This is part of a sequence titled, "Introduction to decision theory"

The previous post is "An introduction to decision theory"

In the previous post I introduced evidential and causal decision theories. The principle question that needs resolving with regards to these is whether using these decision theories leads to making rational decisions. The next two posts will show that both causal and evidential decision theories fail to do so and will try to set the scene so that it’s clear why there’s so much focus given on Less Wrong to developing new decision theories.

Newcomb’s Problem

Newcomb’s Problem asks us to imagine the following situation:

Omega, an unquestionably honest, all knowing agent with perfect powers of prediction, appears, along with two boxes. Omega tells you that it has placed a certain sum of money into each of the boxes. It has already placed the money and will not now change the amount. You are then asked whether you want to take just the money that is in the left hand box or whether you want to take the money in both boxes.

However, here’s where it becomes complicated. Using its perfect powers of prediction, Omega predicted whether you would take just the left box (called “one boxing”) or whether you would take both boxes (called “two boxing”).Either way, Omega put $1000 in the right hand box but filled the left hand box as follows:

If he predicted you would take only the left hand box, he put $1 000 000 in the left hand box.

If he predicted you would take both boxes, he put $0 in the left hand box.

Should you take just the left hand box or should you take both boxes?

An answer to Newcomb’s Problem

One argument goes as follows: By the time you are asked to choose what to do, the money is already in the boxes. Whatever decision you make, it won’t change what’s in the boxes. So the boxes can be in one of two states:

Left box, $0. Right box, $1000.
Left box, $1 000 000. Right box, $1000.

Whichever state the boxes are in, you get more money if you take both boxes than if you take one. In game theoretic terms, the strategy of taking both boxes strictly dominates the strategy of taking only one box. You can never lose by choosing both boxes.

The only problem is, you do lose. If you take two

...