I wasn’t arguing that we should all be actually doing Solomonoff induction. (Clearly we can’t.) I was saying that there is a somewhat-usable sense in which preferring simpler hypotheses seems to be The Right Thing, or at least A Right Thing. Namely, that basing your probabilities miraculously accurately on simplicity leads to good results. The same isn’t true if you put something other than “simplicity” in that statement.
I wonder whether there are any theorems along similar lines that don’t involve any uncomputable priors. (Something handwavily along the following lines: If p,q are two computable priors and p is dramatically enough “closer to Occamian” than q, then an agent with p as prior will “usually” do better than an agent with q as prior. But I have so far not thought of any statement of this kind that’s both credible and interesting.)
I wasn’t arguing that we should all be actually doing Solomonoff induction. (Clearly we can’t.) I was saying that there is a somewhat-usable sense in which preferring simpler hypotheses seems to be The Right Thing, or at least A Right Thing. Namely, that basing your probabilities miraculously accurately on simplicity leads to good results. The same isn’t true if you put something other than “simplicity” in that statement.
I wonder whether there are any theorems along similar lines that don’t involve any uncomputable priors. (Something handwavily along the following lines: If p,q are two computable priors and p is dramatically enough “closer to Occamian” than q, then an agent with p as prior will “usually” do better than an agent with q as prior. But I have so far not thought of any statement of this kind that’s both credible and interesting.)