(Just as it's absolutely, utterly trivial from the definitions that CDT is correct for Sam Beckett and EDT is correct for the spectator.)
CDT is not correct in game-theoretic situations where other agents can know things about you, with the effect of its incorrectness gradual. See Ch. 7 of TDT paper:
Modeling agents as influenced to some greater or lesser degree by "the sort of decision you make, being the person that you are", realistically describes present-day human existence.
The error could be tiny, but it could even be present where no other agents are around. On a bet with finely tuned probabilities and utilities, you'll rule wrong if you use CDT.
It's not at all clear in what sense one can be correct about "hoping for a particular outcome". The problem statement to which EDT is supposed to be an answer seems to be nonsense.
Let me explain about Sam Beckett (which admittedly I should have done at the outset): In each episode of Quantum Leap, Sam's consciousness teleports ("leaps") into the brain of some random person, and Sam then has to Do Something Important (e.g. Stop Something Bad From Happening). No-one else expects or notices the leap.
CDT is not correct in game-theoretic situations where other agents can know things about you, with the effect of its incorrectness gradual.
Assuming for argument's sake that Sam's "leap" was not foreseen by "Omeg...
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?