Two errors in the ?Allais Impossibility Theorem?

Abstract

In his so-called ‘Allais Impossibility Theorem’, Allais (1988) asserts that the technique of ‘generalized expected utility analysis’ from Machina (1982) is invalid, on the ground that its key tool, the ‘local utility function’, cannot be well-defined for preferences over finite-outcome lotteries. This paper presents a brief description of the local utility function and a summary of Allais' argument, and points out two separate errors in the latter. The first error consists of believing that two local utility functions should be affinely equivalent even when their outcome variables differ by a nonlinear transformation. The second error consists of an incorrect derivation of the local utility function, resulting from extending a moment representation function beyond its valid domain, and/or invoking the chain rule at a point where this function is not differentiable.