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Morendil comments on Updating, part 1: When can you change your mind? The binary model - Less Wrong
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Apply it to what terms?
I'm not sure what more I can say without starting to repeat myself, too. All I can say at this point, having formalized my reasoning as both a Python program and an analytical table giving out the full joint distribution, is "Where did I make a mistake?"
Where's the bug in the Python code? How do I change my joint distribution?
I like the version of your halfer variant version of your table. I still need to think about your distributions more though. I'm not sure it makes sense to have a variable 'woken that day' for this problem.