Monty Hall Sleeping Beauty

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 12 in this sce­nario.

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