Jeremy Steeger (University of Notre Dame)
Recent discussions of certain non-Kolmogorovian hidden variable theories for quantum theory have used Dutch books to argue that the probabilities in these theories cannot be given a reasonable subjective interpretation (Feintzeig 2014; Feintzeig and Fletcher 2017). Contrasting the theories in question with a popular framework for classical hidden variable theories (Spekkens 2005), I assess the assumptions that go into one plausible reconstruction of this no-go. I argue that the no-go is compelling, but only insofar as one is committed to certain response functions, or stipulations of probabilities conditional on certain facts about the world. Namely: the response functions must determine outcomes, and they must not depend on how a system is measured. I then sketch how the Dutch book argument used in the no-go may be applied to hidden variable theories with other sorts of response functions.
