I don’t understand the theory, but the one-boxing solution seems obvious: given that Omega is correct, if I am such that I would refuse the £10, I would not be offered the choice unless the £1 000 000 is in the envelope, therefore I should refuse the £10 …
… unless I believe Omega is over u(£1 000 000)/u(£10) times more likely to offer the deal to agents who take the £10 than to agents who refuse. In that case, being willing to take the £10 is expected to pay off.
Edit (after timtyler’s reply): Vladimir Nesov’s analysis has caused me to reconsider—I would now take the £10.
That seems like a reasonable analysis to me—assuming that you get to keep the contents of the envelope.
So: the solution depends on information about Omega’s motivation not included in the problem description. Time to consult those mythology textbooks, methinks—so we have appropriate priors :-/
I don’t understand the theory, but the one-boxing solution seems obvious: given that Omega is correct, if I am such that I would refuse the £10, I would not be offered the choice unless the £1 000 000 is in the envelope, therefore I should refuse the £10 …
… unless I believe Omega is over u(£1 000 000)/u(£10) times more likely to offer the deal to agents who take the £10 than to agents who refuse. In that case, being willing to take the £10 is expected to pay off.
Edit (after timtyler’s reply): Vladimir Nesov’s analysis has caused me to reconsider—I would now take the £10.
That seems like a reasonable analysis to me—assuming that you get to keep the contents of the envelope.
So: the solution depends on information about Omega’s motivation not included in the problem description. Time to consult those mythology textbooks, methinks—so we have appropriate priors :-/
[edit: scratch this—I get it now!]