On my friend's site:
We plan to put Beauty to sleep by chemical means, and then we'll flip a (fair) coin. If the coin lands Heads, we will awaken Beauty on Monday afternoon and interview her. If it lands Tails, we will awaken her Monday afternoon, interview her, put her back to sleep, and then awaken her again on Tuesday afternoon and interview her again.The (each?) interview is to consist of the one question: what is your credence now for the proposition that our coin landed Heads?When awakened (and during the interview) Beauty will not be able to tell which day it is, nor will she remember whether she has been awakened before.She knows the above details of our experiment.What credence should she state in answer to our question?
From my philosophy book [101 Philosophy Problems]:
Take an island. There is the possibility that a fatal disease will strike the island and kill 2/3 of the inhabitants. 1/3 of people have natural immunity. Some of those people know they have natural immunity (they had it before and survived) and some do not. If they chew a particular leaf then they will be immunised but 1/20th of people will die of the vaccine. If anyone gets the disease at all then it mutates into a more virulent form in which case chewing the leaves is useful.
Is a majority decision towards vaccination fair and democratic? Should the vaccination program be adopted?