Quantum rational preferences and desirability
  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. 
Alessio Benavoli and Alessandro Facchini and Marco Zaffalon
quant-ph math.PR