Quantum Rational Preferences and Desirability

Alessio Benavoli, Alessandro Facchini, Marco Zaffalon

Abstract: We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann’s axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian matrices. Among other things, this leads us to give a representation theorem showing that quantum complete rational preferences are obtained by means of expected utility considerations.