My initial reaction is to find that aggravating and to try to come up with another experiment that would allow me to poke at the universe by exploiting the Predictor, but it seems likely that this too would be sidestepped using the same tactic. So we could generalize to say that any experiment you come up with that involves the Predictor and gives evidence regarding the temporal direction of causation will be sidestepped so as to give you no new information.
But intuitively, it seems like this condition itself gives new information in the paradox, yet I haven't yet wrapped my head around what evidence can be drawn from it.
On another note, even if causality flows always forward, it is possible that humans might be insufficiently affected by nondeterministic phenomena to produce significantly nondeterministic behavior, at least at the time scale we're talking about. If that is the case, then it could potentially be the case that human reasoning has approximate t-symmetry over short time scales, and that this can be exploited to "violate causality" with respect to humans without actually violating causality with respect to the universe at large.
Which means that I have a more general hypothesis, "human reasoning causality can be violated" for which the violation of causality in general would be strong evidence, but the non-violation of causality would only be weak counter-evidence. And in learning of the Predictor's success, I have observed evidence strongly recommending this hypothesis.
So upon further consideration, I think that one-boxing is probably the way to go regardless, and it must simply be accepted that if you actually observe the Predictor, you can no longer rely on CDT if you know that such an entity might be involved.
The only part of the paradox that still bugs me then is the hand-waving that goes into "assume you believe the Predictor's claims". It is actually hard for me to imagine what evidence I could observe for that which would both clearly distinguish "the Predictor is honest" hypothesis from the "I'm being cleverly deceived" and "I've gone crazy" hypotheses, and also does not directly tip the Predictor's hand as to whether human reasoning causality can be violated.
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.