Maybe he means something along the lines of same cause, same effect is just a placeholder for as long as all the things which matter stay the same, you get the same effect. After all, some things, such as time since the man invented fire and position relative to Neptune and so on and so forth cannot possibly be the same for two different events. And this in turn sort of means things which matter → same effect is a circular definition. Maybe he means to say that the law of causality is not the actually useful principle for making predictions, while there are indeed repeatable experiments and useful predictions to be made.
incogn
Karma: 53
(Thanks for discussing!)
I will address your last paragraph first. The only significant difference between my original example and the proper Newcomb’s paradox is that, in Newcomb’s paradox, Omega is made a predictor by fiat and without explanation. This allows perfect prediction and choice to sneak into the same paragraph without obvious contradiction. It seems, if I try to make the mode of prediction transparent, you protest there is no choice being made.
From Omega’s point of view, its Newcomb subjects are not making choices in any substantial sense, they are just predictably acting out their own personality. That is what allows Omega its predictive power. Choice is not something inherent to a system, but a feature of an outsider’s model of a system, in much the same sense as random is not something inherent to a Eeny, meeny, miny, moe however much it might seem that way to children.
As for the rest of our disagreement, I am not sure why you insist that CDT must work with a misleading model. The standard formulation of Newcomb’s paradox is inconsistent or underspecified. Here are some messy explanations for why, in list form:
Omega predicts accurately, then you get to choose is a false model, because Omega has predicted you will two-box, then you get to choose does not actually let you choose; one-boxing is an illegal choice, and two-boxing the only legal choice (In Soviet Russia joke goes here)
You get to choose, then Omega retroactively fixes the contents of the boxes is fine and CDT solves it by one-boxing
Omega tries to predict but is just blindly guessing, then you really get to choose is fine and CDT solves it by two-boxing
You know that Omega has perfect predictive power and are free to be committed to either one- or two-boxing as you prefer is nowhere near similar to the original Newcomb’s formulation, but is obviously solved by one-boxing
You are not sure about Omega’s predictive power and are torn between trying to ‘game’ it and cooperating with it is not Newcomb’s problem
Your choice has to be determined by a deterministic algorithm, but you are not allowed to know this when designing the algorithm, so you must instead work in ignorance and design it by a false dominance principle is just cheating
I am not sure where our disagreement lies at the moment.
Are you using choice to signify strongly free will? Because that means the hypothetical Omega is impossible without backwards causation, leaving us at (b) but not (a) and the whole of Newcomb’s paradox moot. Whereas, if you include in Newcomb’s paradox, the choice of two-boxing will actually cause the big box to be empty, whereas the choice of one-boxing will actually cause the big box to contain a million dollars by a mechanism of backwards causation, then any CDT model will solve the problem.
Perhaps we can narrow down our disagreement by taking the following variation of my example, where there is at least a bit more of choice involved:
Imagine John, who never understood why he gets thirsty. Despite there being a regularity in when he chooses to drink, this is for him a mystery. Every hour, Omega must predict whether John will choose to drink within the next hour. Omega’s prediction is made secret to John until after the time interval has passed. Omega and John play this game every hour for a month, and it turns out that while far from perfect, Omega’s predictions are a bit better than random. Afterwards, Omega explains that it beats blind guesses by knowing that John will very rarely wake up in the middle of the night to drink, and that his daily water consumption follows a normal distribution with a mean and standard deviation that Omega has estimated.
Thanks for the link.
I like how he just brute forces the problem with (simple) mathematics, but I am not sure if it is a good thing to deal with a paradox without properly investigating why it seems to be a paradox in the first place. It is sort of like saying that this super convincing card trick you have seen, there is actually no real magic involved without taking time to address what seems to require magic and how it is done mundanely.
I do not agree that a CDT must conclude that P(A)+P(B) = 1. The argument only holds if you assume the agent’s decision is perfectly unpredictable, i.e. that there can be no correlation between the prediction and the decision. This contradicts one of the premises of Newcomb’s Paradox, which assumes an entity with exactly the power to predict the agent’s choice. Incidentally, this reduces to the (b) but not (a) from above.
By adopting my (a) but not (b) from above, i.e. Omega as a programmer and the agent as predictable code, you can easily see that P(A)+P(B) = 2, which means one-boxing code will perform the best.
Further elaboration of the above:
Imagine John, who never understood how the days of the week succeed each other. Rather, each morning, a cab arrives to take him to work if it is a work day, else he just stays at home. Omega must predict if he will go to work or not the before the cab would normally arrive. Omega knows that weekdays are generally workdays, while weekends are not, but Omega does not know the ins and outs of particular holidays such as fourth of July. Omega and John play this game each day of the week for a year.
Tallying the results, John finds that the score is as follows: P( Omega is right | I go to work) = 1.00, P( Omega is right | I do not go to work) = 0.85, which sums to 1.85. John, seeing that the sum is larger than 1.00, concludes that Omega seems to have rather good predictive power about whether he will go to work, but is somewhat short of perfect accuracy. He realizes that this has a certain significance for what bets he should take with Omega, regarding whether he will go to work tomorrow or not.
I don’t really think Newcomb’s problem or any of its variations belong in here. Newcomb’s problem is not a decision theory problem, the real difficulty is translating the underspecified English into a payoff matrix.
The ambiguity comes from the the combination of the two claims, (a) Omega being a perfect predictor and (b) the subject being allowed to choose after Omega has made its prediction. Either these two are inconsistent, or they necessitate further unstated assumptions such as backwards causality.
First, let us assume (a) but not (b), which can be formulated as follows: Omega, a computer engineer, can read your code and test run it as many times as he would like in advance. You must submit (simple, unobfuscated) code which either chooses to one- or two-box. The contents of the boxes will depend on Omega’s prediction of your code’s choice. Do you submit one- or two-boxing code?
Second, let us assume (b) but not (a), which can be formulated as follows: Omega has subjected you to the Newcomb’s setup, but because of a bug in its code, its prediction is based on someone else’s choice than yours, which has no correlation with your choice whatsoever. Do you one- or two-box?
Both of these formulations translate straightforwardly into payoff matrices and any sort of sensible decision theory you throw at them give the correct solution. The paradox disappears when the ambiguity between the two above possibilities are removed. As far as I can see, all disagreement between one-boxers and two-boxers are simply a matter of one-boxers choosing the first and two-boxers choosing the second interpretation. If so, Newcomb’s paradox is not as much interesting as poorly specified. The supposed superiority of TDT over CDT either relies on the paradox not reducing to either of the above or by fiat forcing CDT to work with the wrong payoff matrices.
I would be interested to see an unambiguous and nontrivial formulation of the paradox.
Some quick and messy addenda:
Allowing Omega to do its prediction by time travel directly contradicts box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Also, this obviously make one-boxing the correct choice.
Allowing Omega to accurately simulate the subject reduces to problem to submit code for Omega to evaluate; this is not exactly paradoxical, but then the player is called upon to choose which boxes to take actually means the code then runs and returns its expected value, which clearly reduces to one-boxing.
Making Omega an imperfect predictor, with an accuracy of p<1.0 simply creates a superposition of the first and second case above, which still allows for straightforward analysis.
Allowing unpredictable, probabilistic strategies violates the supposed predictive power of Omega, but again cleanly reduces to payoff matrices.
Finally, the number of variations such as the psychopath button are completely transparent, once you decide between choice is magical and free will and stuff which leads to pressing the button, and the supposed choice is deterministic and there is no choice to make, but code which does not press the button is clearly the most healthy.
Only in the sense that the term “pro-life” implies than there exist people opposed to life.