A unified theory of counterfactual reasoning

A successful theory of causal reasoning should be able to account for inferences about counterfactual scenarios. Pearl (2000) has developed a formal account of causal reasoning that has been highly influential but that suffers from at least two limitations as an account of counterfactual reasoning: it does not distinguish between counterfactual observations and counterfactual interventions, and it does not accommodate backtracking counterfactuals. We present an extension of Pearl’s account that overcomes both limitations. Our model provides a unified treatment of counterfactual interventions and backtracking counterfactuals, and we show that it accounts for data collected by Sloman and Lagnado (2005) and Rips (2010). In addition to reasoning about actual states of affairs, humans find it natural to reason about what might have been. A doctor may ask “if Alice had not been treated with the experimental drug, would she have survived?” and a parent might tell a child that “if you had been paying attention, you wouldn’t have gotten hurt.” Researchers from several disciplines have developed formal models of counterfactual reasoning, and recent empirical studies have evaluated the psychological merits of some of these models (Rips, 2010; Dehghani, Iliev, & Kaufmann, 2012). This paper describes a new model of counterfactual reasoning and evaluates it using data sets from the psychological literature. The problems that we consider can be illustrated using a causal chain over three variables (Figure 1a). For example, suppose that A, B, and C are variables that indicate whether three transponders are active. Transponder A is active about half of the time, and whenever it is active it tends to activate B, which in turn tends to activate C. Suppose that we observe on a certain occasion that all three transponders are active. We can now ask counterfactual questions such as “if B had not been active, would C have been active?” The formal approach that we present is inspired by the work of Pearl (2000), who developed a model of counterfactual reasoning that we refer to as the modifiable structural model, or MSM for short. The MSM assumes that the causal system in question is a functional causal model, where exogenous variables are introduced if necessary so that the variables of primary interest are deterministic functions of their parents. For example, the system in Figure 1a may be represented more precisely by adding exogenous variables UA, UB and UC such that UA determines whether or not node A is active, and UB and UC capture factors such as atmospheric conditions that determine whether the links in the chain operate successfully. Suppose now that A, B and C are all observed to be active, and that we want to know whether C would be active if B were not active. The MSM addresses this question by using the observations in the actual world to update (d) (a) (b) (c)