Nonlinear desirability as a linear classification problem

This paper presents an interpretation as classification problem for standard desirability and other instances of nonlinear desirability ( convex coherence and positive additive coherence ). In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject respects these axioms on the basis of a finite set of acceptable and a finite set of rejectable gambles can be reformulated as a binary classification problem where the family of classifiers used changes with the axioms considered. Moreover, by borrowing ideas from machine learning, we show the possibility of defining a feature mapping , which allows us to reformulate the above nonlinear classification problems as linear ones in higher-dimensional spaces. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries , as well as to provide a practical tool to check the rationality of an agent.