Allais’s paradox a puzzle about rationality devised by Maurice Allais (b. 1911). Leonard Savage (1917–71) advanced the sure-thing principle, which states that a rational agent’s ranking of a pair of gambles having the same consequence in a state S agrees with her ranking of any other pair of gambles the same as the first pair except for having some other common consequence in S. Allais devised an apparent counterexample with four gambles involving a 100-ticket lottery. The table lists prizes in units of $100,000. Ticket Numbers Gambles 1 2 – 11 12 – 100 A 5 5 5 B 0 25 5 C 5 5 0 D 0 25 0 Changing A’s and B’s common consequence for tickets 12–100 from 5 to 0 yields C and D respectively. Hence the sure-thing principle prohibits simultaneously preferring A to B, and D to C. Yet most people have these preferences, which seem coherent. This conflict generates the paradox. Savage presented the sure-thing principle in The Foundations of Statistics (1954). Responding to preliminary drafts of that work, Allais formulated his counterexample in ‘The Foundations of a Positive Theory of Choice Involving Risk and a Criticism of the Postulates and Axioms of the American School’ (1952). See also DECISION THEORY, EMPIRICAL DECI- SION THEORY. P.We.