Why Do People Two-Box in Newcomb's Paradox?

In Newcomb's Paradox, "two-boxers" argue that the only rational choice is to take both Box A (the transparent box with $1,000) and Box B (the opaque box). Their argument is rooted in Causal Decision Theory (CDT) and the Dominance Principle. To a two-boxer, choosing only Box B is an irrational act of wishful thinking that confuses correlation with causation.

The Dominance Principle

The core of the two-boxer argument is the Dominance Principle, a fundamental rule of game theory. This principle states that if one strategy (Action Y) yields a better outcome than another strategy (Action Z) in every possible state of the world, then Action Y is the dominant, rational choice.

In Newcomb's Paradox, there are only two possible states of the world at the moment you make your choice:

1. State 1: Box B contains $1,000,000.
2. State 2: Box B is empty ($0).

Let's look at the payoffs for each state:

• If the world is in State 1 (Box B is full): Taking both boxes gives you $1,001,000. Taking only Box B gives you $1,000,000. Two-boxing wins by $1,000.
• If the world is in State 2 (Box B is empty): Taking both boxes gives you $1,000. Taking only Box B gives you $0. Two-boxing wins by $1,000.

No matter what the Predictor did yesterday, you are strictly better off by exactly $1,000 if you take both boxes. To choose only Box B is to voluntarily leave $1,000 on the table.

The Causal Impotence of the Present Choice

Two-boxers emphasize the timeline of the experiment. The Predictor made their prediction yesterday. The money was either placed in Box B yesterday, or it was not. The physical state of Box B is causally sealed.

Because backward causation is physically impossible, your physical act of reaching out to grab one box or two boxes cannot causally affect what is already inside Box B. If you choose to one-box, you cannot magically cause the $1,000,000 to appear if it isn't already there. If it is already there, it will remain there whether you take Box A or not.

The "Psychopath's Choice" and the Illusion of Control

Two-boxers argue that one-boxers are falling prey to an illusion of control. They compare one-boxing to a medical scenario: suppose a certain gene causes both a high likelihood of heart disease and a strong preference for drinking tea. Drinking tea does not *cause* heart disease; they merely share a genetic common cause. In this scenario, a person who stops drinking tea in order to avoid heart disease is acting irrationally.

Similarly, two-boxers argue that while one-boxing correlates with getting a million dollars, it does not cause it. A truly rational agent must act on the causal levers available to them, which means taking both boxes to maximize their immediate physical return.

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