Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: What is causality to an evidential decision theorist?, published by paulfchristiano on April 17, 2022 on LessWrong.
(Subsumed by: Timeless Decision Theory, EDT=CDT)
People sometimes object to evidential decision theory by saying: “It seems like the distinction between correlation and causation is really important to making good decisions in practice. So how can a theory like EDT, with no role for causality, possibly be right?”
Long-time readers probably know my answer, but I want to articulate it in a little bit more detail. This is essentially identical to the treatment of causality in Eliezer Yudkowsky’s manuscript Timeless Decision Theory, but much shorter and probably less clear.
Causality and conditional independence
If a system is well-described by a causal diagram, then it satisfies a complex set of statistical relationships. For example:
In the causal graph A ⟶ B ⟶ C, the variables A and C are independent given B.
In the graph A ⟶ B ⟵C, the variables A and C are independent, but are dependent given B.
To an evidential decision theorist, these kinds of statistical relationships are the whole story about causality, or at least about its relevance to decisions. We could still ask why such relationships exist, but the answer wouldn’t matter to what we should do.
EDT = CDT
Now suppose that I’m making a decision X, trying to optimize Y.
And suppose further that there is a complicated causal diagram containing X and Y, such that my beliefs satisfy all of the statistical relationships implied by that causal diagram.
Note that this diagram will necessarily contain me and all of the computation that goes into my decision, and so it will be (much) too large for me to reason about explicitly.
Then I claim that an evidential decision theorist will endorse the recommendations of CDT (using that causal diagram):
EDT recommends maximizing the conditional expectation of Y, conditioned on all the inputs to X. Write Z for all of these inputs.
It might be challenging to condition on all of Z, given limits on our introspective ability, but we’d recommend doing it if possible. (At least for the rationalist’s interpretation EDT, which evaluates expected utility conditioned on a fact of the form “I decided X given inputs Z.”)
So if we can describe a heuristic that gives us the same answer as conditioning on all of Z, then an EDT agent will want to use it.
I’ll argue that CDT is such a heuristic.
In a causal diagram, there is an easy graphical condition (d-connectedness) to see whether (and how) X and Y are related given Z:
We need to have a path from X to Y that satisfies certain properties:
That path can start out moving upstream (i.e. against the causal arrows); it may switch from moving upstream to downstream at any time (including at the start); it must switch direction whenever it hits a node in Z; and it may only switch from moving downstream to upstream when it hits a node in Z.
If Z includes exactly the causal parents of X, then it’s easy to check that the only way for X and Y to be d-connected is by a direct downstream path from X to Y.
Under these conditions, it’s easy to see that intervening on X is the same as conditioning on X. (Indeed you could check this more directly from the definition of a causal intervention, which is structurally identical to conditioning in cases where we are already conditioning on all parents.)
Moreover, once the evidential decision-theorist’s problem is expressed this way, they can remove all of the causal nodes upstream of X, since they have no effect on the decision. This is particularly valuable because that contains all of the complexity of their own decision-making process (which they had no hope of modeling anyway).
So if the EDT agent can find a causal structure that reflects their (statistical) beliefs about the world, then they will ...