Newcomb's Paradox Part 2

And here's the paradox, in the words of the philosopher Robert Nozick: "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly." (Oh right, here's Part 1)

One half thinks as follows:

There's a 99.9% chance that Olivia made an accurate prediction. If I reach for both Box A and Box B, there is a 99.9% chance that there is nothing in Box B, and I'll end up with a measly $1000. Sure, there is a .1% she's wrong and I'll get 1,001,000 dollars - but those are terrible odds! If, instead, I only reach for Box B, there is a 99.9% chance that Olivia left a million bucks in it, which I'll end up with. There's a .1% chance she's wrong and I'll end up with nothing, but those are very low odds!

If you want to get all mathematical about it, the expected value of choosing Box A and B is:

(.999)(1000) + (.001)(1001000) = 999 + 100 = 1999

while the expected value of choosing just Box B is:

(.999)(1000000) + (.001)(0) = 999000.

Choosing just Box B wins! In game theory, we call this approach the expected utility hypothesis.


However, the other half of humanity, thinks differently:
Regardless of how Olivia acts, it is always better for me to choose both boxes. There are four possible outcomes, summarized in the following chart.

	Box B contains nothing	Box B contains $1,000,000
Choose Box B	$0	$1000000
Choose Box B and A	$1000	$1,000,1000

Notice that "Choose Box B and A" always produces a higher payout! If Box B contains nothing, then choosing both boxes gets you 1000 dollars instead of nothing; if Box B contains something, choosing both boxes again nets you an additional 1000 dollars. In game theory lingo, the "Choose Box B and A" strategy strictly dominates the "Choose Box B" strategy. Choosing both boxes wins!

In technical terms, we have a conflict between the Dominance Principle and the Expected Utility Hypothesis. In layman's terms, an ability to predict the future (even a non-perfect ability!) seriously screws with the way we think.

We're relatively comfortable with the idea that decisions today can affect events in the future; when future-seeing is allowed into the mix, we have to start pondering whether decisions today can affect events in the pass. We have to wonder: can my decision right now about which box to choose affect what Olivia - in the past - decided to put into Box B?