Wigner's friend as a rational agent

In a joint paper Jeff Bub and Itamar Pitowski argued that the quantum state represents `the credence function of a rational agent [...] who is updating probabilities on the basis of events that occur'. In the famous thought experiment designed by Wigner, Wigner's friend performs a measurement in an isolated laboratory which in turn is measured by Wigner. Here we consider Wigner's friend as a rational agent and ask what her `credence function' is. We find experimental situations in which the friend can convince herself that updating the probabilities on the basis of events that happen solely inside her laboratory is not rational and that conditioning needs to be extended to the information that is available outside of her laboratory. Since the latter can be transmitted into her laboratory, we conclude that the friend is entitled to employ Wigner's perspective on quantum theory when making predictions about the measurements performed on the entire laboratory, in addition to her own perspective, when making predictions about the measurements performed inside the laboratory.