The invention of the indepence condition for preferences

This paper discusses the history and interrelations of three central ideas in preference theory: the independence condition in decision making under risk, the sure-thing principle in decision making under uncertainty, and independence in consumer theory. Independence and the sure-thing principle are equivalent for decision making under risk, but in a less elementary way than has sometimes been thought. The sure-thing principle can be formulated, more generally, for decision making under uncertainty. In a mathematical sense, the sure-thing principle and independence in consumer theory are identical. Independence was recognized as an important component of decision making under risk in the late 1940s by Jacob Marschak, John Nash, Herman Rubin and Norman Dalkey, and first appeared in publication in Marschak (1950) and Nash (1950). The sure-thing principle can be credited to Savage (1953, 1954). Independence for consumer theory was introduced by Sono (1943) and Leontief (1947a,b); a form of it can also be recognized in Samuelson (1947, Formula 32). The mathematics of the above results had been known before. The independence condition for decision making under risk can be recognized in the characterization of "associative means," the independence condition of consumer theory in the solutions to the "generalized associativity functional equation."