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ike comments on Anthropic decision theory I: Sleeping beauty and selflessness - Less Wrong Discussion

10 Post author: Stuart_Armstrong 01 November 2011 11:41AM

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Comment author: ike 15 September 2014 02:25:22AM *  2 points [-]

An explanation could be that Beauty is only is asked for her credence in Heads during an awakening event, regardless of the time, and that such an event occurs twice in the Tails-world. That is, out of the 4 possible observer-moments in the Tails-world there are only two in which she is interviewed. That means that simply the fact that she is asked the same question twice is reason enough for thirders to distribute their credence, and it is no longer about the number of observer moments. So if she would be asked the same question a million times then her credence in Heads would drop to 1/1000001!

This is actually correct, assuming her memory is wiped after each time.

We can magnify the absurdity of this reasoning by imagining a modified version of the Sleeping Beauty Problem in which a coin is tossed that always lands on Tails. Again, she is awakened one million times and given an amnesia-inducing potion after each awakening. Thirder logic would lead to Beauty’s credence in Tails being 1/1000000, as there are one million observer-moments where she is asked for her credence within the only possible world; the Tails-world. To recapitulate: Beauty is certain that she lives in a world where a coin lands Tails, but due to the fact that she knows that she will answer the same question a million times her answer is 1/1000000. This would be tantamount to saying that Mt. Everest is only 1m high when knowing it will be asked 8848 times! It is very hard to see how amnesia could have such an effect on rationality.

No! Her credence in "This is the first (or xth) time I've been awakened in Tails" is 1/1000000. Her credence in "this is Tails" is ~1.

What would you put the probability of it being the xth question, x ranging from 1 to 1 1,000,000?