Hm. Should “S” be representing “Beauty is asleep or the experiment is over”? Seeing as how the experiment ends after one day if heads comes up. But then, we can just modify the problem to say she’s put back to sleep for the rest of Tuesday in the case of heads; that shouldn’t change anything.
It seems to me that if we make the experiment last three days instead of two, that ambiguity goes away: then it becomes clear that Beauty must assign non-zero probability mass to (H,T,S). (Or does it?)
However, that means I’d have to change my mind once again, and decide that the correct answer is in fact 1⁄3.
Here is a Google spreadsheet showing my reasoning. Any feedback welcome.
The three day version goes: “Beauty is explained the rules on Sunday and put to sleep, then a coin is flipped. If it comes up heads, Beauty is awakened on Monday and sleeps through Tuesday and Wednesday. If it comes up tails, Beauty is awakened on Monday, Tuesday and Wednesday. On all awakenings (with the previous day’s memories erased by the sleeping drug) she is asked for her credence in Heads.”
This differs from the original which says “the experiment ends on Monday is the coin comes up heads”. But Beauty would have the same uncertainty if you decided, in the original version, to wake Beauty on Tuesday in the event of heads, rather than Monday.
BTW the Google spreadsheet has a chat area, if you’d like to discuss this live.
Hm. Should “S” be representing “Beauty is asleep or the experiment is over”? Seeing as how the experiment ends after one day if heads comes up. But then, we can just modify the problem to say she’s put back to sleep for the rest of Tuesday in the case of heads; that shouldn’t change anything.
It seems to me that if we make the experiment last three days instead of two, that ambiguity goes away: then it becomes clear that Beauty must assign non-zero probability mass to (H,T,S). (Or does it?)
However, that means I’d have to change my mind once again, and decide that the correct answer is in fact 1⁄3.
Here is a Google spreadsheet showing my reasoning. Any feedback welcome.
Can you explain what the three day version means in English, I’m having a little trouble parsing the spreadsheet.
See here and its grandparent.
The three day version goes: “Beauty is explained the rules on Sunday and put to sleep, then a coin is flipped. If it comes up heads, Beauty is awakened on Monday and sleeps through Tuesday and Wednesday. If it comes up tails, Beauty is awakened on Monday, Tuesday and Wednesday. On all awakenings (with the previous day’s memories erased by the sleeping drug) she is asked for her credence in Heads.”
This differs from the original which says “the experiment ends on Monday is the coin comes up heads”. But Beauty would have the same uncertainty if you decided, in the original version, to wake Beauty on Tuesday in the event of heads, rather than Monday.
BTW the Google spreadsheet has a chat area, if you’d like to discuss this live.