This Paradox Splits Smart People 50/50

Key Concepts

• Newcomb’s Paradox: A thought experiment in decision theory involving a super-intelligent predictor, highlighting the conflict between two rational decision-making frameworks.
• Evidential Decision Theory (EDT): The principle of choosing the action that provides the highest expected utility based on available evidence (correlation).
• Causal Decision Theory (CDT): The principle of choosing the action that one can actually cause to bring about the best outcome, ignoring correlations that cannot be influenced.
• Strategic Dominance: A strategy that yields a better outcome than any other strategy, regardless of the state of the world.
• Expected Utility (EU): A weighted average of all possible outcomes of a decision, calculated by multiplying the value of each outcome by its probability.
• Mutually Assured Destruction (MAD): A military doctrine where the threat of total annihilation prevents a first strike, provided the commitment to retaliate is credible.
• Game Theory: The study of strategic decision-making, including the Prisoner’s Dilemma and the game of Chicken.

1. The Setup of Newcomb’s Paradox

The problem involves a supercomputer (or "predictor") that has observed thousands of people and is nearly 100% accurate. You are presented with two boxes:

• Box A: Contains $1,000.
• Box B (Mystery Box): Contains either $0 or $1,000,000.
• The Rule: If the computer predicted you would take only the mystery box, it placed $1,000,000 inside. If it predicted you would take both, it placed $0 inside. The prediction was made before you entered the room.

2. The Two Camps of Thought

The paradox divides people into two distinct, equally confident groups:

The "One-Boxers" (Evidential Decision Theory)

• Argument: They focus on the high correlation between their choice and the reward. Since the computer is almost always right, choosing one box is the only way to "ensure" the million dollars is there.
• Evidence: A Guardian poll of 31,000 people showed a 53.5% preference for one-boxing. A Veritassium audience poll showed a two-thirds preference for one-boxing.
• Calculation: $EU = (\text{Probability of Prediction} \times \text{Reward})$. If the computer is better than random, the expected utility of one-boxing is higher.

The "Two-Boxers" (Causal Decision Theory)

• Argument: The money is already in the box (or not) before you arrive. Your current choice cannot change the past. Therefore, taking both boxes is a "dominant strategy."
• Calculation: Regardless of whether the box contains $0 or $1,000,000, taking both boxes always yields $1,000 more than taking just the mystery box.
• Key Quote: "Your decision-making does not affect... your little thought does not change God's mind." (Attributed to the host/participants).

3. Philosophical Implications

• Free Will: If a perfect predictor exists, it implies that our choices are predetermined, rendering free will an illusion. However, the host argues that society must operate as if free will exists to maintain moral and legal accountability.
• Rationality vs. Results: The "Why ain't you rich?" argument challenges two-boxers: if they are so rational, why do they end up with less money? Philosophers Gibbert and Harper suggest that in such rigged games, "irrationality is richly rewarded."
• Rational Acts vs. Rational People: A rational person might choose to be a "cooperator" (one-boxer) to achieve better long-term outcomes, even if a single "rational act" (two-boxing) seems superior in isolation.

4. Real-World Applications: Pre-commitment

The video links the paradox to scenarios where committing to a "worse" option is actually the most rational strategy:

• Nuclear Deterrence (MAD): A leader must convince an enemy they will retaliate (a catastrophic, irrational act) to prevent the attack from happening in the first place.
• The Game of Chicken: The best strategy is to visibly throw the steering wheel out the window, signaling to the opponent that you cannot swerve, forcing them to be the one to yield.
• Dr. Strangelove: The "Doomsday Device" is the ultimate example of pre-commitment—making a response automatic to remove the possibility of human hesitation.

5. Synthesis and Conclusion

The resolution to Newcomb’s Paradox lies in reframing the decision. Rather than viewing it as a one-time event, one should view it as a test of one's character or "programming." By deciding to be the kind of person who adheres to ideal pre-commitments (like one-boxing), you align your actions with the best possible outcome. As the host concludes, being rational isn't just about calculating the best move in the moment; it is about deciding what rules you are going to live by.