Omega has been observed to have a less than 1% error rate, I assume.
I've been curious why all the formulations of Newcomb's I've read give Omega/Predictor an error rate at all. Is it just to preempt reasoning along the lines of "well he never makes an error that means he is a god so I one-box" or is there a more subtle, problem-relevant reason that I'm missing?
Here is Wikipedia's description of Newcomb's problem:
Most of this is a fairly general thought experiment for thinking about different decision theories, but one element stands out as particularly arbitrary: the ratio between the amount the Predictor may place in box B and the amount in box A. In the Newcomb formulation conveyed by Nozick, this ratio is 1000:1, but this is not necessary. Most decision theories that recommend one-boxing do so as long as the ratio is greater than 1.
The 1000:1 ratio strengthens the intuition for one-boxing, which is helpful for illustrating why one might find one-boxing plausible. However, given uncertainty about normative decision theory, the decision to one-box can diverge from one's best guess at the best decision theory, e.g. if I think there is a 1 in 10 chance that one-boxing decision theories I may one-box on Newcomb's problem with a potential payoff ratio of 1000:1 but not if the ratio is only 2:1.
So the question, "would you one-box on Newcomb's problem, given your current state of uncertainty?" is not quite the same as "would the best decision theory recommend one-boxing?" This occurred to me in the context of this distribution of answers among target philosophy faculty from the PhilPapers Survey:
Newcomb's problem: one box or two boxes?
If all of these answers are about the correct decision theory (rather than what to do in the actual scenario), then two-boxing is the clear leader, with a 2.85:1 ratio of support (accept or lean) in its favor, but this skew would seem far short of that needed to justify 1000:1 confidence in two-boxing on Newcomb's Problem.
Here are Less Wrong survey answers for 2012:
NEWCOMB'S PROBLEM
One-box: 726, 61.4%
Two-box: 78, 6.6%
Not sure: 53, 4.5%
Don't understand: 86, 7.3%
No answer: 240, 20.3%
Here one-boxing is overwhelmingly dominant. I'd like to sort out how much of this is disagreement about theory, and how much reflects the extreme payoffs in the standard Newcomb formulation. So, I'll be putting a poll in the comments below.