The question "which decision theory is superior?" has this flavor of "can my dad beat up your dad?"

CDT is what you use when you want to make decisions from observational data or RCTs (in medicine, and so on).

TDT is what you use when "for some reason" your decisions are linked to what counterfactual versions/copies of yourself decided. Standard CDT doesn't deal with this problem, because it lacks the language/notation to talk about these issues. I argue this is similar to how EDT doesn't handle confounding properly because it lacks the language to describe what confounding even means. (Although I know a few people who prefer a decision algorithm that is in all respects isomophic to CDT, but which they prefer to call EDT for I guess reasons having to do with the formal epistemology they adopted. To me, this is a powerful argument for not adopting a formal epistemology too quickly :) )

I think it's more fruitful to think about the zoo of decision theories out there in terms of what they handle and what they break on, rather than in terms of anointing some of them with the label "rational" and others with the label "irrational." These labels carry no information. There is probably no total ordering from "best to worst" (for example people claim EDT correctly one boxes on Newcomb, whereas CDT does not. This does not prevent EDT from being generally terrible on the kinds of problems CDT handles with ease due to a worked out theory of causal inference).

This is essentially what the TDT paper argues. It's been a while since I've read it, but at the time I remember being sufficiently convinced that it was strictly superior to both CDT and EDT in the class of problems that those theories work with, including problems that reflect real life.

I think people have slightly misunderstood what I was referring to with this:

• There exist no problems shown to be possible in real life for which CDT yields superior results.
• There exists at least one problem shown to be possible in real life for which TDT yields superior results.

My question was whether there is a conclusive, formal proof for this, not whether this is widely accepted on this site (I already realized TDT is popular). If someone thinks such a proof is given somewhere in an article (this one?) then please direct me to the point in the article where I can find that proof. I'm very suspicious about this though, since the wiki makes blatantly false claims, e.g. that TDT performs better in one-shot PD than CDT, while in fact it can only perform better if access to source coude is given. So the wiki article feels more like promotion than anything.

Also, I would be very interested to hear about what kind of reaction from the scientific community TDT has received. Like, very very interested.

"Shown to be possible in real life" excludes Omega, many-worlds, or anything of similar dubiousness.

Then no. In "normal" situations CDT does as well as anything else.