I agree with the conclusions to most of the ways you frame the Sleeping Beaty problem, but not this important one.
Each interview consists of Sleeping Beauty being told whether the coin landed on heads or tails, followed by one question, “How surprised are you to hear that?” Should Sleeping Beauty be more surprised to learn that the coin landed on heads than that it landed on tails?
I would say no; this seems like a case where the simple probability-theoretic reasoning applies.
I disagree—I think Monday’s Sleeping Beauty should be surprised to learn that the coin landed on heads. I think my logic would be clear to you*, but your logic is opaque to me. This makes me suspect I’m missing something, and if I am, it’s something important. Perhaps we’re using different definitions of “surprised”?
*see the credence and log-scoring framing
ETA I’d appreciate an explanation as to what surprise has to do with likelihood. If I smell bacon when I wake up tomorrow, I’ll be quite surprised to learn that George Foreman is grilling me bacon burgers. There’s a high likelihood that I will smell bacon when I wake up tomorrow given George Foreman is grilling me bacon burgers, but that high likelihood would not temper my surprise.
I agree with the conclusions to most of the ways you frame the Sleeping Beaty problem, but not this important one.
I disagree—I think Monday’s Sleeping Beauty should be surprised to learn that the coin landed on heads. I think my logic would be clear to you*, but your logic is opaque to me. This makes me suspect I’m missing something, and if I am, it’s something important. Perhaps we’re using different definitions of “surprised”?
*see the credence and log-scoring framing
ETA I’d appreciate an explanation as to what surprise has to do with likelihood. If I smell bacon when I wake up tomorrow, I’ll be quite surprised to learn that George Foreman is grilling me bacon burgers. There’s a high likelihood that I will smell bacon when I wake up tomorrow given George Foreman is grilling me bacon burgers, but that high likelihood would not temper my surprise.