Assuming your priors for each individual explanation is about equal, is there a Bayesian explanation for our intuition that we should bet on Explanation Set A?
Do you mean your prior for A is about your prior for B, or your priors for each element are about the same?
If you mean the first, then there is no reason to favor one over the other. Occam’s razor just says the more complex explanation has a lower prior.
If you mean the second, then there is a very good reason to favor A. If A has n explanations, B has m, all explanations are independant and of probability p, then P(A) = p^n and P(B) = p^m. A is exponentially more likely than B. In real life, assuming independence tends to be a bad idea, so it won’t be quite so extreme, but the simpler explanation is still favored.
Do you mean your prior for A is about your prior for B, or your priors for each element are about the same?
If you mean the first, then there is no reason to favor one over the other. Occam’s razor just says the more complex explanation has a lower prior.
If you mean the second, then there is a very good reason to favor A. If A has n explanations, B has m, all explanations are independant and of probability p, then P(A) = p^n and P(B) = p^m. A is exponentially more likely than B. In real life, assuming independence tends to be a bad idea, so it won’t be quite so extreme, but the simpler explanation is still favored.