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CuSithBell comments on Timeless Decision Theory: Problems I Can't Solve - Less Wrong
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What if it's offered just once - but if the coin comes up tails, Omega simulates a universe in which it came up heads, asks you this question, then acts based on your response? (Do whatever you like to ignore anthropics... say, Omega always simulates the opposite result, at the appropriate time.)
To be clear:
Are both I and my simulation told this is a one-time offer?
Is a simulation generated whether the real coin is heads or tails?
Are both my simulation and I told that one of us is a simulation?
Does the simulation persist after the choice is made?
I suppose the second and fourth points don't matter particularly... as long as the first and third are true, then I consider it plus EV to pay the $1000.
Should you pay the money even if you're not told about the simulations, because Omega is a good predictor (perhaps because it's using simulations)?
If I judge the probability that I am a simulation or equivalent construct to be greater than 1/499500, yes.
(EDIT: Er, make that 1/999000, actually. What's the markup code for strikethrough 'round these parts?)
(EDIT 2: Okay, I'm posting too quickly. It should be just 10^-6, straight up. If I'm a figment then the $1000 isn't real disutility.)
(EDIT 3: ARGH. Sorry. 24 hours without sleep here. I might not be the sim, duh. Correct calculations:
u(pay|sim) = 10^6; u(~pay|sim) = 0; u(pay|~sim) = -1000; u(~pay|~sim) = 0
u(~pay) = 0; u(pay) = P(sim) * 10^6 - P(~sim) * (1000) = 1001000 * P(sim) - 1000
pay if P(sim) > 1/1001.
Double-checking... triple-checking... okay, I think that's got it. No... no... NOW that's got it.)