THE INVENTION OF THE INDEPENDENCE CONDITION FOR PREFERENCES

This paper discusses the history and interrelations of three central i deas in preference theory: the independence condition in decision unde r risk, the sure-thing principle in decision under uncertainty, and co njoint independence for multiattribute decisions and consumer theory. Independence was recognized as an important component of decision unde r risk in the late 1940s by Jacob Marschak, John Nash, Herman Rubin, a nd Norman Dalkey, and first appeared in publication in Marschak (1950) and Nash (1950). The sure-thing principle can be credited to Savage ( 1953, 1954). Conjoint independence for consumer theory was introduced by Sono (1943) and Leontief (1947a, b); a form of it can also be recog nized in Samuelson (1947), presented earlier in Samuelson (1940). Inde pendence and the sure-thing principle are equivalent for decision unde r risk, but in a less elementary way than has sometimes been thought. The sure-thing principle for decision under uncertainty and conjoint i ndependence are identical in a mathematical sense. The mathematics und erlying our three preference conditions has an older history. The inde pendence condition for decision under risk can be recognized in the ch aracterization of ''associative means,'' and conjoint independence for multiattribute decisions in solutions to the ''generalized associativ ity functional equation.''