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# Quantum Rational Preferences and Desirability

*Proceedings of the NIPS 2016 Workshop on Imperfect Decision Makers*, PMLR 58:87-96, 2017.

#### 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.