But there is one key property that distinguishes CDT from the decision theories we'll talk about later: in its modeling of the world, X only allows event A to affect the probability of event B if A happens before B. (This is what causal means in Causal Decision Theory.)

This leads to the assumption that X's decision is independent from the simultaneous decisions of the Ys- that is, X could decide one way or another and everyone else's decisions would stay the same.

That doesn't seem to follow.

It is scientifically conventional to have the past causing the future.

However, decisions made by identical twins (and other systems with shared inner workings) aren't independent. Not because of some kind of spooky backwards-in-time-causation, but because both decisions depend on the genetic makeup of the twins - which was jointly determined by the mother long ago.

So: this "independence" property doesn't seem to follow from the "past causality" property.

So: where is the idea that CDT involves "independent decisions" coming from?