Probabilistic generative models for counterfactual reasoning and blame attribution

Why blame Bob? Probabilistic generative models, counterfactual reasoning, and blame attribution John McCoy 1* (jmccoy@mit.edu), Tomer Ullman 1* (tomeru@mit.edu), Andreas Stuhlm uller (ast@mit.edu), Tobias Gerstenberg (t.gerstenberg@ucl.ac.uk) & Joshua Tenenbaum (jbt@mit.edu) 1 Department of Brain and Cognitive Sciences, MIT 2 Cognitive, Perceptual and Brain Sciences, University College London, UK *These authors contributed equally to the paper. Abstract We consider an approach to blame attribution based on coun- terfactual reasoning in probabilistic generative models. In this view, people intervene on each variable within their model and assign blame in proportion to how much a change to a variable would have improved the outcome. This approach raises two questions: First, what structure do people use to represent a given situation? Second, how do they choose what alternatives to consider when intervening on an event? We use a series of coin-tossing scenarios to compare empirical data to different models within the proposed framework. The results suggest that people sample their intervention values from a prior rather than deterministically switching the value of a variable. The results further suggest that people represent scenarios differ- ently when asked to reason about their own blame attributions, compared with the blame attributions they believe others will assign. Keywords: counterfactuals; blame attribution; probabilistic models; causal reasoning Introduction Alice and Bob play a coin-tossing game. If their coin tosses match, they win. Alice goes first and tosses heads, Bob goes second and tosses tails, and hence they lose. Who, if anyone, will be blamed? Counterfactually, what would have happened if Alice had tossed heads? One intuition is that how much someone will be blamed for an outcome is closely related to how strongly they affected the outcome (cf. Spellman, 1997). Through counterfactual thinking, people can reason how a change in the past would have affected the present and use such reasoning for cognitive tasks including social judg- ments, causal attribution, problem solving, and learning (see Roese, 1997; Byrne, 2002, for reviews). But how do peo- ple reason counterfactually? And what is the relationship be- tween counterfactual thinking and blame attribution? Psychological research on counterfactual reasoning has re- vealed factors that influence which events attract counterfac- tual thoughts, including unusual events (Kahneman & Miller, 1986), early events in a causal chain (Wells, Taylor, & Turtle, 1987), and late events in a temporal chain (Byrne, Segura, Culhane, Tasso, & Berrocal, 2000). There have also been formal accounts which aim to explain the empirical findings in terms of principled mental operations that do not depend on event features (Spellman, 1997; Byrne, 2002; Chockler & Halpern, 2004; Rips, 2010; Petrocelli, Percy, Sherman, & Tormala, 2011). Some of these formal models have been separately tested against empirical data (Sloman & Lagnado, 2005; Gerstenberg & Lagnado, 2010). Kahneman and Tversky (1982) suggest that people reason counterfactually by using a “simulation heuristic”, whereby they mentally alter events and run a simulation of how things would have gone otherwise given these changes. In this pa- per, we use a computational-level framework that formalizes the spirit of this suggestion: when attributing blame, people mentally alter each possible event in turn, consider the con- sequences for the outcome, and blame an event in proportion to how much the change would have improved the outcome. We model this computation of counterfactual conse- quences using interventions on causal models (Pearl, 2000). We explore what causal models people use to represent the games in our experiments and how they choose alternatives when intervening on a particular event. The plan for the paper is as follows. We first describe the formal framework this work is based on and the space of models we explore. We then report results of experiments in which we varied aspects of the coin-tossing game described above, and suggest a possible explanation for these results within our framework. We conclude by discussing implica- tions and limitations of this account, and possibilities for fu- ture research. Formal framework We assume that, when reasoning counterfactually, people rep- resent the situation they are reasoning about using a proba- bilistic generative framework. Probabilistic models have been used to explain many aspects of high-level cognition, includ- ing perception, prediction, decision making and social rea- soning (Tenenbaum, Kemp, Griffiths, & Goodman, 2011). In this paper, we use causal Bayes nets and the functional equa- tions they are derived from as the underlying probabilistic generative framework (Pearl, 2000). Other representations are possible—see, for example, Gerstenberg and Goodman (in prep) for an approach to counterfactual reasoning based on probabilistic programs. We model people’s reasoning about blame as follows. First, consider each event in the situation—represented by a variable in a causal Bayes net—and intervene on it, i.e., consider a counterfactual value for this event (‘do’ in Pearl, 2000). Each such intervention results in a distribution over