Anthropic Reasoning by CDT in Newcomb's Problem

Answer: It appears to be sufficient that the agent only knows that Omega is always correct. If this is the case, then a simulating-Omega and some-other-method-Omega are indistinguishable, so the agent can freely assume simulation.

This is false. If there is not a conscious simulation running, the agent will know he is not a simulation, and will two box.

Objection 2. The argument does not work for the problems where Omega is not always correct, but correct with, say, 90% probability.

As long as the probability is sufficiently high, and the agent is sufficiently uncertain of whether or not he is the simulation, it works fine.

Answer: The agent in the simulation has exactly the same experiences as the agent outside, so it is the same self, so it values the Omega-offered utilons the same.

If the agent is selfish, and his sense of identity is such that he doesn't consider the being he is a simulation of himself, the simulated self will not care about the non-simulated self.

I admit it does seem a bit weird to have a utility function that depends on something you have no way of knowing. It's not impossible, though.

Objection 3. In order for the CDT agent to one-box, it needs a special "non-self-centered" utility function, which when inside the simulation would value things outside.

To expand on this, it's not inconsistent to have an agent that only cares about how many delicious gummi bears xe personally gets to eat, and definitely not about how many gummi bears any other copy of xerself gets to eat.

Then, even given 50-50 anthropic uncertainty about whether xe is the real-world self or the simulated self, xe will two-box:

50% chance of being in a world where all choices are pointless (I'm presuming that Omega will stop the simulation once xe makes xer choice), since the only consequence is whether someone else's opaque box is full of gummi bears or not.

50% chance of being in the real world, in which case the opaque box contains X gummies (where X=0 or 1000000), so two-boxing earns 1000+X gummies while one-boxing only earns X.

So two-boxing is still worth 500 expected gummies overall, in the CDT formulation.

Of course, a variant on quantum suicide could still lead to one-boxing here, but there are consistent theories of anthropics that reject quantum suicide. Also, Omega could pick a different color for the opaque box in the real and simulated worlds (without the agent knowing which is which), so that the real future agent can't be the successor of the simulated one...

However, I hypothesise that whatever method Omega uses, if the CDT agent knows the method, it will one-box. It is only a "magical Omega" that throws CDT off.

I suspect that if you try to formalize the version of "CDT" that makes the above statement true, it will look suspiciously similar to our formulations of UDT.

Also, thanks for writing this up! I understand your argument, but I think it might be helpful to others if you wrote out the expected-utility calculation explicitly.

If you have just outsmarted the Omega and collected $1001000 - well, it was not the Omega, it was just an impostor or something.

You must always consider the possibility that this is not a real Omega. Be in the Newcomb case, in counterfactual mugging or anywhere else.