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.
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.)