I'm not sure what to think of this paper, it's quite long and I haven't finished checking it for sanity. nevertheless, I noticed it hadn't made its way here, and there are mighty few papers that cite the FDT paper, so I figured I'd drop it off rather than leave it sitting open in a tab forever.
Abstract:
Functional decision theory (FDT) is a fairly new mode of decision theory and a normative viewpoint on how an agent should maximize expected utility. The current standard in decision theory and computer science is causal decision theory (CDT), largely seen as superior to the main alternative evidential decision theory (EDT). These theories prescribe three distinct methods for maximizing utility. We explore how FDT differs from CDT and EDT, and what implications it has on the behavior of FDT agents and humans. It has been shown in previous research how FDT can outperform CDT and EDT. We additionally show FDT performing well on more classical game theory problems and argue for its extension to human problems to show that its potential for superiority is robust. We also make FDT more concrete by displaying it in an evolutionary environment, competing directly against other theories. All relevant code can be found here: https://github.com/noahtopper/FDT-in-an-Evolutionary-Environment.
In your problem description you said you receive the letter:
Given that you did receive the letter, that eliminates 2 of the 4 possible worlds, and we are left with only (infested, dont_pay) and (uninfested, pay). Then the choice is obvious. EDT is correct here.
Obviously if you don't receive the letter you have more options but then its not much of an interesting problem.
This intuition is actually false for perfect predictors. A perfect predictor could simulate your mind (along with everything else) perfectly, which is somewhat equivalent to time travel. Its not actual time travel of course; in these 'perfect prediction' scenarios your future (perfectly predicted) decisions have already effected your past.