Are you saying that the "CDT as it is normally interpreted" cannot help but fight the hypothetical? It doesn't have to fight the hypothetical. CDT counterfactuals don't have to be possible.
The standard CDT algorithm computes the value of each action by computing the expected utility conditional on a miraculous intervention changing one's decision to that action, separately from early deterministic causes, and computing the causal consequences of that. See Anna's discussion here, including modifications in which the miraculous intervention changes other things, like one's earlier dispositions (perhaps before the Predictor scanned you) or the output of one's algorithm (instantiated in you and the Predictor's model).
Say before the contents of the boxes are revealed our CDTer assigns some probability p to the state of the world where box B is full and his internal makeup will deterministically lead him to one-box, and probability (1-p) to the state of the world where box B is empty and that his internal makeup will deterministically lead him to two-box.
That notwithstanding, CDT does take probabilities into account, at least the CDT as described in Wikipedia, so the question is, what is the counterfactual probability that if I were to two-box, then I get $1.001M, as opposed to the conditional probability of the same thing. The latter is very low, the former has to be evaluated on some grounds.
Altering your action miraculously and exogenously would not change the box contents causally. So the CDTer uses the old probabilities for the box contents, the utility of one-boxing is computed to be $1,000,000 times p, and the utility of two boxing is calculated to be $1,001,000p+$1,000 times (1-p).
If she is confident that she will apply CDT based on past experience, or introspection, she will have previously updated to thinking that p is very low.
utility of one-boxing is computed to be $1,000,000 times p,
utility of two boxing is calculated to be $1,001,000p+$1,000 times (1-p).
If she is confident that she will apply CDT based on past experience, or introspection, she will have previously updated to thinking that p is very low.
Right, I forgot. The reasoning is "I'm a two-boxer because I follow a loser's logic and Omega knows it, so I may as well two-box." There is no anticipation of winning $1,001,000. No, that does not sound quite right...
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.