Sleeping Beauty

First off, there's been quite a bit of a discussion on this topic, both in emails to the Minotaur and on the discussion forums. I've seen a lot of really interesting comments.

Secondly, I'd like to thank our reader, Adam, for pointing out a Usenet thread archived on Deja.com which identifies the author of the original version of the paradox as Adam Elga.

Now to the problem at hand. The heart of this paradox is epistemic in nature- how should S.B. make a statement of fact about this probability.

Rather than tackle the problem head, let's step back a moment and ask a more abstract question: What is S.B.'s goal in answering the question presented to her?

This may sound odd- presumably her goal is to give the correct answer. But how is her correctness to be measured? Either answer seems defensible, depending on your perspective. While half the time the coin toss comes up heads, at two thirds of the interrogations, the coin toss has come up tails.

Consider this alternative: What if, on tail tosses, the experimenters dispensed with using the amnestic, and made a perfect clone of S.B. (because this is after all the NIT), and asked both copies of S.B. what the probability was? If S.B. didn't know wetter or not she had been cloned, from her perspective the problem is identical to the original.

This suddenly sounds very familiar- it's almost the same scenario as presented in the solution to the Newcomb Problem which we tackled earlier. But with one important twist- in the Newcomb Problem there was a very clear goal defined- the right answer meant gaining a lot of money, while the wrong answer missing out on a lot of money.

Why does this make a difference? Because we are asking S.B. to defend a probability without defining how the probability will be measured. Is it based on the percentage of runs of the experiment where the coin comes up tails? Or is it based on the percentage of interrogations where the coin comes up tails?

In short, the answer is that no probability can be given, because the experimenters have failed to define how probability is measured.

Feel free to continue this discussion in our forums. If you enjoyed this paradox, there is collection of derived problems here: http://www.maproom.co.uk/sb.html.