A paradox, a paradox!

If you want to read about my Thanksgiving, read the last entry. If you want to read a fun puzzle in decision theory, read this one.

This is a famous philosophical paradox I’ve been thinking about again. I’m just going to set out the question here — I’ll explain why it’s paradoxical in a seperate entry in the near future. I want to hear your answers, though; maybe they will demonstrate why the question is so interesting. I’ve often found, though, that most people think that they see an obvious answer when they first hear the question.

Here’s the story of Newcomb’s Paradox:

There is a person, “The Predictor”, who has an excellent understanding of human psychology. The Predictor presents you with a table, on which sit two boxes. One box is opaque, and you cannot see what is inside. The other box is transparent, and you can see a $1000 bill inside it. The Predictor offers you a choice: you may:

• (A) take the black box, including its contents, and leave the transparent box, or
• (B) take both boxes.

But before you choose the Predictor tells you: “I have observed you carefully, and consulted the best psychological theories, and I have already used my vast expertise to predict which choice you will make. I won’t tell you what my prediction was. But I will tell you this I set up the boxes according to the following rule: if I predict that you will take just the black box, (A), then I put a million dollars inside that box. And if I predict that you will take both boxes (B), then I put nothing inside the black box. Either way, as you can see, there is a thousand dollars in the transparent box.”

The Predictor is very good at predicting. In fact, you’ve observed him present ten other people with this exact choice, and every time, his prediction was correct.

The question is simple: you are faced with a choice between (A) and (B) — you can take the black box alone, or you can take both boxes. Which is the rational choice? What should you do?

Discussion will follow in a new entry (update: here). But I’m really serious about wanting to hear your answers in the meantime.