Should I take one box or two boxes in Newcomb's Paradox?

There are two main rationales: 'One Boxers' believe the predictor is accurate and opt for the mystery box to get $1 million, based on evidential decision theory. 'Two Boxers' believe the past is unchangeable and take both boxes to maximize potential gain, based on causal decision theory.

What is the difference between evidential and causal decision theory?

Evidential decision theory suggests acting based on evidence that correlates with outcomes, like trusting the predictor's accuracy. Causal decision theory suggests acting based only on choices that can directly cause an outcome, ignoring predictors.

Does Newcomb's Paradox relate to free will?

Yes, if a perfect predictor exists, it questions free will, as your choice seems predetermined. However, the video argues that even if free will is an illusion, we must act as though it exists for societal function.

What does it mean to be rational in the context of Newcomb's Paradox?

Rationality is debated. 'Two Boxers' act rationally by maximizing immediate gain, following causal decision theory. However, a 'rational society' might require one-boxing, demonstrating a conflict between individual and collective rationality.

How does Mutually Assured Destruction (MAD) relate to Newcomb's Paradox?

MAD, like Newcomb's Paradox, highlights the power of pre-commitment. Committing to retaliate, even if destructive, deters initial attack, similar to how committing to 'one box' can lead to a better outcome by influencing the predictor.

Is there a 'correct' answer to Newcomb's Paradox?

The video suggests there isn't a single 'right' answer, as both camps are based on valid assumptions about predictability and causality. The value lies in understanding the different decision-making frameworks.

The Obvious Problem That No One Can Agree On

Veritasium

Education4 min read26 min video

Mar 9, 2026|2,517,397 views|96,373|36,066

veritasium science physics Veritasium newcomb paradox free will newcomb philosophical puzzles newcomb's problem supercomputer maths philosophy

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Key Moments

TL;DR

Newcomb's Paradox: One box ($1M) or two ($1k + mystery box). Predictors are highly accurate, but your choice is already made.

Key Insights

Newcomb's Paradox presents a choice between a guaranteed $1,000 plus a potentially empty or million-dollar box, or just the mystery box.

The paradox highlights a fundamental disagreement on decision-making: evidential decision theory (trusting the predictor's accuracy) vs. causal decision theory (acting on what you can influence).

One-boxers prioritize the predictor's accuracy, believing the million dollars is already in the box based on its successful predictions.

Two-boxers focus on strategic dominance, arguing that their current choice cannot alter the past setup of the boxes, making taking both always more profitable.

The paradox touches on concepts of free will, rationality, and the nature of commitment, with no universally agreed-upon correct answer.

Real-world parallels exist in nuclear deterrence and game theory, where pre-commitment to a seemingly irrational action can lead to a better overall outcome.

THE SETUP: TWO BOXES, ONE AMBIGUOUS CHOICE

The core of Newcomb's Paradox involves a supercomputer that predicts human choices with extreme accuracy. The participant faces two boxes: one open with $1,000 and a mysterious, closed box. The predictor has either placed $1 million in the mystery box (if it predicted the participant would choose only the mystery box) or nothing (if it predicted the participant would choose both). The choice is between taking only the expected $1 million or taking both the $1,000 and whatever is in the mystery box, which could be nothing.

TWO CAMPS: THE DIVIDE ON RATIONAL DECISION-MAKING

This paradox creates a stark division among people, forcing them into two camps: 'one-boxers' and 'two-boxers.' While the choice seems trivial to each side, they strongly disagree on the obviousness of the solution. This fundamental disagreement stems from differing philosophical approaches to decision theory and how one factors in the predictor's accuracy against the immediate consequences of one's actions.

THE CASE FOR ONE-BOXING: EVIDENTIAL DECISION THEORY

One-boxers argue that the predictor's proven accuracy is paramount. They accept that the predictor has likely made the correct prediction before they even entered the room. Therefore, if they choose only the mystery box, it's because the predictor foresaw this and placed $1 million inside. This approach aligns with evidential decision theory, where the evidence of the predictor's success informs the expected utility of the choice, leading to the conclusion that taking one box offers the highest expected payout.

