Nonlinear Desirability as a Linear Classification Problem

Abstract

The present paper proposes a generalization of linearity axioms of coherence through a geometrical approach, which leads to an alternative interpretation of desirability as a classification problem. In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject, who provides finite accept and reject statements, respects these axioms, corresponds to solving a binary classification task using, each time, a different (usually nonlinear) family of classifiers. Moreover, by borrowing ideas from machine learning, we show the possibility to define a feature mapping allowing us to reformulate the above nonlinear classification problems as linear ones in a higher-dimensional space. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to reduce the task of proving the rationality of a subject to a linear classification task.