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Show Rationality and the Structure of the Self, Volume I: The Humean Conception 99 Independence of Irrelevant Alternatives condition on preference orderings, 4 what McClennen would call the Context-Free Ordering. This condition states that an ordering Y produced by a series of pairwise comparisons among a set of alternatives X is not changed by the introduction of additional alternatives on some particular occasion that expands X to a larger set X*. So, for example, if I prefer alternatives P to Q, Q to R, and R to S, the introduction of alternative T, on a particular occasion, does not alter my ranking of P, Q, R, and S relative to one another. Either I prefer T to P, or I prefer S to T, or I do not rank T at all. Thus this condition excludes the case in which the introduction of T leads me to reverse my ranking of Q and R. This means that the ranking of a set of alternatives can be inferred from its pairwise rankings and vice versa. The discussions below, in Chapter IV, and in Volume II, 5 6 Chapter III follow Sen and Broome in assuming that considerations of temporal continuity and human cognitive limitations necessitate pairwise comparisons as a necessary precondition of Y, and thereby block the inference to the material equivalence of Y and the series of pairwise rankings that produce it. Nevertheless, each can be read off from the other. (U) is also superficially similar to a different and more nuanced formulation, that if a rational agent acts, she maximizes her preferences, that would seem to avoid the vacuity I argue to be endemic to the utilitymaximization model. On this conception, the agent's preference rankings are numerically represented by the theorems of utility theory interpreted as representation theorems in a theory of measurement, and she chooses from among those alternatives she maximally prefers. The ordering axioms - transitivity, connectedness, asymmetry of strict preference - then ensure the existence of at least one most-preferred alternative in a finite set of such alternatives, and the agent maximizes by choosing that alternative. As Sen has shown that connectedness is not necessary for maximizing in this sense, it can be replaced by his concept of a maximal set, i.e. sets consisting of mutually nondominating alternatives none of which is strictly dispreferred to any 7 other. The transitivity requirement similarly can be replaced by a weaker requirement of acyclicity of strict preference, since maximization requires merely the avoidance of cyclical preferences. It would seem, on the face of it, 4 Edward McClennen, Rationality and Dynamic Choice (New York: Cambridge University Press, 1990), xi, 29-31, 64-67. 5 Amartya K. Sen, Collective Choice and Social Welfare (San Francisco: Holden-Day, Inc., 1970), 3. 6 Broome, John, "Rationality and the Sure-Thing Principle," in Thoughtful Economic Man, edited by Gay Meeks, Cambridge University Press, 1991, pp. 74-102. Cited and discussed in McClennen, op. cit., 66-67. 7 Sen, op. cit. Chapter 1*, Section 1*2. © Adrian Piper Research Archive Foundation Berlin |
