Well obviously. But agents using different decision theories do not disagree about rewards within the class of problems we're talking about. So you can compare different decision theories using the idea of "reflective consistency," where an agent is reflectively consistent only if it doesn't think it could gain by changing itself. A CDT agent watching a TDT agent win a million dollars from Omega believes that if only it could change, it could win a million dollars too, so it is not reflectively consistent within the class of decision-determined problems.
Suppose Omega gave money exclusively to TDT agents. If this were the case, it would be good to precommit to being a TDT agent. This isn't because TDT is better; it's because the contest was unfair.
Maybe this is analagous to Newcomb's problem. Maybe not. The point is, it's not obvious whether or not it is.
I suppose what I'm trying to say is that it's not that CDT usually gives the optimal solution but has a few flaws. It's that CDT, EDT, and TDT agents have a different idea of what the "optimal solution" refers to. It's not that optimal is the one the *DT strategy would pick. It's that the strategy itself is to find the optimal solution, for some value of optimal.
I couldn't find any concise explanation of what the decision theories are. Here's mine:
A Causal Decision Theorist wins, given what's happened so far.
An Evidential Decision Theorist wins, given what they know.
A Timeless Decision Theorist wins a priori.
To explain what I mean, here are two interesting problems. In each of them, two of the decision theories give one choice, and the third gives the other.
In Newcomb's problem and you separate people into groups based on what happened before the experiment, i.e. whether or not Box A has money, CDT will be at least as successful in each group as any other strategy, and notably more successful than EDT and TDT. If you separate it into what's known, there's only one group, since everybody has the same information. EDT is at least as successful as any other strategy, and notably more successful than CDT. If you don't separate it at all, TDT will be at least as successful as any other strategy, and notably more successful than EDT.
In Parfit's hitchhiker, when it comes time to pay the driver, if you split into groups based on what happened before the experiment, i.e. whether or not one has been picked up, CDT will be at least as successful in each group as any other strategy, and notably more successful than TDT. If you split based on what's given, which is again whether or not one has been picked up, EDT will be at least as successful in each group as any other strategy, and notably more successful than TDT. If you don't separate at all, TDT will be at least as successful as any other strategy, and notably more successful than CDT and EDT.
There's one thing I'm not sure about. How does Updateless Decision Theory compare?