NEWCOMBS’ PROBLEM in light of CAUSALITY

CONNOR DENNEHY WORD COUNT: 1879
 
NEWCOMB'S PARADOX in light of CAUSALITY
 
Introduction

Imagine that you are playing a game in which you are presented with two boxes. One is uncovered, visibly containing one thousand dollars; the other is covered, and is known to contain either a million dollars or nothing. You are given the options of taking both, or just the covered. The contents of the covered box depend upon a prediction made by a mysterious Being, regarding which option you will choose. If the Being predicted that you will take both boxes, then the covered box will empty, and if the Being predicted that you will take only the covered box, then it will contain the million dollars. Additionally, it is understood that this Being has impeccable predictive powers, demonstrated by having made a virtually infinite number of accurate predictions for this very game, without one single mistake. In other words, you have every reason to believe that the Being had anticipated you choice correctly. With this in mind, and assuming your goal is to obtain the most money possible, which of the two options do you choose?
 
This thought experiment, devised by theoretical physicist William Newcomb in 1960 and later dubbed “Newcomb’s Paradox”, can be regarded as one of the most enduring problems of decision theory, as it continues to be a source of mass dispute amongst the academic philosophy community (The Worlds of David Darling). That may not be so remarkable however, when considering the elusive nature of the problem. Quite apparently, the narrative of the paradox fails to describe with any explicitness its aspects that are most essential in the determination of a solution; namely the processes that drive the Beings prediction and your final choice, or the degree to which they are dependent on each other. Anyone attempting to solve the problem has the burden of first “filling in the blanks” as it were, based on their own perceptual intuitions, before deciding upon and employing their strategy. Thus, the disparities with regards to the problem do not arise merely from computational differences, but largely interpretational, and so it unsurprising that no consensus has been reached. In this essay, I shall attempt to provide a coherent account for the events contained in the problem and define their parameters in an artless fashion. In doing so, I believe the solution will become obvious. That is, in order to obtain the million dollars it is effectively necessary to take only the covered box.

Main Argument

It appears that the true essence of this problem lies within the relationship that exists between the Beings prediction and your choice, for is it the contours of this framework that govern how you can manoeuvre. For instance, if it is the case that the prediction causes your choice then it is better that you take only the covered box, though your decision is already determined. Conversely, if your choice somehow manifests the respective prediction via backwards causality, then to obtain the million dollars you then again must take only the covered box. Furthermore, suppose that there is no dependence between these events whatsoever, and that the Beings track record is simply the result of an extraordinary number of lucky guesses. In this case, you would of course be wise to take the both boxes in hopes of obtaining the extra $1000, as there is no reason for his streak to continue. None of these scenarios are appealing however, because not only do they border on inconceivable, they also render the problem utterly meaningless, leaving you the player totally confined to either option. Once we reject these premises however, a series of logical assumptions can be made that lead us to gain insight into the solution. Firstly, that prior to the Beings making of his prediction, he in some way can perceive who the next player is. This access to perception is crucial, as without it the Being would have no basis for estimating the future actions of each specific player. Secondly, that given his exceptional success rate, the Being must have some additional information and method which he can use in conjunction with said identity information to make an inference (and likely a highly warranted one at that!). At this point it seems quite reasonable to compare the Beings strategy to that of a meteorologist. Just as a meteorologist makes calculations based on current weather data and additional knowledge of natural laws to predict future conditions, the Being might perform a similar kind of forecast using knowledge of your earlier state of existence with other relevant natural laws that govern human behaviour. While I do not wish to reject all notions of free will, you the player are likely not as free as you may think you are in the moment of making your choice. For if one truly had the ability to arrive at decisions completely independent of prior causes, and then his predictions simply could not have been made with accuracy they displayed. Just as if blizzards could occur in mid-august regardless of context or natural laws then every meteorogists would be out of a job. This is not the case however, as experts in the field can generally foresee weather related events with functional accuracy. And when expected weather events do come to fruition, it is for many of the same reasons the prediction was made, i.e. specific prior conditions of the area subjected to natural laws over time. Similarly, you at the moment of your choosing are no doubt influenced significantly (if not entirely), by your earlier state and subsequent interactions resulting from natural laws, both of which must have been accounted for in the Beings estimation. Even if the Being is not consciously aware of his reasons, he must perceive these factors in some way. Thus, it can be said that the Beings prediction and your choice do not cause each other, but rather they share common causes, so much so that it is overwhelmingly likely that they correlate. While it is rarely stated in plain terms, it should be noted that the only way to formulate an effective hypothesis is to take into account the causal factors for the event. Evidently, the Being has mastered this practice.

