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# Nonlinear Desirability as a Linear Classification Problem

*Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications*, PMLR 147:61-71, 2021.

#### 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.