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. The sure-thing principle can be credited to Savage. Conjoint independence for consumer theory was introduced by Sono and Leontief; a form of it can also be recognized in Samuelson. 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 performance 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’.