¹ I am not suggesting that there is a unique, agreed-upon theory of compensation tests and Social Welfare Functions, but only that the work in both areas has a common intent.

² The notion of the “ideal,” though it now has a considerable history of economic literature, is most consistently explored and used by Baumol, W. J., Welfare Economics and the Theory of the State (2nd ed., Cambridge, Mass., 1965).Google Scholar

³ Arrow, K. J., Social Choice and Individual Values (2nd ed., New York, 1965)Google Scholar. For those not familiar with Arrow's work, the major argument is that unless individual preference orderings satisfy certain rather stringent conditions (in particular, that of single-peakedness) no social ordering can be derived from individual orderings where the social ordering is required to bear certain correspondences to the individual orderings (chap. 3). But see Tullock, G., “The General Irrelevance of the General Impossibility Theorem,” Quarterly Journal of Economics, May 1967.Google Scholar

⁴ The “global” maximum or optimum is the highest of all “local” maxima.

⁵ Popper, K., The Open Society and Its Enemies (2nd ed. rev., London, 1952).Google Scholar

⁶ Braybrooke, D. and Lindblom, C. E., A Strategy of Decision (New York, 1963).Google Scholar

⁷ Such an ideal is not only considered inaccurate as a description of the decision-making process, but it also is considered valueless as an ideal. This is because the “synoptic ideal… does not adapt in any specific way to: (1) man's limited intellectual capacities; (2) his limited knowledge; (3) the costliness of analysis; (4) the analyst's inevitable failure to construct a complete rational-deductive system or welfare function; (5) interdependences between fact and value; (6) the openness of the systems to be analyzed; (7) the analyst's need for strategic sequences to guide analysis and evaluation; (8) the diversity of forms in which policy problems actually arise.” Ibid., 113. The authors admit that the approach is inappropriate for “grand opportunities,” but one would wish to know how these opportunities are to be distinguished from more routine run-of-the-mill opportunities. Are the problems of urban planning and development and air pollution “grand opportunities?”

⁸ It may be that some psychological constraints are of a coercive nature, that is, inescapable without “punishment.” Such constraints are internal, however; here, we are thinking of external constraints imposed by men upon themselves.

⁹ Cf. Easton, David: the political process can be described as “the authoritative allocation of values for a society.” The Political System (New York, 1953).Google Scholar

¹⁰ Buchanan, J. M. and Tullock, G., The Calculus of Consent (Ann Arbor, 1962), 13.CrossRefGoogle Scholar

¹¹ Ibid.

¹² As “democracy” became a “hurrah” word.

¹³ Cf. Macpherson, C. B., The Real World of Democracy (Toronto, 1965)Google Scholar, for an atypical viewpoint. At a time when most (admittedly Western) political theorists are defining democracy in terms of the mechanisms and institutions of the political system, rather than its goals, Macpherson asserts that “the aim [of democracy] is to provide the conditions for the free development of human capacities, and to do this equally for all members of the society” (p. 58).

¹⁴ An Introduction to Democratic Theory (New York, 1960), 6.

¹⁵ Buchanan, J. M., “An Economic Theory of Clubs,” Economica, n. s. XXXII (Feb. 1965).Google Scholar

¹⁶ Let us use the word “collective” for commodities provided through government agency, and “co-operative” for those provided through clubs.

¹⁷ “An Economic Theory of Clubs.”

¹⁸ That is, they do not engage in logrolling. But just as a theory of consumer behaviour presumes that a limited budget consumer must “trade-off” some wants against others, so it would seem reasonable to expect that consumers of political goods will recognize that the “purchase” of some of these goods can only ordinarily be achieved by sacrificing the “purchase” of other goods. Both voters and buyers must, if they are at all rational, think in terms of opportunity costs. The importance of “logrolling” is examined further below.

¹⁹ “It was indubitably a correct description of what had happened in the New World from the time of the Mayflower Compact on to the organization of government along the banks of the Holston and the Watauga and the Tennessee, and of what was to happen, again and again, along the frontier from the Blue Ridge to the Willamette.” Commager, H. S., Majority Rule and Minority Rights (Gloucester, Mass., 1958)Google Scholar, 5. But, of course, “this basis of political obligation runs into immediate difficulty as soon as constitutional rules are made to apply to individuals other than those who might have been party to the original contract.” Buchanan and Tullock, The Calculus of Consent, 314.

²⁰ This and the four succeeding paragraphs are taken almost directly from my review article, “Towards a Social Welfare Function,” Canadian Journal of Economics and Political Science, XXVIII, no. 2 (May 1962), 295–300.

²¹ Rothenberg, J., The Measurement of Social Welfare (Englewood Cliffs, NJ, 1961).Google Scholar

²² For many years I have trotted this out as a Balfourism, without knowing whether it was really Balfour who said it or whether, indeed, anybody at all ever said it. None of the dictionaries of quotations I have checked help me; but I expect the quotation is well known to political scientists.

²³ “These norms, values, expectations, rules of the game… largely define the institution of government… These define the (legislator's) role, but represent the substance of prevailing values without which the political system could not exist.” Truman, David B., The Governmental Process (New York, 1951), 348.Google Scholar

²⁴ It is interesting to note what Thomas Jefferson had to say in this respect. “God forhid we should ever be twenty years without such a rebellion… What signify a few lives lost in a century or two? The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants. It is its natural manure.” Thomas Jefferson to Mr Stiles, Nov. 13, 1787, Letters and Addresses of Thomas Jefferson (New York, 1905), 64.

²⁵ The Logic of Democracy (New York, 1962), 139.

