Similarity of Causal Structure

• Humans have beliefs about the causal structure of the world and they are quite important in how we interact with the world. They can be refuted by experience.
• So we will look at: if we have some beliefs about the causal structure and we get inconsistent information, how should we revise them?

Natural answer: believe a causal structure G that: - is compatible with the new information, - as close as possible to the old beliefs -- but what does it mean to be "close"?

causal struture --> independences = evidential content. - The evidential difference between causal structures is the number of probabilistic independences that are defined by one of the CS but not by both.

conterfactual content = what are the effects of interventions --> is there a path from X -> Y in the graph? - Conterfactual difference = counterfactual dependencies that exist in one CS but not in both.

So when we see contradictory evidence, we update to the closest structure that's compatible with the new evidence. - Which closest: - Alphabetic (evidential diff, counterfactual diff) or the other way around - the best order depends on your use case.

Open problem: in which cases are the outcomes of two orders the same? - Sufficient conditions could be possible and easier. - Maybe we use weights for EC and CC.