So, was the money in there? Photograph: 5second/Getty Images/iStockphoto
The votes are in. They have been counted. It was close. Very close.
But before we get there, the question again:
Two closed boxes, A and B, are on a table in front of you. A contains £1,000. B contains either nothing or £1 million. You don’t know which. You have two options:
You keep the contents of the box/boxes you take, and your aim is to get the most money.
But here’s the thing. The test was set by a Super-Intelligent Being, who has already made a prediction about what you will do. If Her prediction was that you would take both boxes, She left B empty. If Her prediction was that you would take B only, She put a ₤1 million cheque in it.
Before making your decision, you do your due diligence, and discover that the Super-Intelligent Being has never made a bad prediction. She has correctly predicted things you and others have done, including in situations just like this one, never once getting it wrong. It’s a remarkable track-record. So, what do you choose? Both boxes or just box B?
The original post was viewed more than 200,000 times, with well over a thousand comments. We tallied 31,854 votes before we closed submissions. And the results are:
- I choose box B: 53.5 per cent
- I choose both boxes: 46.5 per cent
This is very close – an almost Brexit-like split down the middle of the voting public. And like Brexit, some families were deeply divided. Mine was anyway: I chose box B, while my wife chose both boxes. Arguing about it just entrenched our positions.
In the only other mass survey on Newcomb’s Problem, the results were similar: 55 per cent chose box B, and 45 per cent both boxes.
So many excellent comments were made on the original piece that I will not attempt to summarise them. I do, however, want to add some background. The question is named after William A Newcomb, an American physicist who thought it up when thinking about another famous problem, the prisoner’s dilemma. But it was only when the American philosopher Robert Nozick wrote about the puzzle in 1970 that it became well known.
In the original post, I asked two philosophers to argue each position. One-boxer Arif Ahmed of Cambridge University and two-boxer David Edmonds of Philosophy247.
Responding to his side’s victory, Dr Ahmed said that those who chose two boxes may criticise him as being irrational. “But if Newcomb’s problem is a choice between being rational and being rich then I’ll take the money every time, thank you.”
He added: “I was gratified and enlightened to read so many and such insightful comments. One common theme was that the problem was in some way silly or not worth any thought, because it involves determinism and so excludes free will. Setting aside the vexed question of whether or not determinism rules out free choice (or how randomness somehow supports it), the problem in no way presupposes determinism. After all, the predictor need not be infallible. As long as She is *likely* to be right, the same problem arises (and the same solution applies).
“Other inessential features of the problem also seemed to attract attention. The problem need not involve money – we could replace that with anything else that you value – and it needn’t involve genuine prediction – we could replace that with any appropriate correlation. That is why the problem has real versions in political science, in AI, in quantum theory and elsewhere.”
Meanwhile, Dr Edmonds said: “2016 will be remembered as the year in which democracy threw up some entirely unexpected results. First Brexit, then Trump, and, perhaps most surprising of all, Newcomb’s Box. This is such a teasing conundrum, that I’m not surprised it received such an overwhelming response. That I foresaw. But my crystal ball gazing let me down in one way. I had predicted that people would be more rational. Nonetheless, after discussions with my legal team, I have decided not to demand a recount.
“There were many great comments from readers. The comments and result will be of interest to experimental philosophers – philosophers who make use of empirical data to cast new light on philosophical questions – even though Guardian readers may not be entirely representative of the world as a whole. Still, it would be fascinating to be able to delve a bit deeper. For example, to what extent is there a correlation between selecting just Box B and a belief in God? How do views about free-will affect the choice people make? Were there significant gender, age, regional or class differences (this I doubt).
“One man tweeted me that the Brexit option would be to choose Box A alone. No comment.”
If you would like to find out more, you could try the original paper by Robert Nozick, Arif Ahmed’s book Evidence, Decision and Causality, in which he argues for the one box answer, James M Joyce’s The Foundations of Causal Decision Theory, in which he argues against the one box answer, or Robert Grafstein’s book Choice-Free Rationality, in which he discusses applications of the problem in political science.
Thanks again to everyone who took part.
Photograph: Guardian Faber
I’m the author of several books of popular mathematics, most recently Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles. Available from the Guardian Bookshop and other retailers.
You can check me out on Twitter, Facebook, Google+, my personal website or my Guardian puzzle blog, in which I set a puzzle every other Monday.