Nonlinear desirability theory

Desirability can be understood as an extension of Anscombe and Aumann's Bayesian decision theory to sets expected utilities. At the core desirability lies assumption linearity scale in which rewards are measured. It is a traditional used derive utility model, clashes with general representation rational making, though. Allais has, particular, pointed this out 1953 his famous paradox. We note that plays role closure operator when we regard logical theory. This observation enables us extend nonlinear case by letting represented via operator. The new directly expresses actual currency (money), much Savage's spirit, while arguably weakening founding assumptions minimum. characterise main properties both from perspective gambles their lower upper prices (previsions). show how paradox finds solution theory, discuss probabilities