You could make a similar complaint about the proof of coherence too. Just observe that clearly something that maximizes WCB can only assign probability 1 to tautologies and can only assign probability 0 to contradictions, so that can never happen.
Thanks! I have actually been thinking along these lines for about a year. (Notice that the update function for both the proofs of uniqueness and coherence are generalizations of the strategy I argued for.) I consider doing MIRIx a success just for inspiring me to finally sit down and write stuff up.
That update move is nice in that it updates the Bayes score by the same amount in all models. What I would really like to show is that if you start with the constant 1⁄2 probability assignment, and just apply that update move whenever you observe that your probability assignment is incoherent, you will converge to the WCB maximizer. I think this would be nice because it converges to the answer in such a way that seems unbiased during the entire process.
You could make a similar complaint about the proof of coherence too. Just observe that clearly something that maximizes WCB can only assign probability 1 to tautologies and can only assign probability 0 to contradictions, so that can never happen.
Thanks! I have actually been thinking along these lines for about a year. (Notice that the update function for both the proofs of uniqueness and coherence are generalizations of the strategy I argued for.) I consider doing MIRIx a success just for inspiring me to finally sit down and write stuff up.
That update move is nice in that it updates the Bayes score by the same amount in all models. What I would really like to show is that if you start with the constant 1⁄2 probability assignment, and just apply that update move whenever you observe that your probability assignment is incoherent, you will converge to the WCB maximizer. I think this would be nice because it converges to the answer in such a way that seems unbiased during the entire process.