Anthropic reasoning and correlated decision making

Using these number, it appears that your expected gain is [p2 + 4(1-p)p + p(p+4(1-p))]/(2-p)

Do you mean "1+p" instead of "2-p" at the end there? If not, where does "2-p" come from?

Since there are N=2 individuals, the CDP thus cancels both the 2 and the (1+p) factors

Why do you say that (N=2), since the number of individuals is actually random? If you EXIT at X, then the individual at Y doesn't exist, right?

Do you think CDP can be formalized sufficiently so that it can be applied mechanically after transforming a decision problem into some formal representation (like a decision tree, or world program as in UDT1)? The way it is stated now, it seems too ambiguous to say what is the solution to a given problem under CDP.

I was recently reading Outlawing Anthropics and I thought of a very similar technique (that one random person would be given a button that would change what everyone did). I think that it is a shame that this post didn't receive much attention given that it seems to resolve these problems rather effectively.

There probably could have been a bit more that justifies this argument, apart from the fact that it works. I think a reasonable argument to note that we can either hold the group's choices as fixed and ask about whether an individual would want to change their choice given these fixed choices, or give an individual the ability to change everyone's choice/be a dictator and ask whether they'd want to change their choices then. The problem in outlawing anthropics is that it mixes and matches - it gives the decision to multiple individuals, but tries to calculate the individual benefit from a decision as though they were solely responsible for the choice and so it double-counts.

There seems to be some confusion on how to deal with correlated decision making - such as with absent-minded drivers and multiple copies of yourself; any situation in which many agents will allreach the same decision.

I found this description misleading. It immediately brought to mind examples of games where a correlation of another agent's decision to my own provides me with the opportunity to exploit them.

Sleeping Beauty link is misformed.

I didn't check your application of CDP to the problems, but I think you erred at the beginning:

If you are part of a group of N individuals whose decision is perfectly correlated, then you should reason as if you had a 1/N chance of being the dictator of the group (in which case your decision is applied to all) and a (N-1)/N chance of being a dictatee (in which case your decision is ignored).

If your decisions are perfectly correlated (I assume that means they're all the same), then you are deciding for the group, because you make the same decision as everyone else. So you should treat it as a 100% chance of being the dictator of the group.

If you apply this dictator filter any situation S, then in "S + dictator filter", you should reason as in the CDP. If you apply it to perfectly correlated decision making, however, then the dictator filter changes nothing at all to anyone's decision - hence we should treat "perfectly correlated" as isomorphic to "perfectly correlated + dictator filter", which establishes the CDP.

Wouldn't it also mean that we should treat "perfectly correlated" as isomorphic to "uncorrelated + dictator filter", since you always believe your vote determined the outcome?

(Again, I don't know how this affects your application of it.)

By the way, how would your application of CDP/SIA to the Absent-minded Driver problem take into account additional evidence fed to you about what intersection you're at? (Say, someone shows you something that amplifies the odds of being at X by a factor of [aka has a Bayes factor/likelihood ratio of] L.)