I agree that only the components that are relevant need to be modeled/simulated.
However, for the Newcomb decision - involving a lot of cognitive work and calls to your utility function - and taking into account the many interconnections between different components of our cognitive architecture, non-trivial parts of yourself would need to be modeled - unlike in your cannonball example, where mass and shape suffice.
For your hypothetical, if knowing you're human were enough to perfectly predict that particular decision, to ascertain that relationship an initial simulation of the relevant components must have occurred - how else would that belief of Omega's be justified? I do agree that such a possibility (just one simulation for all of mankind) would lower your belief of just being Omega's simulation, however since Omega predicts perfectly, if there are any human beings who do not follow that most general rule (e.g. human -> 1boxes), the number of simulations would rise again. The possible worlds in which just one simulation suffices should be quite strange, and shouldn't skew the expected number of needed simulations per human too much.
Let's take your cannonball example. Can you explain how predicting where a cannonball will land does not involve simulating the relevant components of the cannonball, and the situation it is in? With the simulation requiring higher fidelity the more accurate it has to be. For a perfect simulation, the involved components would need to be perfectly mimicked.
With the simulation requiring higher fidelity the more accurate it has to be. For a perfect simulation, the involved components would need to be perfectly mimicked.
This is false, unless you're also expecting perfect precision, whatever that means. Omega is looking for a binary answer, so probably doesn't need much precision at all. It's like asking if the cannonball will fall east or west of its starting position - you don't need to model much about it at all to predict its behavior perfectly.
how else would that belief of Omega's be justified
Nobod...
Just developing my second idea at the end of my last post. It seems to me that in the Newcomb problem and in the counterfactual mugging, the completely trustworthy Omega lies to a greater or lesser extent.
This is immediately obvious in scenarios where Omega simulates you in order to predict your reaction. In the Newcomb problem, the simulated you is told "I have already made my decision...", which is not true at that point, and in the counterfactual mugging, whenever the coin comes up heads, the simulated you is told "the coin came up tails". And the arguments only go through because these lies are accepted by the simulated you as being true.
If Omega doesn't simulate you, but uses other methods to gauge your reactions, he isn't lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Doesn't really change much to the arguments here, but it's a thought worth bearing in mind.