Awesome, you even figured out that anthropic indexical belief updating is exactly what minimizes world-expected total surprisal (when non-indexical beliefs about relative world likelihoods are fixed). The proof is just Jensen’s inequality :)
That’s another thing I’ve been delaying a top-level post on: an “explaining away” of anthropic updating by classifying precisely which decision problems it gives naive correct solutions to. I expect I’ll be too busy for the next couple of months to write it in the detail I’d like, but then you can expect to see some introductory content from me on that… unless you write it yourself, which would be even better!
Awesome, you even figured out that anthropic indexical belief updating is exactly what minimizes world-expected total surprisal (when non-indexical beliefs about relative world likelihoods are fixed). The proof is just Jensen’s inequality :)
That’s another thing I’ve been delaying a top-level post on: an “explaining away” of anthropic updating by classifying precisely which decision problems it gives naive correct solutions to. I expect I’ll be too busy for the next couple of months to write it in the detail I’d like, but then you can expect to see some introductory content from me on that… unless you write it yourself, which would be even better!