"The problem is so simple", why are you repeating this over and over again, especially without providing your own answer? You know the opinions are split, so what's the reader supposed to assume the simple answer is? Whatever each individual reader thinks the simple answer is? You filled up your post with a meta-opinion about your opinion, but didn't even bother to give your opinion. I think the question should be reworded WITHOUT you spamming your own opinion about how simple it is throughout the text. It has poisoned your question.

There is a longer analysis of the Newcomb's problem in SEP under Causal Decision Theory, with many references. Sleeping Beauty is another decision problem that prompts diverging responses. This is often the case where probabilities are involved, Bertrand paradox and Monty Hall are other examples. In all cases, much of confusion is attributable to ambiguity.

@TKoL - I'm sorry if I made you curious as to what my own answer would be - I don't think it's possible to give a convincing presentation of that in a post here. But it doesn't really matter for my question, I think, which side I'm on. I'm basically reiterating what Nozick also said: Each side thinks the answer is simple, and the other side is confused. So, my question is what is causing this split?

@TKoL - I've tried to take your criticism to heart, taking out implicit claims that there really is a simple solution. Hopefully it no longer comes across as "spam-like".

@ScottRowe - Everyone is confused. Definitely possible. But why? What is causing this? Is there something that all parties are overlooking?

@Conifold - Ambiguity rather than (or more than) vagueness? Ambiguity surely is often a factor - but isn't it so that academic philosophers are trained in recognizing it and avoiding it in their debates? And is it the main factor that explains the conflicting ways of looking at the Newcomb problem?

The ambiguity is due to different ways of interpreting the probability setup and the decision-making scheme, but there are usually just several of them, not a spectrum as in vagueness. The PhilPapers question leaves that up to the responders, and they have different views of free will, how the prophesizing works, which decision-making scheme is more 'rational', etc. 'Rationality' and decision-making are generally controversial. It is determinate what is optimal according to a mathematically specified setup and criterion, but not which specifications or criteria are 'better'.

@Conifold - You state that (your first sentence) as a fact, but I believe this is also controversial. (It seems to me that you are basically siding here with Wolpert, Benford.) I do understand and agree that how to apply a mathematical model or how to interpret it in a wider context (a more realistic context - actual behavior and reasoning) can still leave open a lot of questions. Questions in that area seem to me typically vague - inevitably vague perhaps.

Wolpert-Benford only consider the Newcomb's problem, ambiguities have been displayed in all of the above. I do not think their role in causing confusions and differences of opinion is particularly controversial, although singling out the "main factor" typically is. "Main" is in the same category as "better", so it is to be expected. Another possible factor is the general lousiness of human probabilistic intuitions described by Kahneman and Tversky, and philosophers are not special in this regard. It compounds the problem, as people do not easily spot probabilistic ambiguities.

@mudskipper I think the answer is relevant. Suppose you and I both agree the answer is simple and straight forward, and have whatever conversation you might want to have about what makes it confusing - and suppose we agree on everything, and then I say "but wait, what do you think the obvious solution is?" and you say the exact opposite solution to the one I think. Don't you think it's bizarre that two people would be circle jerking about an obvious solution when they don't even agree with each other about the solution?

Asking "why is this problem so confusing?", when you clearly think it's not confusing to you, is essentially the same as asking "Why do people not all come to agree with my solution?" And if we don't know what your solution is, how can we effectively answer why other people come to an alternative conclusion? What you think the solution is is ENTIRELY relevant to answerig the question in the way you've asked it.

"easily repeatable as actual experiment" - I mean I guess it would be easy if you happen to have a superintelligent AI that's capable of learning enough about a person to predict what they will do in a specific situation with a high degree of accuracy. Otherwise, not so much.

In elementary school gym, we would sometimes play a game called Newcomb, which I never understood. School is very confusing, they have to teach you all the things you are always going to be bad at before you get to programming. It is something of a paradox, which someone should figure out.

Reading through Wikipedia, it looks like the problem is just ill-defined, and the article even calls that out ("... paradoxes arise when not all relevant details of a problem are specified ..."). This perfectly matches that the two main decisions are based on different objective functions, i.e. the problem does not even say what the objective is. Knowing this, in how far is it confusing to you that the problem is confusing?

"What makes this problem so super controversial?" is the same as asking Why do both sides think what they think? -- which is a much clearer quesiton, I guess. And given you think one side is the obvious answer, you're really only curious about why people who disagree with you think what they think, no? Opening a question and asking clearly, "Why do the people who think the solution to this problem is X think that?" might get you some more interesting responses.