THE CASE FOR TWO-BOXING: CAUSAL DECISION THEORY

Two-boxers employ causal decision theory, asserting that their current choice cannot retroactively alter the past. The boxes are already set, meaning the money is either in the mystery box or it isn't, regardless of their immediate decision. From this perspective, taking both boxes is always the dominant strategy, as it guarantees an extra $1,000. If the mystery box is empty, they get $1,000; if it contains $1 million, they secure $1,001,000. Their decision is based on what they can directly influence now.

BROADER IMPLICATIONS: FREE WILL, RATIONALITY, AND COMMITMENT

Newcomb's Paradox extends beyond a simple financial choice, probing deeper questions. It challenges our understanding of free will: if a perfect predictor exists, does that negate free will? It also questions the definition of rationality, showing how a rational act might not always align with a rational person, or how rationality at an individual level can differ from societal rationality. The paradox also introduces the idea of pre-commitment, suggesting that the ability to commit to an action beforehand, even an apparently suboptimal one, can lead to a more desirable outcome.

REAL-WORLD ANALOGIES: DETERRENCE AND GAME THEORY

The principles behind Newcomb's Paradox are mirrored in real-world scenarios like nuclear deterrence and game theory. Mutually Assured Destruction (MAD) relies on a credible commitment to retaliate, even if launching a counter-attack results in self-destruction. Similarly, the game of chicken involves demonstrating an inability to swerve to force the opponent to yield. In these cases, a pre-commitment to a seemingly irrational or destructive action serves as a powerful deterrent, ultimately leading to a more stable or beneficial outcome.

THE POWER OF PRE-COMMITTMENT AND IDEAL RULES

The video suggests that a rational approach might involve deciding on overarching rules to live by, rather than making isolated decisions. If one could 'wire' themselves to adhere to certain principles, the optimal pre-commitment in Newcomb's Paradox would be to be the kind of person who chooses one box. This reframing emphasizes that consistent adherence to chosen principles, even when it seems disadvantageous in a single instance, can lead to better long-term outcomes, similar to how cooperation is beneficial in repeated games.

CORRELATION VERSUS CAUSATION: THE ULTIMATE QUESTION

Ultimately, Newcomb's Paradox hinges on the interpretation of the predictor's accuracy. Is it merely a strong correlation, or does it imply causation that should influence one's decision? The video posits that while there may not be one single 'correct' answer, the problem reveals much about how we process information, make decisions, and what we value. It encourages viewers to think critically about the assumptions underlying their choices and the nature of rationality itself.

Mentioned in This Episode

●Software & Apps

●Books

●Concepts

Newcomb's Paradox: Expected Outcomes

Data extracted from this episode

Choice	Mystery Box Content	Outcome (Box + Mystery Box)	Decision Theory
One Box	$0	$0	Causal Decision Theory
One Box	$1,000,000	$1,000,000	Causal Decision Theory
Two Boxes	$0	$1,000	Causal Decision Theory
Two Boxes	$1,000,000	$1,001,000	Causal Decision Theory
One Box	$1,000,000	$1,000,000	Evidential Decision Theory (assuming 100% accuracy)
Two Boxes	$0	$1,000	Evidential Decision Theory (assuming 100% accuracy)

Prisoner's Dilemma Payoffs

Data extracted from this episode

Player 1 / Player 2	Cooperate	Defect
Cooperate	3 coins each	Player 1: 5 coins, Player 2: 0 coins
Defect	Player 1: 0 coins, Player 2: 5 coins	1 coin each

Common Questions

Newcomb's Paradox is a thought experiment involving a supercomputer that predicts your choice between taking one or two boxes of money. If it predicts you'll take only one, it puts $1 million in it; otherwise, it puts nothing.