Rational procrastination
Professor Procrastinate has to make an important phone call. The call is long overdue because Procrastinate has been playing Farmville all week. The problem is that Procrastinate values current pleasure higher than future pleasure. So when he applies his decision theory, he finds that it is better to play some more Farmville now and make the phone call later instead of making the call now: it doesn't matter much whether the call is delayed by a few more hours, and this way the immediate future will be much more pleasant.
Of course, the same is true later, in the afternoon. Since current pleasure is more important than past or future pleasure, making the call in the late afternoon is no longer the optimal course of action when that time has come. It would now be better to play some more Farmville, and make the phone call early tomorrow morning. It would have even been better to make the call earlier today: then he could now play Farmville without that feeling of guilt. But this doesn't mean that there was something wrong with his earlier calculation, according to which he should make the phone call in the afternoon: by his earlier preferences, this was the optimal course of action. It's just that his preferences have changed. At noon, he valued pleasure at noon much higher than pleasure at 4pm; now he values pleasure at 4pm much higher than pleasure at noon. If one's preferences change, the rational thing is surely to reconsider one's earlier plans. So Procrastinate decides to play some more Farmville rather than to stick with his original plan.
As the year comes to an end, Procrastinate feels increasingly miserable about all the work he hasn't done. He double-checks his utility calculations. Perhaps the mistake was that he has little control over what his future self will do. He has often decided that his future self would make the phone call, but it has never complied. So he shouldn't weigh the costs and benefits of long-term plans such as "play Farmville now and make the phone call in the afternoon". His genuine options, right now, are only "make the phone call" and "play Farmville". (There's also that dreaded book review, but let's not even think about that.)
Which of these is better depends on what his future self will do. Suppose his future self, in the afternoon, will be productive and make the phone call, unless it's already done. Then the best choice now is to play some more Farmville. This way, the phone call will be done soon and the present will be much more pleasant. However, it seems unlikely to Professor Procrastinate that his future self would make the phone call, seeing as he's been playing Farmville all year. Suppose then that his future self would not make the phone call -- neither today, nor tomorrow, nor at any other day until the year is over. Then the choice is between (1) an unpleasant few minutes in the immediate future followed by a pleasant rest of the year (if he makes the phone call now), and (2) a somewhat less pleasant rest of the year with the constant feeling of guilt about the call (if he doesn't make the call now). Although Procrastinate discounts his future pleasures, he doesn't completely ignore them, and (1) now appears slightly better than (2).
But as he picks up the phone, he realises that he's made another mistake. In his calculations, he assumed that his future self would be very unlikely to make the phone call. But if he is just about to make the phone call now, then his future self would surely do the same if he ended up in a similar situation. Which he would if Procrastinate now resolved to playing some more Farmville. So he might as well return to Farmville and let his future self make the phone call.
So Procrastinate puts down the phone and goes back to his computer. But now it looks like his original reasoning was valid after all: if he is going to play Farmville now, he has no reason to think that his future self will make the phone call. And then it would be better to make the phone call now.
Procrastinate is stumped. He has ran into an unstable decision problem. The more he is inclined to one course of action, the more the other option looks preferable.
Unstable decision problems can only arise in Causal Decision Theory. According to Evidential Decision Theory, the value of an outcome must be weighted not by the unconditional probability of the relevant state of affairs, but by the conditional probability of the state of affairs given the relevant course of action -- even if the state is causally independent of the present choice. What the professor should do then depends on whether the outcome of never making the phone call is better or worse than the outcome of making the phone call now even though his future self would also have made it. (The other two possible outcomes are weighted by very low conditional probabilities and can therefore be ignored.) In effect, the professor would be weighing up the costs and benefits of "always be productive" and "never be productive". Presumably the former would win. So Evidential Decision Theory would recommend making the phone call.
Causal Decision Theory says that this choise is illusory. Professor Procrastinate has little control over his future self -- otherwise he wouldn't have ended up where he is. The evidential impact of his present inclination is not irrelevant. It enters into the deliberation dynamics, as we saw above: the more Procrastinate is inclined towards making the phone call, the more probable it is that his future self would also make the phone call, so the better it is to not make the phone call. And the other way round. In an unstable decision problem, Causal Decision Theory gives no recommendation.
So Procrastinate goes back to Farmville.
The phone call is special because it only requires one quick act of the will. Consider the book review that Professor Procrastinate has also been putting off for much too long. Apart from looking at the acknowledgments, he hasn't even started reading the book, so doing the review would take him at least a couple of days.
As before, suppose Procrastinate starts his deliberation assuming that his future self will probably just play Farmville. On this assumption there is no point starting the book review, since it won't get finished anyway. It seems better to resign and go back to Farmville. This resolution supports the assumption that his future self won't work on the review, and thereby confirms the decision to play Farmville. On the other hand, if he starts with the assumption that his future self will probably work on the review, then it is best to play Farmville now and leave all the work to his future self. This resolution undermines the assumption that his future self will work on the review. The more he is inclined to play Farmville, the less Procrastinate should trust his future self to do work. But unlike in the case of the phone call, this doesn't revert the optimal choice. The optimal choice is always to play Farmville.
Evidential Decision Theory gives the same answer as above, suggesting that Procrastinate should start the review. We have a Newcomb problem. ("If you're so smart, why ain't ya productive?")
PS. In real life, Professor Procrastinate would have more options than just two. For example, he could make a bet with a colleague that he will make the phone call by 4pm. With suitable stakes, the best course of action at noon might then be to make the bet and return to Farmville. As 4pm comes closer, not making the phone call becomes more and more costly, until it becomes preferable to playing Farmville. It is well-known that many people need tricks like these to overcome procrastination. See for example this recent piece in the "New Yorker". In this respect, Causal Decision Theory seems at least descriptively more adequate than the Evidential Theory.