vote Trading in Power-Sharing Systems: A Laboratory Investigation," The Economic Journal, Royal Economic Society, vol. 131(636), pages 1849-1882.
    9. Casella, Alessandra & Macé, Antonin, 2020. "Does Vote Trading Improve Welfare?," CEPR Discussion Papers 15201, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    Majority voting; Minority; Vote buying; Vote trading; Voting;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • P16 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Capitalist Institutions; Welfare State

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