Monty Hall Sleeping Beauty

by PhilGoetz 4y18th Sep 20151 min read18 comments

1


A friend referred me to another paper on the Sleeping Beauty problem. It comes down on the side of the halfers.

I didn't have the patience to finish it, because I think SB is a pointless argument about what "belief" means. If, instead of asking Sleeping Beauty about her "subjective probability", you asked her to place a bet, or take some action, everyone could agree what the best answer was. That it perplexes people is a sign that they're talking non-sense, using words without agreeing on their meanings.

But, we can make it more obvious what the argument is about by using a trick that works with the Monty Hall problem: Add more doors. By doors I mean days.

The Monty Hall Sleeping Beauty Problem is then:

  • On Sunday she's given a drug that sends her to sleep for a thousand years, and a coin is tossed.
  • If the coin lands heads, Beauty is awakened and interviewed once.
  • If the coin comes up tails, she is awakened and interviewed 1,000,000 times.
  • After each interview, she's given a drug that makes her fall asleep again and forget she was woken.
  • Each time she's woken up, she's asked, "With what probability do you believe that the coin landed tails?"

The halfer position implies that she should still say 1/2 in this scenario.

Does stating it this way make it clearer what the argument is about?