TDT doesn't think you can change the past either. TDT behaves as if it decides the past, which it does.
Well, they'd say if you can't change it you can't decide it.
Anyway, my point is that it's not that they figure that if it's better when box A is full, and better when box A is empty, so it must be better under all the conditions. If it was that, they'd think that EDT and TDT give the same results, and would start using TDT when this error is pointed out.
The reason they do it is that they assume that the problem when box A is full, and when it's empty, are essentially two different problems. You don't know which you're in, but they have the same solution an...
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?