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The invention of the independence condition for preferences. (English) Zbl 0843.90011

Summary: 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 and the sure-thing principle are equivalent for decision under risk, but in a less elementary way than has sometimes been tought. 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”.

MSC:

91B16 Utility theory
91B08 Individual preferences
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