This would have been helpful to my 11-year-old self. As I had always been rather unnecessarily called precocious, I developed the pet hypothesis that my life was a simulation of someone whose life in history had been worth re-living: after all, the collection of all possible lives is pretty big, and mine seemed to be extraordinarily neat, so why not imagine some existential video game in which I am the player character?
Unfortunately, I think this also led me to subconsciously be a little lazier than I should have been, under the false assumption that I was going to make great things anyway. If I had realized that given I was a simulation of an original version of me, I would have to perform the exact same actions and have the exact same thoughts original me did, including those about being a simulation, I better buckle up and sweat it out!
Notice your argument does not imply the following: I am either a simulation or the original, and I am far more likely to be a simulation as there can only be one original but possibly many simulations, so I should weigh my actions far more towards the latter. This line of reasoning is wrong because all simulations of me would be identical experience copies, and so it is not the quantity that decides the weight, but the number of equivalence classes: original me, and simulated me. At this point, the weights again become 0.5, one recovers your argument, and finds I should never have had such silly thoughts in the first place (even if they were true!).
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: