A rational measure of irrationality

All possible types of deterministic choice behavior are classified by their degree of irrationality. This classification is performed in three steps: (1) select a benchmark of rationality, for which this degree is zero; (2) endow the set of choices with a metric to measure deviations from rationality; and (3) compute the distance of any choice behavior from the selected benchmark. The natural candidate for step 1 is the family of all rationalizable behaviors. A possible candidate for step 2 is a suitable variation of the metric described by Klamler (2008), which displays a sharp discerning power among different types of choice behaviors. In step 3 we use this new metric to establish the minimum distance of any choice behavior from the benchmark of rationality. Finally we describe a measure of stochastic irrationality, which employs the random utility model as a benchmark of rationality, and the Block-Marschak polynomials to measure deviations from it.