A CDTist when presented with Newcomb's paradox, would say that, given his situation, $1,000 is the best he could hope for. Sure he could do better if box A had a million dollars in it, but he could also do better if box B had a million dollars. It doesn't, so he can't. He can't make box A had a million dollars any more than he can make box B had a million dollars. He's not a time-traveler. If you put a TDTist in this scenario, he'd get nothing. If you put anyone in a different scenario
An EDTist, when presented with a non-ideal Parfit's Hitchhiker, when asked for the money, would say that he knows the guy picked him up. It's one thing to change the past when it's unknown. That's really the only way it's different from the future. But there is no way refusing at this point could possibly leave him stranded in the desert.
"Gets agents who use it maximal rewards" is a fairly obvious criterion to say, but there are some obvious unspoken assumptions. The difference between CDT, EDT, and TDT is what assumptions exist.
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.
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?