32 lines
1.8 KiB
Plaintext
32 lines
1.8 KiB
Plaintext
;Background on the task
|
|
In [[wp:Decision theory|decision theory]], [[wp:Sleeping Beauty problem|The Sleeping Beauty Problem]]
|
|
is a problem invented by Arnold Zoboff and first publicized on Usenet. The experimental
|
|
subject, named Sleeping Beauty, agrees to an experiment as follows:
|
|
Sleeping Beauty volunteers to be put into a deep sleep on a Sunday. There is then a fair coin toss.
|
|
If this coin toss comes up heads, Sleeping Beauty wakes once (on Monday) and is asked to
|
|
estimate the probability that the coin toss was heads. Her estimate is recorded and she is
|
|
then put back to sleep for 2 days until Wednesday, at which time the experiment's results are tallied.
|
|
<br />
|
|
|
|
If instead the coin toss is tails, Sleeping Beauty wakes as before on Monday and asked to
|
|
estimate the probability the coin toss was heads, but is then given a drug which makes her forget
|
|
that she had been woken on Monday before being put back to sleep again. She then wakes only 1 day
|
|
later, on Tuesday. She is then asked (on Tuesday) again to guess the probability that the coin toss
|
|
was heads or tails. She is then put back to sleep and awakes as before 1 day later, on Wednesday.
|
|
<br />
|
|
|
|
Some decision makers have argued that since the coin toss was fair Sleeping Beauty should always
|
|
estimate the probability of heads as 1/2, since she does not have any additional information. Others
|
|
have disagreed, saying that if Sleeping Beauty knows the study design she also knows that she is twice
|
|
as likely to wake up and be asked to estimate the coin flip on tails than on heads, so the estimate
|
|
should be 1/3 heads.
|
|
|
|
;Task
|
|
|
|
Given the above problem, create a Monte Carlo estimate of the actual results. The program should find the
|
|
proportion of heads on waking and asking Sleeping Beauty for an estimate, as a credence or as a percentage of the times Sleeping Beauty
|
|
is asked the question.
|
|
|
|
|
|
|