This post gives two distinct (but related) “pieces of knowledge”.
A counterexample to the “counterfactual incentive algorithm” described in section 5.2 of The Incentives that Shape Behaviour. Moreover, this failure seems to generalize to any causal diagram where all paths from the decision node to the utility node contain a control incentive, and where the controlled variables have mutual information that forbid applying the counterfactual only to some.
A concrete failure mode for the task of ensuring that a causal diagram fits a concrete situation: arrows without node might implicitly hide variables on which there are control incentives, in which case their mutual information with the other variables with control incentives is crucial to removing the control incentives.
Notably, this post doesn’t seem to question the graphical criterion given in Theorem 7 of The Incentives that Shape Behaviour for control incentives.
What I’m really curious about is whether we can generally find paths without node from the decision node to the utility node. If that’s the case, then the counterfactual incentive algorithm probably still works in most cases. This is because I think that the counterexample given here dissolves if there is an additional path without node from the matchmaking policy to the priced payed—then we can take the counterfactual of R and K together, in a way that is probably consistent.
Whether such paths exists is a question about the task of judging a causal diagram against a concrete situation. I believe that this post provided a very valuable failure mode for exploring this question in more details, and I hope further work will build on it.
This is because I think that the counterexample given here dissolves if there is an additional path without node from the matchmaking policy to the priced payed
I think you are using some mental model where ‘paths with nodes’ vs. ‘paths without nodes’ produces a real-world difference in outcomes. This is the wrong model to use when analysing CIDs. A path in a diagram -->[node]--> can always be replaced by a single arrow --> to produce a model that makes equivalent predictions, and the opposite operation is also possible.
So the number of nodes on a path better read as a choice about levels of abstraction in the model, not as something that tells us anything about the real world. The comment I just posted with the alternative development of the game model may be useful for you here, it offers a more specific illustration of adding nodes.
This post gives two distinct (but related) “pieces of knowledge”.
A counterexample to the “counterfactual incentive algorithm” described in section 5.2 of The Incentives that Shape Behaviour. Moreover, this failure seems to generalize to any causal diagram where all paths from the decision node to the utility node contain a control incentive, and where the controlled variables have mutual information that forbid applying the counterfactual only to some.
A concrete failure mode for the task of ensuring that a causal diagram fits a concrete situation: arrows without node might implicitly hide variables on which there are control incentives, in which case their mutual information with the other variables with control incentives is crucial to removing the control incentives.
Notably, this post doesn’t seem to question the graphical criterion given in Theorem 7 of The Incentives that Shape Behaviour for control incentives.
What I’m really curious about is whether we can generally find paths without node from the decision node to the utility node. If that’s the case, then the counterfactual incentive algorithm probably still works in most cases. This is because I think that the counterexample given here dissolves if there is an additional path without node from the matchmaking policy to the priced payed—then we can take the counterfactual of R and K together, in a way that is probably consistent.
Whether such paths exists is a question about the task of judging a causal diagram against a concrete situation. I believe that this post provided a very valuable failure mode for exploring this question in more details, and I hope further work will build on it.
I think you are using some mental model where ‘paths with nodes’ vs. ‘paths without nodes’ produces a real-world difference in outcomes. This is the wrong model to use when analysing CIDs. A path in a diagram -->[node]--> can always be replaced by a single arrow --> to produce a model that makes equivalent predictions, and the opposite operation is also possible.
So the number of nodes on a path better read as a choice about levels of abstraction in the model, not as something that tells us anything about the real world. The comment I just posted with the alternative development of the game model may be useful for you here, it offers a more specific illustration of adding nodes.