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AnnaSalamon comments on Decision theory: Why Pearl helps reduce “could” and “would”, but still leaves us with at least three alternatives - Less Wrong
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Comments (70)
Good question.
If we're surgically setting a decision node in a Bayes net to a given value (e.g., setting the "my action" node to "one-box"), we always imagine snipping any parents of that node, so that the node can just be arbitrarily set, and setting the node to a particular value does not affect our probability distribution on any siblings of that node.
So, we could add parents in the graphs if we want, but we'd basically be ignoring them in our decision procedure.
This means that in effect, an actions-CSA must (after conditionalizing on its information) view its action as uncorrelated with the state of any of the rest of the world, except for the children/effects of its action. (For example, it must view its action as uncorrelated with Omega's belief about its action.)
Similarly, an innards-CSA must (after conditionalizing on its information) view its innards as uncorrelated with everything that is not a physical effect of its innards, such as Clippy's innards.
Similarly, a timeless, aka algorithm-output, CSA must (after conditionalizing on its information)view its algorithm output as uncorrelated with everything that is not a child of the "its algorithm" node, such as perhaps (depending on its architecture) the output of similar algorithms.
Thanks, that makes sense. I was thinking that the diagrams represented all the nodes that the agents looked at, and that based on what nodes they saw they would pick one to surgically set. I didn't realize they represented the result of setting a node.
Follow-up stupid questions:
They have different graphs, but the one necessary difference is the node that they do surgery on.
Presumably you would remove the arrow from platonic algorithm to your action and add arrows from platonic algorithm to your innards and from your innards to your actions.