¹ A Dictionary of Americanisms (1951), which is probably the most authoritative collection, cites many political examples from 1812 (Ninian Edwards) to 1949 (Time magazine), in every one of which the word is clearly used in a pejorative sense. In the quotation from Edwards, logrolling is specifically identified with intrigue; and the climate of intrigue is conveyed by almost all the later quotations. The Oxford Dictionary (i.e., A New English Dictionary on Historical Principles) cites political usage from both sides of the Atlantic from 1823 (Niles Weekly) on to the end of the century, and its quotations also are uniformly pejorative. Bartlett's, Dictionary of Americanisms (1859)Google Scholar contains a lengthy and righteously indignant explication of the political sense of “logrolling.” None of these sources indicate any pejorative connotation at all for the word when it refers to clearing land or building houses. It must have acquired the sense of intrigue, therefore, only when it was transferred from the bartering of labor to the bartering of votes. And this demonstrates that the bartering of votes has regularly been socially disapproved.

² Schattschneider, E. E., Politics, Pressures and the Tariff (New Jersey: Prentice-Hall, 1935), p. 293 Google Scholar. Schattschneider interpreted the process of tariff writing as an “attempt to set up a beneficently discriminatory set of privileges”—beneficient in the sense that a few particular industries deemed worthy would benefit. This attempt failed, he argued, because the legislation as actually written protected so “indiscriminately … as to destroy the logic and sense of the policy” (p. 283). One of the purposes of this essay is to explain the conditions for such failure.

³ Committee on Political Parties of the American Political Science Association, Toward a More Responsible Two-Party System (New York: Rinehart, 1950)Google Scholar.

⁴ Buchanan, James and Tullock, Gordon, The Calculus of Consent (Ann Arbor: University of Michigan Press, 1962), p. 145 CrossRefGoogle Scholar.

⁵ Ibid.

⁶ Tullock, Gordon, “A Simple Algebraic Logrolling Model,” American Economic Review, vol. 60 (June, 1970), pp. 419–26Google Scholar.

⁷ Coleman, James, “The Possibility of a Social Welfare Function,” American Economic Review, vol. 56 (December, 1966), 1105–22Google Scholar.

⁸ Mueller, Dennis C., “The Possibility of a Social Welfare Function: Comment” American Economic Review, vol. 57 (December, 1957), 1304–11Google Scholar; and, in an especially lucid and compelling argument, Wilson, Robert, “An Axiomatic Model of Logrolling,” American Economic Review, vol. 59 (June, 1969), 331–41Google Scholar, shows that, except in one unlikely circumstance, logrolling necessarily involves a violation of Arrow's condition of independence from irrelevant alternatives.

⁹ See Wilson, op. cit.; Haefle, Edwin T., “Coalitions, Minority Representation, and Vote-Trading Probabilities,” Public Choice, vol. 8 (Spring, 1970), 75–90 CrossRefGoogle Scholar; and Mueller, Dennis C., Philpotts, Geoffrey C., and Vanek, Jaroslav, “The Social Gains from Exchanging Votes: A Simulation Approach,” Public Choice, vol. 13 (Fall, 1972), 55–79 CrossRefGoogle Scholar.

¹⁰ To say R is connected means that either XRY or YRX is true; to say R is transitive means it is true that if XRY and YRZ, then XRZ; to say R is reflexive means that it is true that XRX.

¹¹ Black, Duncan, The Theory of Committees and Elections (Cambridge, Cambridge University Press, 1958), p. 44 Google Scholar, uses the former phrase and Farquharson, Robin, Theory of Voting (New Haven, Yale, 1970), pp. 17–18 Google Scholar, uses the latter. Voting in accord with one's true tastes (defined over motions) seems “sincere.” But if utility is defined over outcomes, it seems merely naive to confuse means and ends.

¹² An exception is Coleman, p. 1121, where it is noted in passing that the inclusion of such costs requires a “much more extensive calculation” than offered in that essay. More recently Coleman has provided an explicit calculation that leads to the conclusion that vote trading is profitable only under conditions of “absolutely free and frictionless political exchange” that preclude arbitrary decision rules. Coleman, James S., “Beyond Pareto Optimality,” in Philosophy, Science, and Method, ed. Morgenbesser, Sidney, Suppes, Patrick, and White, Morton (New York, St. Martin's, 1969), pp. 415–39Google Scholar.

¹³ We assume that the utility of a member for a majority position on a motion he disagrees with, (T_d(x)), is the same for him as the utility of a minority position on that same motion, ( − T(x)), because in both cases his sincere position differs from the prevailing one.

¹⁴ Haefle, Edwin T., “Paradox Lost” (Washington D.C., mineographed, 1972)Google Scholar.

¹⁵ For the case of cardinal utility, R. E. Park has shown that there is in general no stable equilibrium if there is a majority that can, through vote trading, improve the payoffs to all its members over the payoffs without vote trading. Furthermore, he has shown that if there is a stable equilibrium with vote trading, it must be exactly the same as the outcome without vote trading. Park, R. E., “The Possibility of a Social Welfare Function: Comment,” American Economic Review, vol. 57 (December 1967), 1301–04Google Scholar. In “The Possibility of a Social Welfare Function: Reply,” ibid., pp. 1311–17, however, James Coleman argues that Park's assumptions are unrealistically restrictive.