Newcomb's problem: why do two good arguments clash?

Newcomb's problem is a thought experiment in decision theory. A predictor with a very high success rate has already decided what is in a mystery box, and you must choose between taking that box alone or taking it together with a second box holding a small sum. It divides people because two respected principles of rational choice recommend opposite answers, and each looks obviously right to those who hold it. [1] [2]

The case for one-boxing rests on expected utility. Because the predictor is so accurate, people who take only the opaque box almost always end up with about a million dollars, while two-boxers typically get about $1,000. Arif Ahmed, a Cambridge philosopher, puts it this way: whatever you do, the predictor will have foreseen it, so taking the one box is the way to be rich. This reasoning is often tied to evidential decision theory. [1] [3] [4]

The case for two-boxing rests on strategic dominance. The contents were fixed before you chose, so whatever is in the opaque box, taking both boxes yields $1,000 more than taking one. This reasoning is associated with causal decision theory, which looks at what your choice can actually bring about. The two leading approaches to rational choice, evidentialism and causalism, are standardly taken to recommend one-boxing and two-boxing respectively. [1] [2] [4]

Nozick reported that nearly everyone found the answer obvious, yet people split almost evenly, each half thinking the other was being silly. Professional philosophers remain divided. In the 2014 survey by David Bourget and David Chalmers, of the roughly 55% who took a stand, about 40% were one-boxers and about 60% two-boxers. A 2020 survey found a modest plurality for two-boxing, 39.0% against 31.2%. So two-boxing is somewhat more common among specialists, but there is no consensus. [2] [1]

Critics of causal decision theory, such as Caspar Oesterheld and Vincent Conitzer, argue that it makes agents lose money in a range of scenarios. David Wolpert and Gregory Benford suggest the dispute arises because the problem leaves details unspecified, and different ways of filling them in produce two distinct games, each with a different best strategy. Some writers also dispute whether the case is truly a paradox. [1]

The reviewer Jack Spencer says the problem endures partly because it bears on other questions, including the nature of time and causation, fairness, freedom and agency, and how descriptive and normative decision theory relate. He also notes that realistic analogues might arise in monetary policy, elections and prisoner's dilemmas. [2]