With much help from crazy88, I'm still developing my Decision Theory FAQ. Here's the current section on Decision Theory and "Winning". I feel pretty uncertain about it, so I'm posting it here for feedback. (In the FAQ, CDT and EDT and TDT and Newcomblike problems have already been explained.)

One of the primary motivations for developing TDT is a sense that both CDT and EDT fail to reason in a desirable manner in some decision scenarios. However, despite acknowledging that CDT agents end up worse off in Newcomb's Problem, many (and perhaps the majority of) decision theorists are proponents of CDT. On the face of it, this may seem to suggest that these decision theorists aren't interested in developing a decision algorithm that "wins" but rather have some other aim in mind. If so then this might lead us to question the value of developing one-boxing decision algorithms.

However, the claim that most decision theorists don’t care about finding an algorithm that “wins” mischaracterizes their position. After all, proponents of CDT tend to take the challenge posed by the fact that CDT agents “lose” in Newcomb's problem seriously (in the philosophical literature, it's often referred to as the Why ain'cha rich? problem). A common reaction to this challenge is neatly summarized in Joyce (1999, p. 153-154 ) as a response to a hypothetical question about why, if two-boxing is rational, the CDT agent does not end up as rich as an agent that one-boxes:

Rachel has a perfectly good answer to the "Why ain't you rich?" question. "I am not rich," she will say, "because I am not the kind of person [Omega] thinks will refuse the money. I'm just not like you, Irene [the one-boxer]. Given that I know that I am the type who takes the money, and given that [Omega] knows that I am this type, it was reasonable of me to think that the $1,000,000 was not in [the box]. The $1,000 was the most I was going to get no matter what I did. So the only reasonable thing for me to do was to take it."

Irene may want to press the point here by asking, "But don't you wish you were like me, Rachel?"... Rachael can and should admit that she does wish she were more like Irene... At this point, Irene will exclaim, "You've admitted it! It wasn't so smart to take the money after all." Unfortunately for Irene, her conclusion does not follow from Rachel's premise. Rachel will patiently explain that wishing to be a [one-boxer] in a Newcomb problem is not inconsistent with thinking that one should take the $1,000 whatever type one is. When Rachel wishes she was Irene's type she is wishing for Irene's options, not sanctioning her choice... While a person who knows she will face (has faced) a Newcomb problem might wish that she were (had been) the type that [Omega] labels a [one-boxer], this wish does not provide a reason for being a [one-boxer]. It might provide a reason to try (before [the boxes are filled]) to change her type if she thinks this might affect [Omega's] prediction, but it gives her no reason for doing anything other than taking the money once she comes to believes that she will be unable to influence what [Omega] does.

In other words, this response distinguishes between the winning decision and the winning type of agent and claims that two-boxing is the winning decision in Newcomb’s problem (even if one-boxers are the winning type of agent). Consequently, insofar as decision theory is about determining which decision is rational, on this account CDT reasons correctly in Newcomb’s problem.

For those that find this response perplexing, an analogy could be drawn to the chewing gum problem. In this scenario, there is near unanimous agreement that the rational decision is to chew gum. However, statistically, non-chewers will be better off than chewers. As such, the non-chewer could ask, “if you’re so smart, why aren’t you healthy?”. In this case, the above response seems particularly appropriate. The chewers are less healthy not because of their decision but rather because they’re more likely to have an undesirable gene. Having good genes doesn’t make the non-chewer more rational but simply more lucky. The proponent of CDT simply extends this response to Newcomb’s problem.

One final point about this response is worth nothing. A proponent of CDT can accept the above argument but still acknowledge that, if given the choice before the boxes are filled, they would be rational to choose to modify themselves to be a one-boxing type of agent (as Joyce acknowledged in the above passage and as argued for in Burgess, 2004). To the proponent of CDT, this is unproblematic: if we are sometimes rewarded not for the rationality of our decisions in the moment but for the type of agent we were at some past moment then it should be unsurprising that changing to a different type of agent might be beneficial.

The response to this defense of two-boxing in Newcomb’s problem has been divided. Many find it compelling but others, like Ahmed and Price (2012) think it does not adequately address to the challenge:

It is no use the causalist's whining that foreseeably, Newcomb problems do in fact reward irrationality, or rather CDT-irrationality. The point of the argument is that if everyone knows that the CDT-irrational strategy will in fact do better on average than the CDT-rational strategy, then it's rational to play the CDT-irrational strategy.

Given this, there seem to be two positions one could take on these issues. If the response given by the proponent of CDT is compelling, then we should be attempting to develop a decision theory that two-boxes on Newcomb’s problem. Perhaps the best theory for this role is CDT but perhaps it is instead BT, which many people think reasons better in the psychopath button scenario. On the other hand, if the response given by the proponents of CDT is not compelling, then we should be developing a theory that one-boxes in Newcomb’s problem. In this case, TDT, or something like it, seems like the most promising theory currently on offer.