The Invention of the Independence Condition for Preferences

This paper discusses the history and interrelations of three central ideas in preference theory: the independence condition in decision under risk, the sure-thing principle in decision under uncertainty, and conjoint independence for multiattribute decisions and consumer theory. Independence was recognized as an important component of decision under risk in the late 1940s by Jacob Marschak, John Nash, Herman Rubin, and Norman Dalkey, and first appeared in publication in Marschak (Marschak, J. 1950. Rational behavior, uncertain prospects, and measurable utility. Econometrica 18 111--141.) and Nash (Nash, J. F. 1950. The bargaining problem. Econometrica 18 155--162.). The sure-thing principle can be credited to Savage (Savage, L. J. 1953. Une Axiomatisation du Comportement Raisonnable Face à l'Incertitude. Colloq. Internal. Centre National Rech. Sci. 40 Econométrie 29--40; Savage, L. J. 1954. The Foundations of Statistics. Wiley, New York (2nd edn., Dover, New York, 1972.). Conjoint independence for consumer theory was introduced by Sono (Sono, M. 1943. The effect of price changes on the demand and supply of separable goods (in Japanese). Kokumin Keisai Zasshi 74 1--51.) and Leontief (Leontief, W. W. 1947a. A note on the interrelation of subsets of independent variables of a continuous function with continuous first derivatives. Bull. Amer. Math. Soc. 53 343--350; Leontief, W. W. 1947b. Introduction to a theory of the internal structure of functional relationships. Econometrica 51 361--373.); a form of it can also be recognized in Samuelson (Samuelson, P. A. 1947. Foundations of Economic Analysis. Harvard University Press, Cambridge, MA.), presented earlier in Samuelson (Samuelson, P. A. 1940. Foundations of analytical economics, the observational significance of economic theory. Ph.D. dissertation, Harvard University, Boston, MA.). Independence and the sure-thing principle are equivalent for decision under risk, but in a less elementary way than has sometimes been thought. The sure-thing principle for decision under uncertainty and conjoint independence are identical in a mathematical sense. The mathematics underlying our three preference conditions has an older history. The independence condition for decision under risk can be recognized in the characterization of "associative means," and conjoint independence for multiattribute decisions in solutions to the "generalized associativity functional equation."