“all conjectures” is a pretty natural reference class
I agree, but then you’d have to come up with a dataset of conjectures.
if the resolution rate diverges substantially from the Laplace rule prediction I think it would still be interesting.
Yep!
I think, because we expect the resolution rate of different conjectures to be correlated, this experiment is a bit like a single draw from a distribution over annual resolution probabilities rather than many draws from such a distribution ( if you can forgive a little frequentism).
I think that my thinking here is:
We could model the chance of a conjecture being resolved with reference to internal details. For instance, we could look at the increasing number of mathematicians, at how hard a given conjecture seems, etc.
However, that modelling is tricky, and in some cases the assumptions could be ambiguous
But we could also use Laplace’s rule of succession. This has the disadvantage that it doesn’t capture the inner structure of the model, but it has the advantage that it is simple, and perhaps more robust. The question is, does it really work? And then I was looking at one particular case which I could be somewhat informative.
I think I used to like Laplace’s law a bit more in the past, for some of those reasons. But I now like it a bit less, because maybe it fails to capture the inner structure of what is predicting.
a single draw
I agree. On the other hand, I kind of expect to be informative nonetheless.
I agree, but then you’d have to come up with a dataset of conjectures.
Yep!
I think that my thinking here is:
We could model the chance of a conjecture being resolved with reference to internal details. For instance, we could look at the increasing number of mathematicians, at how hard a given conjecture seems, etc.
However, that modelling is tricky, and in some cases the assumptions could be ambiguous
But we could also use Laplace’s rule of succession. This has the disadvantage that it doesn’t capture the inner structure of the model, but it has the advantage that it is simple, and perhaps more robust. The question is, does it really work? And then I was looking at one particular case which I could be somewhat informative.
I think I used to like Laplace’s law a bit more in the past, for some of those reasons. But I now like it a bit less, because maybe it fails to capture the inner structure of what is predicting.
I agree. On the other hand, I kind of expect to be informative nonetheless.