Given this, if one had a hyperprior over different possible Beta distributions, shouldn’t 2000 centuries of no event occurring cause one to update quite hard against the (0.5, 0.5) or (1, 1) hyperparameters, and in favour of a prior that was massively skewed towards the per-century probability of no-lock-in-event being very low?
(And noting that, depending exactly on how the proposition is specified, I think we can be very confident that it hasn’t happened yet. E.g. if the proposition under consideration was ‘a values lock-in event occurs such that everyone after this point has the same values’.)
That’s interesting. Earlier I suggested that a mixture of different priors that included some like mine would give a result very different to your result. But you are right to say that we can interpret this in two ways: as a mixture of ur priors or as a mixture of priors we get after updating on the length of time so far. I was implicitly assuming the latter, but maybe the former is better and it would indeed lessen or eliminate the effect I mentioned.
Your suggestion is also interesting as a general approach, choosing a distribution over these Beta distributions instead of debating between certainty in (0,0), (0.5, 0.5), and (1,1). For some distributions over Beta parameters these the maths is probably quite tractable. That might be an answer to the right meta-rational approach rather than an answer to the right rational approach, or something, but it does seem nicely robust.
Given this, if one had a hyperprior over different possible Beta distributions, shouldn’t 2000 centuries of no event occurring cause one to update quite hard against the (0.5, 0.5) or (1, 1) hyperparameters, and in favour of a prior that was massively skewed towards the per-century probability of no-lock-in-event being very low?
(And noting that, depending exactly on how the proposition is specified, I think we can be very confident that it hasn’t happened yet. E.g. if the proposition under consideration was ‘a values lock-in event occurs such that everyone after this point has the same values’.)
That’s interesting. Earlier I suggested that a mixture of different priors that included some like mine would give a result very different to your result. But you are right to say that we can interpret this in two ways: as a mixture of ur priors or as a mixture of priors we get after updating on the length of time so far. I was implicitly assuming the latter, but maybe the former is better and it would indeed lessen or eliminate the effect I mentioned.
Your suggestion is also interesting as a general approach, choosing a distribution over these Beta distributions instead of debating between certainty in (0,0), (0.5, 0.5), and (1,1). For some distributions over Beta parameters these the maths is probably quite tractable. That might be an answer to the right meta-rational approach rather than an answer to the right rational approach, or something, but it does seem nicely robust.