Newcomb's Paradox Explained: A Decision Theory Problem About Prediction and Choice

Veritasium

What is Newcomb’s Paradox? [0:00]

• Introduction to a problem that sparks debate among intelligent people, causing disagreements even within the Veritasium team. [0:00]
• The setup involves a participant, a supercomputer, and two boxes on a table:
  • An open box with $1,000. [0:31]
  • A mystery box that cannot be seen inside. [0:38]
• The supercomputer is highly accurate at predicting human choices, having been correct thousands of times in this exact problem. [0:43]
• Before the participant enters the room and knows about the problem, the supercomputer makes a prediction: [1:10]
  • If it predicts the participant will take only the mystery box, it places $1,000,000 in the mystery box. [1:25]
  • If it predicts the participant will take both boxes, it places $0 in the mystery box. [1:31]
• The supercomputer's only goal is to make a correct prediction; it is not trying to trick or deprive anyone. [1:44]
• The participant's choice is to take either both boxes or just the mystery box. [1:48]
• The nature of the predictor (computer, alien, demon, psychologist team) doesn't change the core problem; only its extreme accuracy matters. [1:53]
• Robert Nozick notes that while the optimal choice seems obvious to almost everyone, people divide almost evenly on the problem, with each side thinking the other is "being silly." [2:54]
  • A Guardian newspaper poll in 2016 showed 53.5% chose the mystery box only, and 46.5% chose both boxes. [3:15]

Pick 1 Box! (Evidential Decision Theory) [3:24]

• One camp, the "one-boxers," reason based on expected utility, which considers the probability of the computer's prediction being right (C) or wrong (1-C). [3:33]
• If the participant takes both boxes:
  • There's a C chance of getting $1,000 (if the computer predicted taking both boxes, thus putting $0 in the mystery box). [3:57]
  • There's a (1-C) chance of getting $1,001,000 (if the computer predicted taking only one box, thus putting $1,000,000 in the mystery box, plus the $1,000 open box). [4:01]
  • Expected Utility (Two Boxes) = $1,000 * C + $1,001,000 * (1-C) = $1,001,000 - $1,000,000 * C. [4:10]
• If the participant takes one box:
  • There's a C chance of getting $1,000,000 (if the computer predicted taking one box, thus putting $1,000,000 in the mystery box). [4:21]
  • There's a (1-C) chance of getting $0 (if the computer predicted taking both boxes, thus putting $0 in the mystery box). [4:24]
  • Expected Utility (One Box) = $1,000,000 * C + $0 * (1-C) = $1,000,000 * C. [4:31]
• If C (the probability of correct prediction) is greater than 50.05%, then the expected utility of taking one box is higher. [4:42]
• Since the supercomputer is known to be highly accurate (much better than 50.05%), one-boxers conclude that taking only the mystery box is the rational choice to maximize gain. [4:54]
• This reasoning is based on Evidential Decision Theory, which uses prior evidence to calculate probabilities. [8:00]

Pick Both! (Causal Decision Theory) [5:24]

• The "two-boxers" argue that the computer has already made its prediction and set up the boxes; therefore, the participant's current choice cannot change the past. [5:29]
• This leads to four possible outcomes after the boxes are set: [5:40]
  • If the mystery box has $0: Taking one box yields $0; taking both yields $1,000.
  • If the mystery box has $1,000,000: Taking one box yields $1,000,000; taking both yields $1,001,000.
• In either scenario, taking both boxes always results in $1,000 more than taking just one box. [6:01]
• This is known as the principle of Strategic Dominance, where one strategy always yields a better outcome regardless of the external state (what's in the box). [6:04]
• This reasoning is based on Causal Decision Theory, which only considers factors the decision-maker can causally influence. [9:08]
• Both theories derive valid answers from their underlying assumptions, leading to a true paradox. [11:27]

What does Newcomb’s Paradox say about free will? [11:27]

• If a perfect predictor exists (e.g., 100% accurate), then the concept of free will becomes problematic, as all choices are predetermined. [12:01]
• Derek Muller suggests that even if free will is an illusion, humans must still act as if it's real, otherwise society and moral responsibility collapse. [12:35]
• This implies that, whether free will exists or not, humans live in a world indistinguishable from one where it does, making the paradox reflect a fundamental tension in human understanding of choice and determinism. [12:44]

What does it mean to be rational? [13:25]

• The paradox challenges the definition of rationality. Is rationality about maximizing expected outcome based on past evidence (Evidential Decision Theory), or about maximizing outcomes based on direct causal influence (Causal Decision Theory)? [13:25]
• The "Why Ain't cha Rich?" argument: If one-boxers are so smart, why are they rich and two-boxers poor (in past simulations)? [13:54]
  • The reply is that no choice was given about the million; the riches were reserved for the irrational (those who didn't choose to one-box when predicted). [13:56]
• Gilbert and Harper argue that taking both boxes is rational, even if it leads to less money in simulations. [14:12]
• The video suggests three ways to resolve the paradox, effectively making the one-box choice rational:
  1. If choices can change the past: If the act of choosing one box retroactively causes the $1,000,000 to be in the box. [16:04]
  2. If there are multiple trials: Over repeated games, choosing one box repeatedly establishes a reputation that is rewarded. [16:20]
  3. If pre-commitment is possible: By committing to one-box before the prediction, the supercomputer would know this commitment and place the million dollars in the box. [16:34]

Mutually Assured Destruction (MAD) [16:49]

• The concept of pre-commitment is vital in real-world scenarios like Mutually Assured Destruction (MAD) during the Cold War. [16:49]
• In 1949, the Soviet Union tested its first nuclear weapon, leading to an arms race with the US. [16:57]
• By the mid-1960s, both the US and USSR had enough nuclear warheads to destroy each other multiple times. [17:10]
• Robert McNamara, US Secretary of Defense, advocated for "assured destruction" (later MAD), a strategy where the ability to inflict unacceptable damage on an aggressor would deter a first strike. [17:21]
• This required a commitment to retaliate, even if it meant mutual annihilation. [17:47]

Precommitment Is The Ultimate Strategy [20:02]

• The movie "Dr. Strangelove" satirizes this with the Doomsday Device, which automatically triggers a global catastrophe upon detecting a nuclear attack or tampering, ensuring no second thoughts or human error could prevent retaliation. [19:47]
• The device's purpose is to be so devastating and automatic that the enemy would never even consider launching an attack, making pre-commitment to a worse outcome beneficial. [20:11]
• In both Newcomb's Paradox and MAD, the best outcome stems from a pre-commitment to a seemingly "worse" or "irrational" option. [20:25]
• This commitment ensures the favorable scenario (million dollars, stable peace) is realized, by influencing the predictor's (or opponent's) initial action. [20:31]
• The video concludes that rationality in such situations might involve deciding on rules to live by and committing to them, even if a one-time "rational" act seems different. [20:47]