This may be kinda cheating, but how’s this for a solution: First, I check to see if my left shoe is untied. If it isn’t, I say my credence is 50% and then untie it. If it is already untied, I say my credence is 0% because I know for certain that it is tuesday and the coin landed on tails. I won’t remember coming up with this plan on tuesday, but I’ll think of it again and then derive that I already implemented it. This does, of course, require that the interviewers don’t realize what I’m doing and tie it while I’m asleep (and that it was tied to begin with). If I’m not mistaken, this method maximizes my expected score on the negative log test, at −1 bit regardless of the result.
This may be kinda cheating, but how’s this for a solution: First, I check to see if my left shoe is untied. If it isn’t, I say my credence is 50% and then untie it. If it is already untied, I say my credence is 0% because I know for certain that it is tuesday and the coin landed on tails. I won’t remember coming up with this plan on tuesday, but I’ll think of it again and then derive that I already implemented it. This does, of course, require that the interviewers don’t realize what I’m doing and tie it while I’m asleep (and that it was tied to begin with). If I’m not mistaken, this method maximizes my expected score on the negative log test, at −1 bit regardless of the result.