²⁶ “… for any individual with many values… The most rational rule to follow would appear to be something like this: select a political society that contains individuals whose goals are sufficiently like your own to provide the highest probability that you will maximize all your key values.” Dahl, R. A., A Preface to Democratic Theory (Chicago, 1956), 53–4.Google Scholar

²⁷ Professor Braybrooke has suggested that this may not be true even for a complete egoist, “for even egoists might prefer the company of free people who had voluntarily chosen to display love and friendship” (criticism of draft). I am not really sure whether this is a paradox or not. What I mean by “dictator” is an individual who could secure the social outcome he prefers. This might include “the company of free people.” Can one dictatorially command into existence a “company of free people”?

²⁸ “… a political system… is composed of methods of making public policies, those policies embodied in laws, orders, agreements, understandings and ‘conventions,’ at varying levels of generality related to government, and binding upon all within the system.” Mayo, H. B., “How can we justify Democracy?” American Political Science Review, LVI (Sept. 1962), 555.CrossRefGoogle Scholar

²⁹ In spite of Little's contention that “the essence of democracy is something which must escape definition in terms of any functional relation between decisions and individual preferences.” Little, I. M. D., “Social Choice and Individual Values,” Journal of Political Economy, LX (Oct. 1952), 422–32.CrossRefGoogle Scholar

³⁰ “… for legislation to be said to be by the people, it must stand in some positive relation to what the individual citizens would like legislation to be like.” Wollheim, R., “A Paradox in the Theory of Democracy,” in Laslett, P. and Runciman, W. G., eds., Philosophy, Politics and Society (2nd series Oxford, 1964), 74.Google Scholar

³¹ See for example, Downs, A., An Economic Theory of Democracy (New York, 1957)Google Scholar; Mayo, An Introduction to Democratic Theory; Ranney, A. and Kendall, W., Democracy and the American Party System (New York, 1956)Google Scholar; Dahl, A Preface to Democratic Theory.

³² See Bentley, A., The Process of Government (Chicago, 1908)Google Scholar; Truman, The Governmental Process.

³³ The assumption which underlies much of Buchanan and Tullock, The Calculus of Consent.

³⁴ As in Downs, An Economic Theory of Democracy.

³⁵ “It has been argued that though the majority principle may be alright in practice, it certainly is inadequate to any ideal construction of Democracy; and since any justification of Democracy is most likely to relate to an ideal construction, this is important.” Wollheim, “A Paradox in the Theory of Democracy,” 74. The “real-world” approximation to democracy, in this theoretical sense, is often called “polyarchy.” See Dahl, R. A. and Lindblom, C. E., Politics, Economics, and Welfare (New York, 1953), 43Google Scholar; and Dahl, A Preface to Democratic Theory, chap. 3.

³⁰ Riker, William H., Theory of Political Coalitions (New Haven, 1962)Google Scholar, discusses parties in terms analogous to those of Buchanan, “An Economic Theory of Clubs.” Riker makes a rather strange assumption. Coalitions are assumed to tend towards a “minimum winning” size in order to maximize the gain per member from the coalition. But of course there is no reason why gains per member should be maximized at that point unless there are very special assumptions about the marginal costs and marginal benefits from increasing membership of the coalition. (Clearly decreasing membership is not possible, since then the coalition will no longer be “winning.”) Riker's argument, while of considerable interest, is not of direct relevance to our problem.

³⁷ Unless some kind of ranking scheme is used. It might be technically more correct to say that the usual assumption is that each voter may cast only one ballot, whatever the number of votes he is allowed to indicate on that one ballot.

³⁸ That is one reason why I introduced the assumption that a 60–40 per cent split in the representative assembly corresponded to 60–40 per cent in the population at large. This rules out the kind of inequalities that can arise through the existence of very small majorities in some constituencies, and very large majorities in others, and from the existence of constituencies differing considerably in size.

³⁹ In a later article I hope to make a suggestion as to how we might loosen the usual requirement under this heading, so that intensities of preference might be expressed yet political equality be retained.

⁴⁰ Thorson, T. L., “Epilogue on Absolute Majority Rule,” Journal of Politics, XXIII (Aug. 1961), 557CrossRefGoogle Scholar. See also Ranney and Kendall, Democracy and the American Party System, chaps. 2 and 3; Ranney, A., “Postlude to the Epilogue,” Journal of Politics, XXIII (Aug. 1961), 566–9CrossRefGoogle Scholar. Thorson's own position is that “the argument for absolute majority rule is specious, and that the position in its categorical form is utterly without justification,” “Epilogue,” 558.

⁴¹ I do not mean when unique decisions are to be made, but when decisions relating to a particular activity are to be made.

⁴² The Calculus of Consent, chap. 6.

⁴³ This is the justification for the State, in Baumol, Welfare Economics.

⁴⁴ See Samuelson, P. A., “The Pure Theory of Public Expenditure,” Review of Economics and Statistics, XXXVI (Nov. 1964), 387–9.Google Scholar

⁴⁵ Review of Buchanan, and Tullock, , The Calculus of Consent, in Economic Journal, LXXIII (March 1963), 101–4.Google Scholar

⁴⁶ Though, as is well known, it does not eliminate the possibility that electors will choose, by simple majority voting, A over B, B over C, but C over A. Notice also that this form of motion is important to the argument. If N_a were 30 per cent, then a motion which said “the United Kingdom should stay out of the EEC ” would leave the United Kingdom permanently out.

⁴⁷ Review of The Calculus of Consent.

⁴⁸ Truman, The Governmental Process.

⁴⁹ Dahl, A Preface to Democratic Theory, 132.