The Pareto Efficiency and Expected Costs of k-Majority Rules

Politics, Philosophy & Economics

Volumn 3, Issue 2, 2004, Pages 161-189

  Dougherty, Keith L ^a   Edward, Julian ^b  

^a UNIVERSITY OF GEORGIA   (United States)

^b FLORIDA INTERNATIONAL UNIVERSITY   (United States)

Author keywords

constitutional design; external costs; Pareto criterion; social contract

Indexed keywords

EID: 26644439776     PISSN: 1470594X     EISSN: 17413060     Source Type: Journal    
DOI: 10.1177/1470594X04042962     Document Type: Article

References (26)

1. Dennis Mueller, ‘The Importance of Uncertainty in a Two-Stage Theory of Constitutions’, Public Choice 108 (2001): 223-258; Zane A. Spindler, ‘Constitutional Design for a Rent-Seeking Society: Voting Rule Choice’, Constitutional Political Economy 1(3) (1990): 73-82; Joel Guttman, ‘Unanimity and Majority Rule: The Calculus of Consent Reconsidered’, European Journal of Political Economy 14 (1998): 189-207; Douglas Rae, ‘Decision Rules and Individual Values in Constitutional Choice’, American Political Science Review 63(1) (1969): 40-56.
2. James M. Buchanan and Gordon Tullock, The Calculus of Consent (Ann Arbor: University of Michigan Press, 1962).
3. Other authors seem to have used this criterion while calling it the Pareto criterion. See for example, John Head, Public Goods and Public Welfare (Durham, NC: Duke University Press, 1974); and Niclas Berggren, ‘Social Order Through Constitutional Choice’, Public Choice 89 (1996): 339-361.
4. External costs are the costs an individual expects to endure from the actions of others. Decision costs are the costs in time and effort needed to reach an agreement.
5. Buchanan and Tullock, Calculus of Consent; Dennis Mueller, Public Choice II (New York: Cambridge University Press, 1989); Dennis Mueller, Constitutional Democracy (New York: Oxford University Press, 1996); and Dennis Mueller, ‘Constitutional Public Choice’, in Perspectives on Public Choice, edited by Dennis Mueller (New York: Cambridge University Press, 1997): 124-146.
6. Buchanan and Tullock, Calculus of Consent, pp. 64–65.
7. Dennis Mueller, Public Choice II.
8. Spindler, ‘Constitutional Design for a Rent-Seeking Society’; Rae, ‘Decision Rules and Individual Values in Constitutional Choice’; Guttman, ‘Unanimity and Majority Rule’.
9. Dennis Mueller, ‘The Importance of Uncertainty in a Two-Stage Theory of Constitutions’.
10. See for example, Rae, ‘Decision Rules and Individual Values in Constitutional Choice’; Michael Taylor, ‘Proof of a Theorem on Majority Rule’, Behavioral Science 14 (1969): 228-231; Andrew Caplin and Barry Nalebuff, ‘On 64%-Majority Rule’, Econometrica 56(4) (1988): 787-814; Timothy J. Fedderson and Wolfgang Pesendorfer, ‘The Swing Voters Curse’, American Economic Review 86(3) (1996): 408-424; and Keith L. Dougherty and Julian Edward, ‘Simple vs. Absolute Majority Rule’ (Florida International University, mimeo, 2003).
11. The terms ‘absolute’ and ‘simple’ are based on a distinction made by William Riker, Liberalism against Populism (Prospect Heights, IL: Waveland Press, 1982), pp. 17, 44-45. For a similar distinction using different nomenclature see Amartya K. Sen, Collective Choice and Social Welfare (New York: North-Holland, 1979), pp. 71, 181. For a discussion of how the distinction is misunderstood in the literature see Dan Felsenthal and Moshé Machover, ‘Misreporting Rules’, Homo Oeconomicus 27(4) (2001): 371-390; and Dan Felsenthal and Moshé Machover, ‘Models and Reality: The Curious Case of the Absent Abstention’, in Power Indices and Coalition Formation, edited by Manfred J. Holler and Guillermo Owen (Boston: Kluwer Academic Publishers, 2001): 87-103.
