¹ When ranked by preference alone (with indifference not allowed), the alternatives are said to be strongly ordered. Weak orderings are especially appropriate when choice occurs in a continuum, while strong orderings are appropriate when the alternatives are discrete. Economists, who deal with continuous phenomena like money, find weak orderings most useful; but political scientists may find strong orderings simpler to work with and just as useful (for many political alternatives are discrete).

² At least three coherent opinions are possible on Rousseau's two questions. If “a” is a yes answer to (a) and “ã” a no answer to it, and similarly for (b), then at least these distinct and coherent opinions are possible, x: (a,b), y: (a,b), z:(ã,b), and possibly w: (ã,b). In any event the paradox may then arise.

³ There is a substantial amount of recent work on individual choice in gambling situations, most of which is, however, ancillary to our present interests. The most significant and relevant of this work is: Davidson, Donald, Suppes, Patrick, and Siegel, Sidney, Decision Making: An Experimental Approach (Stanford, Stanford University Press, 1957)Google Scholar; Davidson, Donald and Marshak, Jacob, “Experimental Tests of a Stochastic Decision Theory,” in Churchman, C. W. and Ratoosh, P., ed., Measurement: Definition and Theories (New York, John Wiley and Sons, 1959)Google Scholar, chapter 13; and Royden, H. L., Suppes, P., and Walsh, K., “A Model for the Experimental Measurement of the Utility of Gambling,” Behavioral Science, Vol. 4 (1959), pp. 11–18 CrossRefGoogle Scholar.