Operationalizing FDT

Summary

This post is an attempt to better operationalize FDT (functional decision theory).  It answers the following questions: given a logical causal graph, how do we define the logical do-operator? what is logical causality and how might it be formalized? how does FDT interact with anthropic updating? why do we need logical causality?  why FDT and not EDT? Defining the logical do-operator Consider Parfit's hitchhiker: A logical causal graph for Parfit's hitchhiker, where blue nodes are logical facts An FDT agent is supposed to reason as follows: I am deciding the value of the node "Does my algorithm pay?" If I set that node to "yes", then omega will save me and I will get +1000 utility.  Also I will pay and lose 1 utility.  Total is +999. If I set that node to "no", then omega will not save me.  I will get 0 utility. Therefore I choose to pay. The bolded phrases are invoking logical counterfactuals.  Because I have drawn a "logical causal graph", I will call the operation which generates these counterfactuals a "logical do-operator" by analogy to the do-operator of CDT. In ordinary CDT, it is impossible to observe a variable that is downstream of your action, because such a variable is in your future.  Therefore, the following two definitions of the CDT do-operator are equivalent: Cut the incoming connections of the action node, and then condition on it having the value X. Cut the incoming connections of the action node and forget the values of all nodes downstream of it, then condition on the action node having the value X. For physical causality these are equivalent because the downstream nodes are in the future, so we can't have observed them and there is nothing to forget. However, in our logical causal graph, we can observe the node "I am in town" even though it is downstream of our action node ("Does my algorithm pay").  So for FDT these two definitions are not equivalent and we need to pick one. If we want to pay in Parfit's hitchhiker, we must choose definition 2.  This allows us to "forget" our observation that we are already in town. There's one more interesting choice we could consider for the logical do-operator -- we could have it forget future nodes but not cut incoming connections.  This would make it an EDT variant with "logicausal un-updating" rather than a logicausal version of CDT. We can see all of our options in the following 2x2 table:  Don't forget downstream nodesForget downstream nodes Cut incoming connectionsoption 1: cut incoming then conditionoption 2: cut incoming and forget downstream, then condition Don't cut incoming connectionsoption 3: just conditionoption 4: forget downstream then condition Option 3 is just EDT.  Options 1 and 3 are missing the "forget downstream nodes" step, so they don't pay in Parfit's hitchhiker without commitment-style updatelessness.   If we want FDT to "automatically" pay in Parfit's hitchhiker, we must choose between options 2 and 4.  I personally think it's unclear which of these to prefer.  The main disagreements are: Option 4 pays in logical XOR blackmail, while option 2 doesn't. Option 4 seems more likely to have ECL-like behavior. Where does this leave us?  So far we have deduced one property of the logical do-operator -- in order to pay in Parfit's hitchhiker without commitments, it must forget the values of downstream nodes.  But we have not yet answered the following questions: How do we construct the logical causal ("logicausal") graph in the first place?  What does it even mean? How do we forget the value of a logical fact without forgetting its causal relationship to other facts? The next section will try to answer these questions. Logical causality There is an intuition that some logical facts cause others, and that unlike "correlation" or "relatedness" this relationship is both directional and intuitively "causal".  I think this intuition is pointing to something real and can be defined using conditional independence (the same way that ordinary causal graphs are defined).[1] First, let me list a few examples to ground the discussion: In Newcomb's problem, the logical fact "My algorithm one-boxes" causes the fact "Omega puts a million dollars in box A", not the other way around. The logical fact " mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0; } mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; margin: 1em 0; } mjx-container[jax="CHTML"][display="true"][width="full"] { display: flex; } mjx-container[jax="CHTML"][display="true"] mjx-math { padding: 0; } mjx-container[jax="CHTML"][justify="left"] { text-align: left; } mjx-container[jax="CHTML"][justify="right"] { text-align: right; } mjx-ms