12. Although Buchanan and Tullock do not define their notion of social preference as rigorously as done here, they do claim that a desirable change can be made ‘only if all persons agree, that is, only if there is the unanimous consent of all members of the group. To be able to go beyond the Pareto rule and to judge a change “desirable” when all parties do not agree, the economist would find it necessary to compare the utility of one individual with that of another. Unwilling to take this step, the welfare economist stops at the Pareto rule and disavows all claims to positive conclusions beyond its limits’ (Buchanan and Tullock, Calculus of Consent, pp. 92–93). Other authors suggest that Buchanan and Tullock employ the BT criterion as well. See Sen, Collective Choice and Social Welfare, p. 25; Niclas Berggren, ‘Social Order Through Constitutional Choice’, pp. 339–340; and James Buchanan, ‘The relevance of Pareto Optimality’, Journal of Conflict Resolution 6(4) (1962): 341-354.
13. Also see James Buchanan, The Limits of Liberty (Chicago: University of Chicago Press, 1975); and Sen, Collective Choice and Social Welfare, p. 25.
14. Knut Wicksell, ‘New Principle of Just Taxation’, reprinted in Classics in the Theory of Public Finance, 3rd edition, by Richard Musgrave and Alan Peacock (New York: McGraw-Hill, [1896] 1967): 72-118.
15. Buchanan and Tullock, Calculus of Consent, p. 64.
16. In many ways it would be more natural to describe external costs in terms of an individual's expected negative utility, but this requires interpersonal comparisons of utility that we want to avoid. Similar problems are discussed by Rae, ‘Decision Rules and Individual Values in Constitutional Choice’, p. 41, n. 6; and Mueller, Public Choice II, pp. 100–101, 105-107.
17. See for example Mueller, Constitutional Democracy; Spindler, ‘Constitutional Design for a Rent-Seeking Society’; and Buchanan and Tullock, Calculus of Consent.
18. Buchanan and Tullock, Calculus of Consent, p. 68.
19. If we now used a criterion based on the net number of gainers to choose among the supermajority rules that minimized total costs, the preferred voting rule would be the smallest of these supermajority rules. See Rae, ‘Decision Rules and Individual Values in Constitutional Choice’; Dougherty and Edward, ‘Simple vs Absolute Majority Rule’; and Guttman, ‘Unanimity and Majority Rule’ for examples of such criteria.
20. Buchanan and Tullock, Calculus of Consent, pp. 81–82; Mueller, Public Choice II, p. 56.
21. Other shapes of the decision cost curve have also been considered. See Mueller, Constitutional Democracy, pp. 154–157; Mueller, ‘Constitutional Public Choice’, pp. 127–130.
22. Mueller, Public Choice II, pp. 28, 103.
23. See Richard A. Brody and Benjamin I. Page, ‘Indifference, Alienation, and Rational Decisions’, Public Choice 15 (1973) (summer): 1-17; and Fedderson and Pesendorfer, ‘The Swing Voters Curse’. A conservative estimate of indifference might be the amount of roll-off in an election. Roll-off is the ‘tendency of the electorate to vote for “prestige” offices but not for lower offices on the same ballot’. See Walter D. Burnham, ‘The Changing Shape of the American Political Universe’, American Political Science Review 59(1) (1965): 7-28. In the Florida 2000 election, for example, 26 percent of those voting did not mark a preference for Justice Quince. This probably understates the indifference toward the election of this judge because the percentage does not consider indifference among non-voters.
24. Buchanan and Tullock, Calculus of Consent, pp. 258–259, emphasis in text.
25. Sen, Collective Choice and Social Welfare, p. 25, n. 6.
26. Harry Beran, The Consent Theory of Political Obligation (New York: Croom Helm, 1987), p. 31. For a more general view on consent theory see A. John Simmons, Moral Principles and Political Obligations (Princeton, New Jersey: Princeton University Press, 1979), p. 71.