Motivation/ Objections

Robert Nozick, his 1969 paper Newcomb’s Problem and Two Principles of Choice, provided the first published analysis of the paradox. In it, he relentlessly tackles the problem for some 21 pages before arriving at his conclusion “I believe one should take what is in both boxes” (Nozick 135). Since Nozick’s paper
is so quintessential, and he happens to hold a view opposing my own, I would like to expose some potential flaws in his theses.

Following his introduction, Nozick summarizes what he considers to be the most intuitive arguments for either choice. For the two box option, he contends that since the Being has already made its prediction, the contents of the covered box are already determined and not subject to change given your choice, so you are prudent to take the additional $1000 which is guaranteed (Nozick 115). While the extra cash is certainly alluring, what this theory fails to recognize is that the Being would almost certainly have predicted this, and thus you will likely receive no more than $1000. He then supposes a situation in which another person is sitting behind the covered box, and can see into it as its back side is transparent (p. 116.). While this person cannot express their advice to you, he states that in either case that the person would suggest taking both boxes (Nozick 116). Again, this completely flies in the face of the parameters set by the game. If this person could give their instruction in any way, surely the Being could account for this (as it is included in your decision), and thus it can be expected that he or she will be looking into an empty box.

Nozick then spends a large portion of his paper comparing Newcomb’s Paradox to other problems that involve weighing the dominance principle, where one chooses their action solely based on highest utility (both box solution), against the expected utility principle, where one chooses the action which has the highest expected utility given the probabilities of what state you are in (one box solution). Generally, he agrees that in cases where states are probabilistically dependent on actions, one should not apply the dominance principle (Nozick, 124). However, in what appears to be his most compelling argument, Nozick changes his mind. He envisions a scenario in which a man is faced with the decision of whether or not to pursue his ideal life in academia when it is known that if he has the gene that prompts academic inclination, then it is likely he also is predisposed to a terminal illness (Nozick 125). Here, while the states are clearly not independent, Nozick challenges using the expected utility principle, because the man’s having the predisposition or not is already determined and so avoiding academic pursuit will not prevent him from said terminal illness (Nozick 126). While I do not have an answer for this problem, I can say that it differs significantly from Newcombs’ Paradox as it does not involve the element of prediction. Once the man becomes aware of his predicament, his willingness to pursue academia is now polluted, which could not have been foreseen by the disease. The event of this man avoiding further education yet still dying prematurely seems much more probable then than you deciding to take only the covered box and it being empty.
 
Furthermore, Nozick contends the following: 
"Your deciding to do as you do is not part of the explanation of why he makes   the prediction he does, though your being in a certain state earlier, is part of the explanation of why he makes the prediction he does, and why you decide to do as you do.” (Nozick 134)

This, perhaps inadvertently, confirms the very argument I made previously. Yes, your choice and the beings prediction share common causes, so much so that they are likely to correlate. Of course, your decision itself is not part the Beings estimate, for it is the very event that he is trying to predict! Your prior state of existence however, combined with relevant external forces, does inform his prediction, as well as your choice. Apparently Nozick believes that with enough consideration, you may somehow break free of prior causality. This I believe is the very misstep in thinking that makes problems like Newcomb’s Paradox seem much more intriguing than they actually are if you are willing to forfeit privacy of your mind.

Conclusion:

Ultimately, it appears that Newcomb’s Paradox is particularly troublesome for many people as it requires one to accept the causality that influences their decisions. This persistent temptation to take both boxes is largely predicated on the belief that not even a hypothetical Being with seemingly infinite knowledge and ability could anticipate the actions arising from your conscious thoughts. While I am reluctant to say ones choice in this problem is entirely deterministic, it appears that within the context of this problem, your choice is significantly circumscribed by causal factors. And so, while the answer is simple and practically guarantees that you receive the million dollars, it is not quite so satisfying as this decision is largely out of your control.

Works Cited (MLA style)
 
“Newcomb’s paradox.” The Worlds of David Darling. n.p, n.d. Web. 20 Nov. 2013.

Nozick. R. Newcomb’s problem and two principles of choice:. Essays in honor of Carl G. Hempel: A Tribute on the Occasion of His Sixty-Fifth Birthday. Ed. Nicholas Rescher. New York; Springer; 1969. 115-146. Print