Newcomb's Paradox - Attempted Resolutions

Attempted Resolutions

Many argue that the paradox is primarily a matter of conflicting decision making models. Using the expected utility hypothesis will lead one to believe that one should expect the most utility (or money) from taking only box B. However if one uses the Dominance principle, one would expect to benefit most from taking both boxes.

More recent work has reformulated the problem as a noncooperative game in which players set the conditional distributions in a Bayes net. It is straightforward to prove that the two strategies for which boxes to choose make mutually inconsistent assumptions for the underlying Bayes net. Depending on which Bayes net one assumes, one can derive either strategy as optimal. In this there is no paradox, only unclear language that hides the fact that one is making two inconsistent assumptions.

Some argue that Newcomb's Problem is a paradox because it leads logically to self-contradiction. Reverse causation is defined into the problem and therefore logically there can be no free will. However, free will is also defined in the problem; otherwise the chooser is not really making a choice.

Other philosophers have proposed many solutions to the problem, many eliminating its seemingly paradoxical nature:

Some suggest a rational person will choose both boxes, and an irrational person will choose just the one, therefore rational people fare better, since the Predictor cannot actually exist. Others have suggested that an irrational person will do better than a rational person and interpret this paradox as showing how people can be punished for making rational decisions.

Others have suggested that in a world with perfect predictors (or time machines because a time machine could be the mechanism for making the prediction) causation can go backwards. If a person truly knows the future, and that knowledge affects their actions, then events in the future will be causing effects in the past. Chooser's choice will have already caused Predictor's action. Some have concluded that if time machines or perfect predictors can exist, then there can be no free will and Chooser will do whatever they're fated to do. Others conclude that the paradox shows that it is impossible to ever know the future. Taken together, the paradox is a restatement of the old contention that free will and determinism are incompatible, since determinism enables the existence of perfect predictors. Some philosophers argue this paradox is equivalent to the grandfather paradox. Put another way, the paradox presupposes a perfect predictor, implying the "chooser" is not free to choose, yet simultaneously presumes a choice can be debated and decided. This suggests to some that the paradox is an artifact of these contradictory assumptions. Nozick's exposition specifically excludes backward causation (such as time travel) and requires only that the predictions be of high accuracy, not that they are absolutely certain to be correct. So the considerations just discussed are irrelevant to the paradox as seen by Nozick, which focuses on two principles of choice, one probabilistic and the other causal - assuming backward causation removes any conflict between these two principles.

Newcomb's paradox can also be related to the question of machine consciousness, specifically if a perfect simulation of a person's brain will generate the consciousness of that person. Suppose we take the Predictor to be a machine that arrives at its prediction by simulating the brain of the Chooser when confronted with the problem of which box to choose. If that simulation generates the consciousness of the Chooser, then the Chooser cannot tell whether they are standing in front of the boxes in the real world or in the virtual world generated by the simulation in the past. The "virtual" Chooser would thus tell the Predictor which choice the "real" Chooser is going to make.