What do you mean by "simulated"? In Parfit's hitchhiker scenario, as I understand it, the driver isn't doing anything remotely like a full simulation of Alice; just understanding her thinking well enough to make a guess at whether he'll get paid later. In which case, why should anyone think they are equally likely to be Alice or SimAlice?
[EDITED to add:] For that matter, in Newcomb's problem it's not generally stated explicitly that simulation is involved. Maybe Omega is just really good at proving theorems about people's behaviour and can do it at a high enough level of abstraction that no simulation is needed. Or maybe Omega has a chronoscope and is just looking at the future, though it's not obvious that this case doesn't need treating differently.
So perhaps SCDT needs to be reformulated in terms of some principle to the effect that when someone or something might try to predict your actions you need to imagine yourself as being simulated. And I suspect that formalizing this ends up with it looking a lot like TDT.
Maybe Omega is just really good at proving theorems about people's behaviour and can do it at a high enough level of abstraction that no simulation is needed.
How is it not a simulation? How do you define simulation in a way that includes manipulating bits (running a program) but excludes manipulating strings according to a set of rules (proving theorems)?
Or maybe Omega has a chronoscope and is just looking at the future
This is basically isomorphic to simulation, only now Omega is included in it. How would such a device work? The opaque box is full/e...
Finding a good decision theory is hard. Previous attempts, such as Timeless Decision Theory, work, it seems, in providing a stable, effective decision theory, but are mathematically complicated. Simpler theories, like CDT or EDT, are much more intuitive, but have deep flaws. They fail at certain problems, and thus violate the maxim that rational agents should win. This makes them imperfect.
But it seems to me that there is a relatively simple fix one could make to them, in the style of TDT, to extend their power considerably. Here I will show an implementation of such an extension of CDT, that wins on the problems that classic CDT fails on. It quite possibly could turn out that this is not as powerful as TDT, but it is a significant step in that direction, starting only from the naivest of decision theories. It also could turn out that this is nothing more than a reformulation of TDT or a lesser version thereof. In that case, this still has some value as a simpler formulation, easier to understand. Because as it stands, TDT seems like a far cry from a trivial extension of the basic, intuitive decision theories, as this hopes to be.
We will start by remarking that when CDT (or EDT) tries to figure out the expected value or a action or outcome, the naive way which it does so drops crucial information, which is what TDT manages to preserve. As such, I will try to calculate a CDT with this information not dropped. This information is, for CDT, the fact that Omega has simulated you and figured out what you are going to do. Why does a CDT agent automatically assume that it is the "real" one, so to speak? This trivial tweak seems powerful. I will, for the purpose of this post, call this tweaked version of CDT "Simulationist Causal Decision Theory", or SCDT for short.
Let's run this tweaked version though Newcomb's problem. Let Alice be a SCDT agent. Before the problem begins, as is standard in Newcomb's problem, Omega looks at Alice and calculates what choice Alice will make in the game. Without to much loss of generality, we can assume that Omega directly simulates Alice, and runs the simulation through the a simulation of the game, in order make the determination of what choice Alice will make. In other formulations of Newcomb's problem, Omega figures in out some other way what Alice will do, say by doing a formal analysis of her source code, but that seems intuitively equivalent. This is a possible flaw, but if the different versions of Newcomb's problem are equivalent (as they seem to be) this point evaporates, and so we will put it aside for now, and continue.
We will call the simulated agent SimAlice. SimAlice does not know, of course, that she is being simulated, and is an exact copy of Alice in all respects. In particular, she also uses the same SCDT thought processes as Alice, and she has the same utility function as Alice.
So, Alice (or SimAlice, she doesn't know which one she is) is presented with the game. She reasons thusly: