UDT's behavior here is totally determined by its prior. The question is which prior is more reasonable. 'Closeness to Solomonoff induction' is a good proxy for reasonableness here.

I think a prior putting greater weight on Omega, given that one has seen Omega, is much more reasonable. Here's the reasoning. Let's say that the description complexity of both Omega and Nomega is 1000 bits. Before UDT has seen either of them, it assigns a likelihood of to worlds where either of them exist. So it might seem that it should weight them equally, even having seen Omega.

However, the question then becomes -- why is Nomega choosing to simulate the world containing Omega? Nomega could choose to simulate any world. In fact, a complete description of Nomega's behavior must include a specification of which world it is simulating. This means that, while it takes 1000 bits to specify Nomega, specifying that Nomega exists and is simulating the world containing Omega actually takes 2000 bits.^[1]

So UDT's full prior ends up looking like:

999/1000: Normal world
$2^{- 1000}$ : Omega exists
$2^{- 1000}$ : Nomega exists
$2^{- 2000}$ : Nomega exists and is simulating the world containing Omega

Thus, in a situation where UDT has seen Omega, it has influence over the Omega world and Nomega/Omega world, but no influence over the normal world and Nomega world. Since the Omega world has so much more weight than the Omega/Nomega world, UDT will effectively act as if it's in the Omega world.

You might object that Nomega is defined by its property of messing with Omega, so it will naturally simulate worlds with Omega. In that case, it's strictly more complex to specify than Omega, probably by several hundred bits due to the complexity of 'messing with' ↩︎