JGWeissman comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong

6 Post author: neq1 07 May 2010 02:34PM

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Comment author: JGWeissman 07 May 2010 07:13:04PM 1 point [-]

Before she wakes, the probabilities SB would assign if she were conscious are P(monday and heads) = P(monday and tails) = p(tuesday and heads) = p(tuesday and tails) = 1/4.

After waking, she would update to p(tuesday and heads) = 0 and P(monday and heads) = P(monday and tails) = p(tuesday and tails) = 1/3, since p(tuesday and heads | wakes up) = 0 and p(monday and heads | wakes up) = p(monday and tails | wakes up) = p(tuesday and tails | wakes up) = 1.

Comment author: neq1 07 May 2010 08:47:15PM -1 points [-]

Ugh. That makes no sense. Can you explain why she would update in such a manner?

Comment author: JGWeissman 07 May 2010 08:57:49PM 2 points [-] 
Odds(monday and heads : monday and tails : tuesday and heads : tuesday and tails | wakes up)
= Odds(monday and heads : monday and tails : tuesday and heads : tuesday and tails) * Likelihood(wakes up | monday and heads : monday and tails : tuesday and heads : tuesday and tails)
= (1 : 1 : 1 : 1) * (1 : 1 : 0 : 1)
= (1 : 1 : 0 : 1)
= (1/3 : 1/3 : 0 : 1/3)

SB starts out with four equaly likely possibilities. On observing that she wakes up, she eliminates one of them, but does not distinguish between the remaining possiblities. Renormalizing the probabilities gives probability 1/3 to the remaining possibilities.

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