5. Speaking of beauty, here is another example of misapplying the Sklanksy Principle. It is the
Sleeping Beauty Paradox. A fair coin is flipped. If it comes up heads, Beauty goes to sleep on Monday and is awoken later that evening. She then goes back to sleep for a week. If the coin is tails Beauty also goes to sleep on Monday and is awakened and then goes back to sleep. But after she has gone back to sleep a magic wand is waved that gives her Amnesia. She will not remember her Monday Awakening. She then sleeps until Tueday evening when she is awakened once again, than goes back to sleep for the rest of the week.
Beauty is perfectly rational. She is told how all this is going to work. Now she has an awakening. She doesn't know if it's monday or tuesday. What is her Credence or Belief about how the coin landed? The Paradox argument claims she now believes there is a 1/3 chance the coin landed on heads. Why does she have that belief?
The argument goes that she knows she can have three kinds of awakenings. One due to heads. And two due to tails. She applies Sklanskyish thinking to this to conclude that since she knows nothing about which of these kinds of awakenings she might be having, she concludes they are equally likely. After all, she should experience on average 1.5 awakenings. .5 due to heads .5 due to tails and another .5 due to tails. They are equally likely so there must be 1/3 chance the coin landed on heads.
Here is a link to my treatment for resolving the parodox.
Resolution of the Sleeping Beauty Paradox
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