Reconsiderations in the foundations of decision under uncertainty.

This paper reconsiders the classic confrontation between Maurice Allais and Jimmie Savage at the 1952 Paris colloquium on decision under uncertainty in light of new developments in the theory of preference for uncertain situations. We outline the theories of Savage and Allais, note their points of agreement and disagreement, and recall their famous encounter about the normative standing of independence axioms and Savage's sure-thing principle. It is suggested that their debate concerning independence can be refocused on the axiom of transitivity and the reduction principle (which says that preference between uncertain acts should be based solely on their probability distributions over outcomes).