neq1 comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong

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

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (335)

Comments (335)

Sort By: Best

Show:

You are viewing a single comment's thread. Show more comments above.

Comment author: neq1 comment score below threshold [+] (8 children)

Comment author: PhilGoetz 07 May 2010 06:06:45PM * 1 point [-]

On a random waking moment, Monday preceded by heads is equally likely as Monday preceded by tails.

I think you're thinking of a similar problem that we discussed last year, which involves a forgetful driver who is driving past 1 to n intersections, and needs to turn left at at least one of them. That problem is different, because it's asking about the probability of turning left at least once over the course of his drive.

Comment author: Vladimir_Nesov 07 May 2010 09:21:57PM 1 point [-]

The absent-minded driver is essentially the same problem, but it's easier to analyze because explicit payoff specification prompts you to estimate expected value of possible strategies. In estimating those strategies, we use the same probability model that would say "1/2" in the Beauty problem.

Comment author: neq1 comment score below threshold [+] (5 children)

Comment author: timtyler 09 May 2010 02:19:24PM * 1 point [-]

How come P(monday and heads) and P(monday and tails) are not the same? This is an ordinary unbiased coin, yes?

How come P(monday and tails) and P(tuesday and tails) are not the same. Nothing happens in the interim, yes?

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.

neq1 comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong

Article Navigation

Comments (335)

Nearest Meetups

Virtual Study Room

Recent Comments

Recent Posts

Recent Rationality Quotes

Recent Wiki Edits

Top Contributors, 30 Days

Recent Karma Awards

Comments (335)

Top Contributors, 30 Days

You'll need to login or register to do that

(Don't worry, it only takes a few seconds)

Create

Login