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Some of the commenters are claiming that our thought experiment is “just a rephrasing of Hardy’s paradox”. As mentioned in our paper, our construction indeed invokes ideas due to Hardy, as well as, by the way, ideas from Wigner and Deutsch.
However, in contrast to Hardy-type (as well as Bell-type) arguments, our paradox does not rely on concepts such as “locality” or “free choice”. (In fact, in our setup, the agents do not make any choices at all.) Rather, our argument is based on the idea that any universally valid theory should have the property that “the theory can be used to describe users of the same theory”.
I am not sure whether the commenters really meant that this requirement is equivalent to the assumptions that enter Hardy’s argument. But if they think so, I would appreciate if they could explain in more detail how they translate, for instance, Hardy’s locality assumption, or the assumption of free choice, to our setup.
