We have to determine what counts as "unfair". Newcomb's problem looks unfair because your decision seems to change the past. I have seen another Newcomb-like problem that was (I believe) genuinely unfair, because depending on their decision theory, the agents were not in the same epistemic state.
Here what I think is a "fair" problem. It's when
If we think of the agent as a program, I think we can equate "decision" with the agent's output. It's harder however to equate "epistemic state" with its input: recall Omega saying "Here is the 2 usual boxes. I have submitted this very problem in a simulation to TDT. If it one boxed, box B has the million. If it two boxed, box B is empty". So, if you're TDT, this problem is equivalent to the old Newcomb problem, where oneBox <=> $$$. But any other agent could 2 box, and get the million and the bonus. (Also, "TDT" could be replaced by a source code listing that the agent would recognize as its own.)
Anyway, I believe there's a good chance a decision theory exists such that it gets the best results out of any "fair" problem.Though now that I think of it, condition 2 may be a sufficient criterion for "fairness", for the problem above violates it: if TDT two-boxes, it does not get the million. Well except it does not two box, so my counter-factual doesn't really mean anything…
It still seems to me that you can't have a BestDecisionAgent. Suppose agents are black boxes -- Omegas can simulate agents at will, but not view their source code. An Omega goes around offering agents a choice between:
Does this test meet your criteria for a fair test? If not, why not?
Follow-up to: Normative uncertainty in Newcomb's problem
Philosophers and atheists break for two-boxing; theists and Less Wrong break for one-boxing
Personally, I would one-box on Newcomb's Problem. Conditional on one-boxing for lawful reasons, one boxing earns $1,000,000, while two-boxing, conditional on two-boxing for lawful reasons, would deliver only a thousand. But this seems to be firmly a minority view in philosophy, and numerous heuristics about expert opinion suggest that I should re-examine the view.
In the PhilPapers survey, Philosophy undergraduates start off divided roughly evenly between one-boxing and two-boxing:
Newcomb's problem: one box or two boxes?
But philosophy faculty, who have learned more (less likely to have no opinion), and been subject to further selection, break in favor of two-boxing:
Newcomb's problem: one box or two boxes?
Specialists in decision theory (who are also more atheistic, more compatibilist about free will, and more physicalist than faculty in general) are even more convinced:
Newcomb's problem: one box or two boxes?
Looking at the correlates of answers about Newcomb's problem, two-boxers are more likely to believe in physicalism about consciousness, atheism about religion, and other positions generally popular around here (which are also usually, but not always, in the direction of philosophical opinion). Zooming in one correlate, most theists with an opinion are one-boxers, while atheists break for two-boxing:
Less Wrong breaks overwhelmingly for one-boxing in 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%
When I elicited LW confidence levels in a poll, a majority indicated 99%+ confidence in one-boxing, and 77% of respondents indicated 80%+ confidence.
What's going on?
I would like to understand what is driving this difference of opinion. My poll was a (weak) test of the hypothesis that Less Wrongers were more likely to account for uncertainty about decision theory: since on the standard Newcomb's problem one-boxers get $1,000,000, while two-boxers get $1,000, even a modest credence in the correct theory recommending one-boxing could justify the action of one-boxing.
If new graduate students read the computer science literature on program equilibrium, including some local contributions like Robust Cooperation in the Prisoner's Dilemma and A Comparison of Decision Algorithms on Newcomblike Problems, I would guess they would tend to shift more towards one-boxing. Thinking about what sort of decision algorithms it is rational to program, or what decision algorithms would prosper over numerous one-shot Prisoner's Dilemmas with visible source code, could also shift intuitions. A number of philosophers I have spoken with have indicated that frameworks like the use of causal models with nodes for logical uncertainty are meaningful contributions to thinking about decision theory. However, I doubt that for those with opinions, the balance would swing from almost 3:1 for two-boxing to 9:1 for one-boxing, even concentrating on new decision theory graduate students.
On the other hand, there may be an effect of unbalanced presentation to non-experts. Less Wrong is on average less philosophically sophisticated than professional philosophers. Since philosophical training is associated with a shift towards two-boxing, some of the difference in opinion could reflect a difference in training. Then, postings on decision theory have almost all either argued for or assumed one-boxing as the correct response on Newcomb's problem. It might be that if academic decision theorists were making arguments for two-boxing here, or if there was a reduction in pro one-boxing social pressure, there would be a shift in Less Wrong opinion towards two-boxing.
Less Wrongers, what's going on here? What are the relative causal roles of these and other factors in this divergence?
ETA: The SEP article on Causal Decision Theory.