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
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.