Next topic: the upcoming elections...

@TKoL - I do think there is an (somewhat?) obvious answer to the puzzle, but people who come to the same conclusion (in the game) may do so for different, perhaps spurious reasons. So, I'm curious about the reasonings that various approaches propose for the player in the game. I've only browsed thru the literature a little bit and so far I have not found any approach that is totally satisfactory to me, though I have found some that are very unsatisfactory (like causal decision theory)(which doesn't imply that CDT is totally wrong, it may be just being misapplied).

@TKoL - Based on your ciritical review -- with which I partially agree -- I might have edited my post again. But since some people have already posted some answers, I've decided to leave it as is so that I don't -as it were- pull the rug out from underneath those answers.

In lieu of voting to close (as opinion-based), I'll point out that the prerequisites for Newcomb's theorem aren't physically possible; any predictor can be humbled by a coin toss, bringing them down to 50%, and this can be made rigorous using quantum mechanics. So, don't worry about it; it's a silly thought experiment for a fictional universe.

@Corbin - (1) What is opinion based in my question? (2) I agree that the predictor can be defeated by a coin toss (I pointed this out myself in a comment to another reply). However the Newcomb scenario explicitly stipulates that this is not an allowed strategy for the player. Only pure strategies are acceptable (Nozick also points this out). (3) It's an empirical fact that this problem has been and still is one of the most controversial problems in the last 50 years. This fact makes me wonder, why. This fact and the question why seem philosophical relevant to me.

(1) It's not confusing. People confuse themselves by forcing interpretations onto it. So, you're going to get peoples' interpretations of the paradox as answers, even if they're well-reasoned. (2) Too bad, I'm bringing a coin. You have to understand: at least two cults use this paradox as a recruiting mechanism, and we can't let them pretend that this is a physically-realizable experiment. (3) This could be an interesting line of inquiry!

(1) What you are saying there is an answer (or the vague hint of an answer) to the question I asked. It's an answer with which I partially agree: The interpretation of the stories (how the problem is presented) is relevant and there are elements in the stories themselves that may be confusing or that may be misrepresented in the interpretation. (2) I didn't know about those sects - this is pretty interesting. Do you have links to that?

As an aside: In all the literature that I looked at people overlook the fact (or don't discuss it) that it is very easy to implement an infallible predictor - namely by cheating. Another way to implement a pretty good, but fallible predictor is by simply asking the player in advance what their choice would be and telling them that if they're suspected of lying the experimenter may remove the 1M from the one box.

@Corbin - In regards to your first point - I'm actually struggling with that ("opionion-based")(I've also seen - not about my post, but about other people's posts: "this is a question-answer site, not an open discussion site", "stop pushing your own opinions").

What is the right balance there? I don't quite see how it's possible/sensible to have well-defined rules for this on a philosophy site. If you strictly define them, then it can basically only be a site were people ask for historical info or references - but then you might as well just google them/use wikipedia/use SEP. I

n a way, the kind of illdefined vague questions or opinionated questions and the opinionated answers of people (since all answers unless they merely point to SEP for instance) are debatable opinions - that's exactly what makes the site (somewhat) interesting (at least to me).

@mudskipper: On (2), I think it's time to mention Roko's basilisk (WARNING: MEMETIC HAZARD). This sort of bullshit is why I am so dour about Newcomb's paradox. The two cults pushing it are LessWrong (Yudkowsky, Gwern, etc.) and neoreactionism (Moldbug, Land, Bostrom, etc.) The entire problem dissolves if predictors can't get good.

On (1), I'm not sure what to tell you. Like, presumably you want some sort of explanation for why any thought experiment like this, particularly the Sleeping Beauty problem, but there isn't a universal statement. Instead, it just happens to be the case that sometimes philosophers are split in opinion.

(That problem is worth examining, BTW. Its solutions change depending on tiny changes to its phrasing and environment. Its solutions are dependent on physics, too; the classical and quantum versions are distinct.)

@Corbin - Thanks for the link. I had actually also come across Yudkowski's blog recently... Haha. So, I do believe some lessons could be learned - but don't have a good picture of what or how. I saw the Sleeping Beauty Problem (also just recently) - and that seems to me (just like Monty Hall) just a statistics problem (I'm on the 1/3 side at the moment).

My first thought about Roko's basiisk is that Yudkowski may have been playing both sides here - I suspect him from being a troll. Or is it known that Roko was not Y. himself?