@inproceedings{Casanova2021,
title = {Nonlinear Desirability as a Linear Classification Problem},
author = {Casanova, Arianna and Benavoli, Alessio and Zaffalon, Marco},
url = {http://alessiobenavoli.com/wp-content/uploads/2021/07/casanova21-1.pdf},
year = {2021},
date = {2021-07-07},
booktitle = {ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR},
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},
keywords = {desirability, imprecise probability},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{benavoli2021quantum,
title = {Quantum indistinguishability through exchangeable desirable gambles},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
url = {https://arxiv.org/abs/2105.04336},
year = {2021},
date = {2021-06-01},
booktitle = {ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR},
abstract = {Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems. },
keywords = {desirability, Quantum mechanics},
pubstate = {published},
tppubtype = {inproceedings}
}