A Definition and Graphical Representation for Causality
This work addresses foundational issues in causality for researchers in AI and statistics, offering a novel theoretical framework that could impact decision-making and causal inference, though it appears incremental relative to existing theories like Pearl's.
The authors tackled the problem of defining causality by introducing a precise definition based on unresponsiveness and Savage's decision theory, which allows causal assertions relative to decisions and enables local reasoning without requiring full causal explanations. They also showed that influence diagrams in canonical form accurately represent causal relationships and established a correspondence with Pearl's causal theory.
We present a precise definition of cause and effect in terms of a fundamental notion called unresponsiveness. Our definition is based on Savage's (1954) formulation of decision theory and departs from the traditional view of causation in that our causal assertions are made relative to a set of decisions. An important consequence of this departure is that we can reason about cause locally, not requiring a causal explanation for every dependency. Such local reasoning can be beneficial because it may not be necessary to determine whether a particular dependency is causal to make a decision. Also in this paper, we examine the graphical encoding of causal relationships. We show that influence diagrams in canonical form are an accurate and efficient representation of causal relationships. In addition, we establish a correspondence between canonical form and Pearl's causal theory.