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| Alex Mennen | v0.0.3Aug 8th 2013 |
Each interview consists of one question,
“What“What is your credence now for the proposition that our coin landed heads?””
A third argument tries to add rigor by considering monetary payoffs. If Beauty'Beauty's bets about the coin get paid out once per experiment, she will do best by acting as if the probability is one half. If the bets get paid out once per awakening, acting as if the probability is one third has the best expected value.
The two popular positions areOne argument says that since Beauty will see the same thing on waking whether the coin came up heads or not, what she sees on waking provides no evidence one way or the other about the coin, and therefore she should stick with the prior probability of one half.
Another argument replies that the answertwo awakenings when the coin comes up tails imply that waking up itself should be considered evidence in favor of tails. Out of all possible situations where Beauty is asked the question, only one half orout of three has the coin showing heads. Therefore, one third, depending on how you interpret .third.
A third argument tries to add rigor by considering monetary payoffs. If Beauty's bets about the coin get paid out once per experiment, she will do best by acting as if the probability is one half. If the bets get paid out once per awakening, acting as if the probability is one third has the best expected value.
The Sleeping Beauty Paradox is a question of how anthropics affects probabilities.probabilities.
The two popular positions are that the answer should be one half or one third.third, depending on how you interpret .
The Sleeping Beauty Paradox is a decision theory problemquestion of how anthropics affects probabilities.
Sleeping Beauty volunteers to undergo the following experiment. On Sunday she is given a drug thatrelatessends her toanthropics.sleep. A fair coin is then tossed just once in the course of the experiment to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday, given a second dose of the sleeping drug, and awakened and interviewed again on Tuesday. The experiment then ends on Tuesday, without flipping the coin again. The sleeping drug induces a mild amnesia, so that she cannot remember any previous awakenings during the course of the experiment (if any). During the experiment, she has no access to anything that would give a clue as to the day of the week. However, she knows all the details of the experiment.
Each interview consists of one question, “What is your credence now for the proposition that our coin landed heads?”
The two popular positions are that the answer should be one half or one third.
The Sleeping Beauty problem in Paradox is a decision theory illustrates a (possibly temporal) time inconsistency between belief and optimal behavior in classical decision theories:
Suppose Sleeping Beauty volunteers problem that relates to undergo the following experiment, which is described to her before it begins. On Sunday she is given a drug that sends her to sleep, and a coin is tossed. If the coin lands heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday, given a second dose of the sleeping drug that makes her forget the events of Monday only, and awakened and interviewed again on Tuesday. The experiment then ends on Tuesday, without flipping the coin again.anthropics.
Beauty wakes up in the experiment and is asked, "With what subjective probability do you believe that the coin landed tails?"
A third argument tries to add rigor by considering monetary payoffs. If Beauty's bets about the coin get paid out once per experiment, some argue that she will do best by acting as if the probability is one
half.half (while others argue that probability one third gives the correct result if decision theory is correctly applied). If instead the bets get paid out once per awakening, one can again argue about whether or not acting as if the probability is one third has the best expected value.