Newcomb’s Paradox – Can You Outsmart a Perfect Predictor?

 

Welcome back to the blog!
Today, we’re diving into one of the most mind-bending thought experiments in decision theory: Newcomb’s Paradox. This puzzle challenges how we think about free will, prediction, and rational choice. It has puzzled philosophers, economists, and mathematicians alike.

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The Setup

Imagine this scenario:

You are presented with two boxes:

• Box A: Transparent — you can see it contains $1,000.

• Box B: Opaque — you don’t know what’s inside, but it contains either $1 million or nothing.

You are given a choice:

• Take both boxes (Box A + Box B)

• Or take only Box B

Now, here’s the twist:
A superintelligent Predictor — who has never been wrong — has already predicted what you will choose:

• If the Predictor predicted you would take only Box B, they placed $1 million inside it.

• If the Predictor predicted you would take both boxes, they left Box B empty.

The decision is yours — but remember, the prediction has already been made.

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The Paradox

There are two competing lines of reasoning:

🧠 The One-Boxer's Argument (Trust the Predictor):

• The Predictor is highly accurate.

• If they predicted you’d take only Box B, you’ll walk away with $1 million.

• If you take both boxes, they likely predicted that — and Box B is empty.

• So, to maximize your gain, you should take only Box B.

🧠 The Two-Boxer's Argument (Dominance Principle):

• The prediction is already made — the money is already in Box B or not.

• No matter what, taking both boxes gives you $1,000 more than just Box B.

• So you should always take both boxes.

Both arguments sound rational, yet they lead to opposite decisions. That’s the paradox.

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What’s Really Going On?

Newcomb’s Paradox exposes a clash between two fundamental ideas in decision theory:

• Expected Utility Theory (choose based on the best expected outcome): favors one-boxing

• Causal Decision Theory (choose based on what your choice can cause): favors two-boxing

In simpler terms:
Should you act based on what your choice reveals about you, or what it actually causes?

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Why It Matters

Newcomb’s Paradox isn’t just a philosophical toy. It sparks debates in:

• Artificial intelligence: Can machines predict our behavior?

• Free will: Are our choices truly independent, or predictable?

• Game theory: How should rational agents behave when others can anticipate their decisions?

It even touches on questions about ethics and responsibility in a world where predictions might influence outcomes.

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Final Thoughts

So what would you do?
Would you trust the Predictor and go for Box B only — hoping for the million?
Or would you take both boxes — just in case?

Newcomb’s Paradox forces us to examine how we define rationality. Sometimes, being “rational” by one definition can seem totally “irrational” by another.

Let us know in the comments — are you a one-boxer or a two-boxer?