Newcomb's Paradox | Surprising Paradoxes

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OMEGA

The Nearly-Perfect Predictor (99.9% accurate)

"I have already examined your decision-making patterns. Based on my prediction of what you will choose, I have either placed $1,000,000 or $0 in Box B. Now... choose."

Box A

$1,000

Transparent

Box B

❓

$0 or $1,000,000

Opaque

You chose...

📊 Simulation Stats

One-Box Avg

Two-Box Avg

One-Box Games

Two-Box Games

🎯 Predictor Accuracy

50% (coin flip) 99.9% 100% (perfect)

⚔️ The Two Arguments

🟣 One-Box Argument

One-boxers tend to get $1M. Two-boxers tend to get $1K. It's better to be rich. Take only Box B.

🟡 Two-Box Argument

The prediction is ALREADY MADE. Box B is already full or empty. My choice can't change the past. Take both boxes.

The Setup

Newcomb's Paradox, created by physicist William Newcomb in 1960 and popularized by philosopher Robert Nozick in 1969, is one of the most divisive problems in decision theory.

Before you are two boxes. Box A is transparent and contains $1,000. Box B is opaque and contains either $1,000,000 or nothing. A nearly-perfect predictor has already decided Box B's contents based on what you will choose.

The predictor's rules:
• If you'll take only Box B → Box B contains $1,000,000
• If you'll take both boxes → Box B contains $0

The prediction was made before you arrived. The contents of Box B are fixed. What do you choose?

Philosophers Are Genuinely Divided

45%

55%

Surveys of philosophers show roughly even splits!

🟣 One-Boxers

"Evidential Decision Theory"

Look at the evidence: one-boxers walk away with $1M. Two-boxers walk away with $1K. The predictor is nearly perfect. Who cares about causation? Be the type of person who one-boxes!

"I want to be rich, not causally consistent."

🟡 Two-Boxers

"Causal Decision Theory"

The prediction is done. Box B is either full or empty—and nothing I do NOW can change that. Taking both boxes strictly dominates: I get $1K more no matter what's in Box B!

"I refuse to leave free money on the table."

The Deep Puzzle

The paradox exposes a tension between two principles that usually agree:

• Dominance: If action A is better than B in every possible state, choose A. (Two-boxing dominates: +$1K in all scenarios)

• Expected Value: Choose the action with highest expected payoff. (One-boxing: ~$999,000 vs two-boxing: ~$1,001)

In Newcomb's Problem, these principles give opposite answers! The predictor creates a correlation between your choice and Box B's contents that makes the "dominated" strategy actually better in expectation.

What If You Could Change Your Mind?

Here's a mind-bender: What if you firmly decide to one-box, then at the last moment grab both boxes? The predictor already saw you as a one-boxer, so Box B has $1M. You walk away with $1,001,000!

But wait—if you're the type of person who would pull this trick, the predictor would have seen THAT too. The paradox runs deep into questions of free will, determinism, and the nature of prediction.