Problematic Problems for TDT
A key goal of Less Wrong's "advanced" decision theories (like TDT, UDT and ADT) is that they should out-perform standard decision theories (such as CDT) in contexts where another agent has access to the decider's code, or can otherwise predict the decider's behaviour. In particular, agents who run these theories will one-box on Newcomb's problem, and so generally make more money than agents which two-box. Slightly surprisingly, they may well continue to one-box even if the boxes are transparent, and even if the predictor Omega makes occasional errors (a problem due to Gary Drescher, which Eliezer has described as equivalent to "counterfactual mugging"). More generally, these agents behave like a CDT agent will wish it had pre-committed itself to behaving before being faced with the problem. However, I've recently thought of a class of Omega problems where TDT (and related theories) appears to under-perform compared to CDT. Importantly, these are problems which are "fair" - at least as fair as the original Newcomb problem - because the reward is a function of the agent's actual choices in the problem (namely which box or boxes get picked) and independent of the method that the agent uses to choose, or of its choices on any other problems. This contrasts with clearly "unfair" problems like the following: Discrimination: Omega presents the usual two boxes. Box A always contains $1000. Box B contains nothing if Omega detects that the agent is running TDT; otherwise it contains $1 million. So what are some fair "problematic problems"? Problem 1: Omega (who experience has shown is always truthful) presents the usual two boxes A and B and announces the following. "Before you entered the room, I ran a simulation of this problem as presented to an agent running TDT. I won't tell you what the agent decided, but I will tell you that if the agent two-boxed then I put nothing in Box B, whereas if the agent one-boxed then I put $1 million in Box B. Regardless of how the si
Thanks again for the useful response.
My initial argument was really a question “Is there any approach to anthropic reasoning that allows us to do basic scientific inference, but does not lead to Doomsday conclusions?” So far I’m skeptical.
The best response you’ve got is I think twofold.