The Measurement of Social Welfare

By Jerome Rothenberg | Go to book overview

Expected Utility and Measurability: II Evaluation

10-1. Evaluation of the Axiom System

Since the expected utility theory is empirically refutable, the controlled experiment, in which predictions made by employing the hypothesis are confronted by experience, would appear an ideally appropriate mode of evaluating the theory. Up to the present time, however, direct empirical verification has not yielded anything like conclusive evidence for or against the theory. Some of the experiential phenomena which lend support to the theory are discussed in articles by Vickrey, and Friedman and Savage. 1 In addition, a formal experimental confrontation has been performed by Mosteller and Nogee.2 This experiment did not contradict the hypothesis, but neither did it offer strong support. On the one hand, the expected utility hypothesis did not in fact significantly exceed the predictive performance of an alternative hypothesis that choices are rationalized by maximization of the mathematical expectation of a gamble (rather than of the moral expectation). On the other hand, the experimental situation may have been structurally incapable of distinguishing even in principle between the performance of the two hypotheses.3

Vickrey, "Measuring Marginal Utility by Reactions to Risk"; Friedman and Savage, "The Utility Analysis of Choices Involving Risk."
"An Experimental Measurement of Utility."
In the experiment, a number of subjects were confronted with a sequence of different (and repeated) gambles, any of which they were free to play or not at a variety of specified odds. The size of money bets, and the range of possible total gambling accumulations, were so small relative to the annual incomes of the subjects that no real test of the hypothesis may have been involved. With the stakes on each play extremely small, the smallest planning unit where the player's utility was involved might well have been the outcome of the entire experiment. If this were so, maximization of moral expectation would lead to a strategy within the experiment aimed at maximizing the total accumulated money reward to be approximately gained from the experiment as a whole. But this goal is rationally met by playing every gamble whose mathematical expectation of money reward is positive, i.e., the goal is met by choosing so as to maximize the mathematical expectation of each gamble. In other words, the two different motivations would lead to indistinguishable behavior within the experimental situation.

I am indebted to Professor William Vickrey for this point.

A qualification of the foregoing would seem in order. The smallness of the single bet was judged in this criticism in relation to each individual's annual income. Yet this may underestimate its importance to the individual in the actual context of the experiment. The experiment was carried on in ten (?) weekly sessions. Each concrete play situation was therefore part of a single weekly session. It is conceivable that the repetitiveness of the gambling situation in the weekly schedule of the subjects might have led some individuals to incorporate their decisions in any one session within the frame of reference of weekly commitments, rather than to view the total experiment as part of one's annual strategy. The influence of one session's accumulation on weekly income is not insignificant; and the far fewer number of possible bets in any one session in comparison with the single bet makes a mathematical expectation strategy for each session less obviously desirable than if the whole experiment were being borne in mind.

The force of this qualification is not known. But its importance is to suggest that we analyze more deeply the time dimension of choosing behavior, certainly the relationship between choices made with respect to different time interval contexts. Much of the content of current economic theory, e.g., the theory of the firm, founders on an inability to give operational content to this relationship.

Over and above this basic reservation concerning the results of the Mosteller experiment, there are reportedly others. For example, it has been reported to the author by Professor A. G. Hart that there were indications during the experiment that the subjects did not grasp the notion of objective probability. Their misunderstanding apparently was concentrated on long odds. Of course, this difficulty may not be exclusively a structural defect of the particular experimental situation; it may well be an experimental conclusion about the hypothesis itself, since the hypothesis claims that individuals do choose on the basis of objective probabilities. See the discussion to follow in this section for more on this.


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