Ok, what about cases where there are multiple causal hypotheses that are observationally indistinguishable:
a → b → c
vs
a ← b ← c
Both models imply the same joint probability distribution p(a,b,c) with a single conditional independence (a independent of c given b) and cannot be told apart without experimentation. That is, you cannot call p(a,b,c) “factually wrong” because the correct causal model implies it. But the wrong causal model implies it too! To figure out which is which requires causal information. You can give it to EDT and it will work—but then it’s not EDT anymore.
I can give you a graph which implies the same independences as my HAART example but has a completely different causal structure, and the procedure you propose here:
will give the right answer in one case and the wrong answer in another.
The point is, EDT lacks a rich enough input language to avoid getting garbage inputs in lots of standard cases. Or, more precisely, EDT lacks a rich enough input languages to tell when input is garbage and when it isn’t. This is why EDT is a terrible decision theory.
Ok, what about cases where there are multiple causal hypotheses that are observationally indistinguishable:
a → b → c
vs
a ← b ← c
Both models imply the same joint probability distribution p(a,b,c) with a single conditional independence (a independent of c given b) and cannot be told apart without experimentation. That is, you cannot call p(a,b,c) “factually wrong” because the correct causal model implies it. But the wrong causal model implies it too! To figure out which is which requires causal information. You can give it to EDT and it will work—but then it’s not EDT anymore.
I can give you a graph which implies the same independences as my HAART example but has a completely different causal structure, and the procedure you propose here:
http://lesswrong.com/lw/hwq/evidential_decision_theory_selection_bias_and/9d6f
will give the right answer in one case and the wrong answer in another.
The point is, EDT lacks a rich enough input language to avoid getting garbage inputs in lots of standard cases. Or, more precisely, EDT lacks a rich enough input languages to tell when input is garbage and when it isn’t. This is why EDT is a terrible decision theory.