Abstract
This article is a companion to Counterfactual Reasoning, Qualitative (Philosophical Aspects). We begin with a brief introduction to counterfactuals, including a historical overview and the semantics for them proposed in classic works by Stalnaker and by Lewis. We discuss the interaction of probabilities and conditionals, sketching some of the so-called ‘triviality results’ against equating probabilities of conditionals with conditional probabilities. More positively, we note a connection between counterfactual reasoning and the rule for belief revision known as imaging. Counterfactual reasoning is essential to rational deliberation, and we discuss its place within quantitative frameworks for decision theory and game theory. Special attention is given to Newcomb's problem and the rival versions of decision theory (evidential and causal), to the importance of counterfactual reasoning to game theoretic solution concepts such as subgame perfect and perfect equilibrium, and to various models for strategic reasoning under probability zero suppositions.
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