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Show Rationality and the Structure of the Self, Volume I: The Humean Conception 129 then would have to further assume that the intervals between levels is the same for all agents, and then compare the different cardinalities assigned to each given option by each agent. It is this last assumption that generates the problem. Why should we assume that the intervals between levels of utility are the same for all agents, when the perceived intervals between seconds and minutes and hours differ so radically from one agent to the next depending on age, circumstance, and neurochemistry? Different individuals might have different feelings of different qualitative intensity about different alternatives at the same level (for example, apples and oranges). Or different individuals might feel differently about the same increase or decrease in utility level, of the sort that might distinguish the response of an emerging novelist from that of John Updike to a single bad review following a succession of favorable ones. To take another example: if an hour can drag by for an eighteen-year-old but rush by for a sixty-year-old, the difference between liking an orange at five units and liking orange juice at one unit more similarly might be vast for the former and negligible for the latter. For these reasons establishing even a subjective cardinal utility function bodes trouble enough. The prospects of establishing an interpersonal one look even gloomier. 1.2. The Von Neumann-Morgenstern Cardinal Measure The Von Neumann-Morgenstern (henceforth the vN-M) cardinal measure 5 for choices under risk presupposes the behavioral interpretation of (U), and amplifies and clarifies a method first developed by Ramsey. Designed to determine the expected utility of some gamble x for an agent, it is based on empirical observation of that agent's choices among gambles. It thereby answers the question, how willing is that agent to gamble on satisfying some preference given the weights and probabilities he assigns to the outcomes of the actions open to him? The answer - the total value V of that preference - is the sum of the weights of each of the possible outcomes a1, a2 , ... an times their respective probabilities p1, p2, ... pn, i.e. V = a1p1 + a2p2 + ... +anpn. The vN-M method derives from three preference axioms stipulating conditions on the relation '>' for the set S of all probability distributions or gambles on a set of outcomes: 5 Although it should be noted that Morgenstern is critical of revealed preference theory. See Oskar Morgenstern, "Thirteen Critical Points in Contemporary Economic Theory: An Interpretation," Journal of Economic Literature 10 (1972), 1163-1189. © Adrian Piper Research Archive Foundation Berlin |
