I was thinking about Wo’s discussion of time travel and Newcomb, and I realised something rather odd about Ted’s most recent discussion of time travel and counterfactuals, at least when it’s combined with my preferred version of decision theory.

Let’s say we have the following Newcomb situation. The demon always makes the correct prediction because after you choose, he travels back in time to either put the million in the box or not. In this kind of Newcomb problem, we really should be one-boxers. But if Lewis’s version of decision theory with counterfactuals everywhere is right, then Ted’s theory suggests that we still take two boxes, even in that situation.

For Lewis, the interesting questions the decision maker has to answer are:

• If I were to choose one box, how much would I get?
• If I were to choose two boxes, how much would I get?

Now Ted suggests that even in time travel cases, facts about what happens after the choice are (more or less) irrelevant to the truth of these counterfactuals. We should just run the laws forward from the facts at that time. But if I apply this algorithm, the answers to those questions are (a) either $0 or $1,000,000 and (b) $1000 more than the answer to (a). So I should choose two boxes.

This is madness! Something has gone wrong, the question is what?

The only options are Lewis’s analysis of decision making in terms of counterfactuals, or Sider’s analysis of counterfactuals in time travel scenarios. One of them has to go. You might not find this a pressing problem, but I think both of those analyses are rather attractive, so I think this is a real puzzle.