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No. 3274:
Newcomb's Paradox

by  Krešo Josić

Today, a paradox that puts into question free will. The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them. 

Ted Chiang, the author of the story that inspired the movie Arrival, often writes about time travel. In another story "The Merchant and the Alchemist's Gate" he imagines a door that takes people 20 years into the future, or 20 years into the past. The story revisits a classic paradox: Can a time-traveler from the future influence what we do? If yes, the future the traveler came from can be changed. If the time-traveler's own past is fixed, then so are our choices. But if our decisions and actions are fixed then do we have free will?

The theoretical physicist William Newcomb created a puzzle to test our thinking about such questions. Newcomb envisioned a being, say an alien, that can tell the future. The alien comes to Earth carrying two boxes - box A and box B - and places the two boxes in front of you. You can see that box B holds 1000 dollars. You can't see inside box A. The alien says: "You have two choices, you can open only box A, and take what is there, or you can open both boxes, and take what is in both. But know that I can tell the future: If I have foreseen that you will only choose box A, then I have placed a million dollars in it. If I have foreseen that you will open both boxes, then I have placed nothing in box A, and you will only get the 1000 dollars you see in box B." What will you do?

The table gives the payouts given the alien's prediction, and your actual choice.

The table gives the payouts given the alien's prediction, and your actual choice. 
  Photo Credit:Wikipedia.

You may be thinking that the answer is obvious. Most people do. However, people also don't seem to agree what that obvious answer is! Even professional philosophers have been at loggerheads over this puzzle. Some reason "The alien knows what I am going to do. Therefore, I should open only box A because knowing that I will choose to open only box A, the alien has placed a million dollars in it. If I were to open both boxes, the alien would have predicted my decision and would have left box A empty. I would then be left with only the 1000 dollars in box B". Others claim this is nonsense. They argue: "When the two boxes are placed in front of me box A either contains a million dollars, or it doesn't, and no one can change that. In either case I am better off choosing both boxes, since I will always end up with a 1000 dollars more if I open both, than if I just open box A!"

Newcomb's paradox seems contrived - not many of us have met all-knowing aliens. However, many people think they are good judges of character and claim they can predict what others will do. They are like the alien in the story: Suppose you meet such a person, and ask them to borrow 10 dollars which you will repay with interest. Now, will this good judge of character predict whether you will honor your promise, and give you the money only if you are trustworthy? Or are you free to choose whether to repay the money once you have it, making their predictions worthless.

We all constantly switch between the two sides in Newcomb's paradox: Like the alien, we forecast the future, and trust our predictions will be borne out. But at the same time, we want our choices to be free, and not preordained and predictable.

This is Krešo Josić at the University of Houston where we are interested in the way inventive minds work.

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The paradox was first published by Robert Nozick, although it was formulated by William Newcomb. A lot has been written about Newcomb's paradox: here is a clear explanation of the paradox, and here is a good video.

There are many variants of the paradox, including the more relatable Parfit's Hitchiker, and the more abstract meta-Newcomb paradox. A mathematical treatment that makes it a bit clearer what is going on can be found here.


This episode was first aired on June 14, 2022