I have been thinking about this for a while, and will probably formalize it at some point, but would like to get some of your thoughts in case there is some obvious case/backgroun  I am missing.

In some more realistic formulations of dilemmas, agents that make decisions under Functional Decision Theory may have generally inferior outcomes to rational agents acting under alternative decision theories (in this case, I am just going to consider causal decision theory), which creates a seeming paradox that I am sure many readers will already expect (though this is not necessarily true logical paradoxes).

For this briefer post, I am going to assume people here are at least somewhat familiar with Yudkowsky and Soares' writings on the theories (note: he may well have covered this in some piece I have not read, I cannot claim to have read everything he has ever written).

Consider a modification of Parfit's Hitchhiker. The classic situation looks at it from the perspective of the hitchhiker making a binary decision to be honor a deal or not. Let's instead imagine a scenario of what one might call "Parfit's Decent Driver" that looks at how a driver and hitchhiker might interact under more realistic (but still extremely simplified) utility functions (represented as dollars for ease). My initial conception of the scenario runs as follows:

A rational agent (whether CDT or FDT won't change this part), Derek, is driving down an empty road. He sees Will, a person he knows well but has no particular ties to, on the side of the road, with nothing on him. Derek recognizes that Will will die of thirst if he does nothing. It would cost Derek $5 to pick up Will, but he has some utility to saving a life and expects some external signaling effects which he values at a total of $6. Derek values being truthful to an extreme degree: let's say he values being truthful to his word at $1,000,000 (this is just to simplify his maximal utility calculations, but it shouldn’t change the outcomes we care about).

Derek knows with a high degree of confidence (which we will assume is correct) Will values his own life at $1,000,000, Derek also knows Will values being honest and paying back commitments at $200. Derek knows Will won’t be able to pay him anything now, but knows when they arrive at a town Will would be able to pay an arbitrarily high amount.

Derek knows Will has no ability to negotiate or change his preferred method of decision making during their interaction. (edit: to be clear, per Firmament's point, we are also assuming that under this asymetry Will is only aware of his own expected value, and that as under Parfitt's Dilemma, he expects that if he were an agent that would lie and not pay Derek back, Derek would leave him to die).

Derek knows Will is also a rational agent that will make decisions based on evaluating the expected value he calculates. Derek also knows how Will evaluates expected value (we will imagine it under either casual decision theory or functional decision theory).

Derek decides he will pull over and offer to give Will a ride back, if and only if Will promises to give him $X when they return to town. How much should Derek ask Will to pay him? What is the value Derek should ask for if he knows Will makes decisions under FDT? What value should he ask for if he knows Will makes decisions under CDT?

Evidently, Derek wants to give Will a ride, his expected utility is positive for giving Will a ride and negative for leaving Will to die. The only question is what amount he should demand to maximize his utility. However, if Will does reject his offer, Derek’s value of truthfulness is such that he would rather leave Will to die (Derek does not want this to happen, so will not select a scenario where it may occur). Derek's offer, as such, is genuine. Under this scenario, Derek has an arbitrarily high confidence in his knowledge of how Will will act, so he will always pick a scenario where Will will truthfully agree to pay him back.

If Derek knows Will makes decisions under CDT, he tells Will “I will drive you to nearest town if and only if you agree to give me $199.99 when we arrive back to town.” Will agrees. When they get back to town, Will estimates the expected value of paying Derek back at $200-$199.99=$0.01 so he does so. Compared to if he hadn't met Will, Derek ends up $200.99 better off, and Will ends up $9,999,800.01 better off.

If Derek knows Will makes decisions under FDT, he tells Will “I will drive you to the nearest town if and only if you agree to give me $100,000,199.99 when we arrive back to town”. When they arrive back, Will estimates his expected value of paying Derek back at $1,000,200 - $100,000,199.99 = $0.01, so he does so. Compared to if he hadn't met Will, Derek ends up $100,000,200.99 better, Will ends up $0.01 better.

Now, let’s imagine making an earlier decision from Will's perspective. Will is evaluating the value of evaluating expected value under CDT or FDT, knowing this scenario will happen.

Under CDT he evaluates that deciding to be a CDT agent will make him better off by $9,999,800 so he decides to be a CDT agent.

Under FDT he evaluates that CDT agents will be better off by $9,999,800 so decides to be a CDT agent.

This is not per say a logical contradiction, but it seems rather counterintuitive that in some scenarios given the choice it would be rational to select an alternative model.

As an outsider, we also may say there are additional ways CDT seems to outperform FDT herein. First and most obviously, Will just does better. But it also creates better outcomes as a whole. For many of us outsiders, it seems unfair that Derek would price a service that costs him $5 at $1,000,199.99. Of course, the service (in both cases) is a net positive (if the service isn't performed, Will dies and neither party benefits from external positive externalities), but if Derek expects Will to be honest or dishonest under CDT, his pricing decisions seem to lead to a fairer distribution of the surplus value--Derek's recognition in the CDT scenario that Will is more willing to be dishonest actually leads him to be less able to leverage his asymmetric advantage over Will.