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Newcomb's Paradox

The best way to Predict the Future is to Create it

Introduction

Newcomb's paradox is a thought experiment created by William Newcomb in 1969. Even 50 years of publishing of the paradox, there is no clear consensus about the solution. After I read this problem was stuck on it for quite a few hours. I read multiple articles and watched several videos to understand it. The Wikipedia article is good but very unintuitive. Please watch this video multiple times if necessary to understand the paradox.

The Paradox Statement

Imagine that in front of you are two boxes. The first box (Box A) has 1000$ and is visible to you. The second box (Box B) contains either 1,000,000$ or 0$ and you don't know which. The contents of Box B are determined before hand by an intelligent AI with a high degree of accuracy.

You have to now choose one of two options, either choose only Box B or choose both boxes. If the intelligent AI thinks that you are going to choose both boxes, then it leaves 0$ in box B. But if it decides that you will choose only Box B, then it will put 1,000,000$ in box B.

After the prediction by the AI, you make your choice. Do you choose only Box B or both Boxes?

Two Schools of Thought

Several surveys have been conducted asking people for whether they are one boxers or two boxers. The results of these surveys seem to be firmly divided without a clear majority. One of the two options instantly made sense to you depending on which school of though you are following.

One Boxers

Since the AI makes accurate predictions about the future, it makes sense to choose just Box B. If you do Baysean analysis and assume that AI can predict 90% accurately, then the expected outcome firmly favours picking just Box B.

Two Boxers

The school of thought is actually pretty simple. It doesn't matter what the AI chose, by picking both boxes, you will 1000$ more (than you would have if you picked just box B) whether the AI predicted correctly or not.

Resolution

After thinking about it for a long time and reading a few articles, I think I've come to a reasonable conclusion.

If Box A was loaded with just 1$ instead of a 1000$ and then the experiment was repeated, then I'm pretty sure that everyone will be a one boxer.

On the other hand if Box A was loaded with 1,000,000$ instead of 1000$ and then the experiment was repeated, then I'm sure that everyone will be a two boxer.

When the amount in between, different people switch from one boxers to two boxers at different amount depending on their loss aversion threshold.

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