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. Building on Nick Bostrom's division-of-responsibility principle mentioned in Outlawing Anthropics, I propose the following correlated decision principle:

CDP: 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).

What justification could there be to this principle? A simple thought experiment: imagine if you were one of N individuals who had to make a decision in secret. One of the decisions is opened at random, the others are discarded, and each person has his mind modified to believe that what was decided was in fact what they decided. This process is called a "dictator filter".

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.

Used alongside the SIA, this solves many puzzles on this blog, without needing advanced decision theory.