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Causality is typically treated an all-or-nothing concept; either A is a cause of B or it is not. We extend the definition of causality introduced by Halpern and Pearl [2004a] to take into account the degree of responsibility of A for B. For example, if someone wins an election 11-0, then each person who votes for him is less responsible for the victory than if he had won 6-5. We then define a notion of degree of blame, which takes into account an agent's epistemic state. Roughly speaking, the degree of blame of A for B is the expected degree of responsibility of A for B, taken over the epistemic state of an agent.