MILTON FRIEDMAN AND L J. SAVAGE behavior that he prefers A to B and b to ing rationally to maximize expected util- C, it is traditional to rationalize this be- ity in accordance with a given utility havior by supposing that he attaches function. Or it may be that some types more utility to A than to B and more of reactions to risk can be rationalized in utility to B than to C. All utility func- this way while others cannot. Whether tions that give the same ranking to pos- a numerical utility function will in fact sible alternatives will provide equally serve to rationalize any particular class good rationalizations of such choices, and of reactions to risk is an empirical ques it will make no difference which particu- tion to be tested; there is no obvious con- lar one is used. If, in addition, the indi- tradiction such as was once thought to vidual should show by his market be- exist havior that he prefers a 5o-5o chance of This paper attempts to provide a A orC to the certainty of B, it seems nat- crude empirical test by bringing to- ural to rationalize this behavior by sup gether a few broad observations about posing that the diference between the the behavior of individuals in choosing utilities he attaches to A and B is greater among alternatives involving risk(sec than the difference between the utilities and investigating whether these observa he attaches to B and C, so that the ex- tions are consistent with the hypothesis pected utility of the preferred combina- revived by von Neumann and Morgen tion is greater than the utility of B. The stern(secs. 3 and 4). It turns out that class of utility functions, if there be any, these empirical observations are entirely hat can provide the same ranking of al- consistent with the hypothesis if a rather ternatives that involve risk is much more special shape is given to the total utility restricted than the class that can provide curve of money(sec. 4). This special he same ranking of alternatives that are shape, which can be given a tolerably certain. It consists of utility functions satisfactory interpretation(sec. 5),not hat differ only in origin and unit of only brings under the aegis of rational measure (i.e, the utility functions in the utility maximization much behavior that class are linear functions of one an- is ordinarily explained in other terms but other). Thus, in effect, the ordinal prop. also has implications about observable erties of utility functions can be used to behavior not used in deriving it(sec. 6) rationalize riskless choices, the numerical Further empirical work should make it properties to rationalize choices involv- possible to determine whether or not ons conform h t does not, of course, follow that there It is a testimony to the strength of the ill exist a utility function that will ra- belief in diminishing marginal utility tionalize in this way the reactions of indi- that it has taken so long for the possibil viduals to risk. It may be that individ- ity of interpreting gambling and similar uals behave inconsistently--sometimes phenomena as a contradiction of univer choosing a so-so chance of A or C instead sal diminishing marginal utility, rather of B and sometimes the reverse; or some- than of utility maximization, to be recog times choosing A instead of B, B instead nized. The initial mistake must have of C, and c instead of A-or that in some been at least partly a product of a strong other way their behavior is different introspective belief in diminishing mar- from what it would be if they were seek- ginal utility: a dollar must mean less to a Ibid., pp. 15-31, esp. p. 25 rich man than to a poor man; see how