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.
Given that you receive the letter, paying is indeed evidence for not having termites and winning $999,000. EDT is elegant, but still can't be correct in my view. I wish it were, and have attempted to "fix" it.
My take is this. Either you have the termite infestation, or you don't.
Say you do. Then
Say you don't. Then
Being a payer has the same result when you do have the termites, but is worse when you don't. So overall, it's worse. Being a payer or a non-payer only influences whether or not you get the letter, and this view is more coherent with the intuition that you can't possibly influence whether or not you have a termite infestation.