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

In Newcomb's Paradox, "one-boxers" argue that the only rational choice is to take only Box B (the opaque box). Their reasoning is grounded in Evidential Decision Theory (EDT) and the mathematical maximization of expected utility. To understand why this position is so compelling to many philosophers and mathematicians, we must look at the probability calculations and the pragmatic defense of the choice.

The Mathematical Argument: Expected Utility

Evidential decision-makers evaluate actions based on the evidence those actions provide about the state of the world. They calculate the "expected value" of each choice by multiplying the probability of each outcome by its payout. Let us assume the Predictor is 99% accurate:

• If you choose only Box B (One-Boxing): There is a 99% chance the Predictor predicted this and put $1,000,000 in Box B, and a 1% chance they got it wrong and left it empty.
  Expected Value = (0.99 * $1,000,000) + (0.01 * $0) = $990,000.
• If you choose both boxes (Two-Boxing): There is a 99% chance the Predictor predicted this and left Box B empty, leaving you with only the $1,000 in Box A. There is a 1% chance they predicted you would one-box, leaving Box B full.
  Expected Value = (0.99 * $1,000) + (0.01 * $1,001,000) = $990 + $10,010 = $11,000.

Comparing $990,000 to $11,000, the evidential decision is clear: one-boxing is vastly superior. To a one-boxer, ignoring these probabilities is a form of mathematical self-sabotage.

The "Why Aren't You Rich?" Argument

The most powerful intuitive defense of one-boxing is the pragmatic "Why Aren't You Rich?" objection, popularized by philosopher David Lewis (who was actually a two-boxer himself). One-boxers point out that if we run this experiment with 1,000 people, the one-boxers will almost all walk away as millionaires, while the two-boxers will almost all walk away with a mere $1,000.

If a theory of rationality (like two-boxing) consistently leads to its practitioners being poorer than those who follow a different strategy, one-boxers argue that the theory itself must be flawed. In their view, rationality should be measured by its real-world success, not by adherence to causal rules that produce inferior results.

Rejecting Causal Independence

Two-boxers argue that because the Predictor's choice is already in the past, your present choice cannot causally affect the boxes. One-boxers do not necessarily believe in backward causation (that their choice physically travels back in time to change the box). Instead, they argue that your choice and the Predictor's prediction are both determined by a common cause—your character, brain state, or decision-making disposition.

Because your choice is a reliable mirror of what the Predictor foresaw, you cannot treat the state of the boxes as independent of your choice. Acting as if they are independent, one-boxers argue, is a form of cognitive delusion.

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