Yeah, that seems like a pretty good way to go. I think creating too much imprecision might be a concern, and that there’s also a concern about motivation. As I understand it, rectangularising in this case means adding probability functions to your representor on which, e.g., Pr(X | Heads)<0.01. But that seems incompatible with characterizing your representor as the set of probability functions you could settle on after ideal reflection on your current evidence, because (we can stipulate that X is such that) ideal reflection won’t lead you to believe that X and Heads are so tightly anti-correlated. And given that, it seems maybe hard to justify including probability functions on which Pr(X | Heads)<0.01 in your representor (and thereby letting those probability functions affect what’s permissible/impermissible for you).
Right, you might want to say that the distributions added to the representor should not have an epistemic interpretation, but should be thought of as a choice-theoretic representation. That is, we have a choice-theoretic reflection principle (something like, if I know that I’ll in future judge A and B to be permissible, I should judge them to both be permissible now), which along with other constraints forces choice behaviour that is representable by the larger representor.
Yeah, that seems like a pretty good way to go. I think creating too much imprecision might be a concern, and that there’s also a concern about motivation. As I understand it, rectangularising in this case means adding probability functions to your representor on which, e.g., Pr(X | Heads)<0.01. But that seems incompatible with characterizing your representor as the set of probability functions you could settle on after ideal reflection on your current evidence, because (we can stipulate that X is such that) ideal reflection won’t lead you to believe that X and Heads are so tightly anti-correlated. And given that, it seems maybe hard to justify including probability functions on which Pr(X | Heads)<0.01 in your representor (and thereby letting those probability functions affect what’s permissible/impermissible for you).
Right, you might want to say that the distributions added to the representor should not have an epistemic interpretation, but should be thought of as a choice-theoretic representation. That is, we have a choice-theoretic reflection principle (something like, if I know that I’ll in future judge A and B to be permissible, I should judge them to both be permissible now), which along with other constraints forces choice behaviour that is representable by the larger representor.