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An expected utility analysis of k-majority rules

Author

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  • Keith L. Dougherty

    (University of Georgia)

  • Robi Ragan

    (Mercer University)

Abstract

Buchanan and Tullok (The calculus of consent: logical foundations of constitutional democracy. University of Michigan Press, Ann Arbor, 1962) argued that the optimal k-majority rule should minimize the sum of external costs and decision costs. Dougherty et al. (Public Choice, 163(1–2):31–52, 2015) formalized their approach using various groups of voters. In this study, we analyze the optimal k-majority rule in terms of expected utility and compare our results to Dougherty et al. (2015), which focuses on costs alone. Specifically, we replace Buchanan and Tullock’s external cost function with an external utility function that accounts for both the benefits and costs of enacting proposals. We find that analyzing k-majority rules in terms of utility, rather than costs, affects the optima. Furthermore, in terms of utility, the optimal k-majority rule can vary depending on the group one expects to be in during a vote. With some interesting exceptions, individuals from groups that favor the proposal often find small k-majority rules optimal. Individuals from groups that oppose the proposal often find large k-majority rules optimal.

Suggested Citation

  • Keith L. Dougherty & Robi Ragan, 2016. "An expected utility analysis of k-majority rules," Constitutional Political Economy, Springer, vol. 27(3), pages 332-353, September.
    • Handle: RePEc:kap:copoec:v:27:y:2016:i:3:d:10.1007_s10602-016-9217-7
    DOI: 10.1007/s10602-016-9217-7
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    References listed on IDEAS

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    1. Z. Spindler, 1990. "Constitutional design for a rent-seeking society: Voting rule choice," Constitutional Political Economy, Springer, vol. 1(3), pages 73-82, September.
    2. Mueller,Dennis C., 2003. "Public Choice III," Cambridge Books, Cambridge University Press, number 9780521894753.
    3. Keith L. Dougherty & Julian Edward, 2011. "The Calculus of Consent and Constitutional Design," Studies in Public Choice, Springer, number 978-0-387-98171-0, June.
    4. Roger Congleton, 2007. "Informational limits to democratic public policy: The jury theorem, yardstick competition, and ignorance," Public Choice, Springer, vol. 132(3), pages 333-352, September.
    5. Thomas Schwartz, 2008. "Parliamentary procedure: principal forms and political effects," Public Choice, Springer, vol. 136(3), pages 353-377, September.
    6. Guttman, Joel M., 1998. "Unanimity and majority rule: the calculus of consent reconsidered," European Journal of Political Economy, Elsevier, vol. 14(2), pages 189-207, May.
    7. Brennan,Geoffrey & Hamlin,Alan, 2000. "Democratic Devices and Desires," Cambridge Books, Cambridge University Press, number 9780521639774.
    8. Keith Dougherty & Julian Edward & Robi Ragan, 2015. "The value of formalism: re-examining external costs and decision costs with multiple groups," Public Choice, Springer, vol. 163(1), pages 31-52, April.
    9. Keith Dougherty & Julian Edward, 2012. "Voting for Pareto optimality: a multidimensional analysis," Public Choice, Springer, vol. 151(3), pages 655-678, June.
    10. Keith L. Dougherty & Julian Edward, 2004. "The Pareto Efficiency and Expected Costs of k-Majority Rules," Politics, Philosophy & Economics, , vol. 3(2), pages 161-189, May.
    11. 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.
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    Cited by:

    1. George Tridimas, 2017. "Constitutional choice in ancient Athens: the evolution of the frequency of decision making," Constitutional Political Economy, Springer, vol. 28(3), pages 209-230, September.

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    More about this item

    Keywords

    k-Majority rules; q-Rules; Constitutional design;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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

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