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. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This paper presents the interpretation of standard desirability and other instances of nonlinear desirability as a classification problem. By analyzing different sets of rationality axioms, the paper shows the possibility of reformulating the problem as a binary classification problem and demonstrates the use of machine learning techniques to define a feature mapping and solve the problem in higher-dimensional spaces.