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?
| Other | 142 / 217 (65.4%) |
| Accept or lean toward: one box | 40 / 217 (18.4%) |
| Accept or lean toward: two boxes | 35 / 217 (16.1%) |
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?
| Other | 441 / 931 (47.4%) |
| Accept or lean toward: two boxes | 292 / 931 (31.4%) |
| Accept or lean toward: one box | 198 / 931 (21.3%) |
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?
| Accept or lean toward: two boxes | 19 / 31 (61.3%) |
| Accept or lean toward: one box | 8 / 31 (25.8%) |
| Other | 4 / 31 (12.9%) |
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:
| Newcomb's problem:two boxes | 0.125 | |||||||||||||||||
Response pairs: 655 p-value: 0.001
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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.
The most charitable interpretation would just be that there happened to be a convincing technical theory which said you should two-box, because it took an even more technical theory to explain why you should one-box and this was not constructed, along with the rest of the edifice to explain what one-boxing means in terms of epistemic models, concepts of instrumental rationality, the relation to traditional philosophy's 'free will problem', etcetera. In other words, they simply bad-lucked onto an edifice of persuasive, technical, but ultimately incorrect argument.
We could guess other motives for people to two-box, like memetic pressure for partial counterintuitiveness, but why go to that effort now? Better TDT writeups are on the way, and eventually we'll get to see what the field says about the improved TDT writeups. If it's important to know what other hidden motives might be at work, we'll have a better idea after we negate the usually-stated motive of, "The only good technical theory we have says you should two-box." Perhaps the field will experience a large conversion once presented with a good enough writeup and then we'll know there weren't any other significant motives.
FWIW, when I first read about the problem I took two-boxing to be the obviously correct answer (I wasn't a compatibilist back then), and I didn't change my mind until I read Less Wrong.