Back on track: Backtracking in counterfactual reasoning

Back on track: Backtracking in counterfactual reasoning Tobias Gerstenberg (t.gerstenberg@ucl.ac.uk), Christos Bechlivanidis (c.bechlivanidis@ucl.ac.uk), David A. Lagnado (d.lagnado@ucl.ac.uk) Cognitive, Perceptual and Brain Sciences, University College London, London WC1H 0AP B Abstract Would Dan have died if Bob hadn’t shot? In this paper, we show that people’s answer depends on whether or not they are asked about what would have caused Bob not to shoot. Some- thing needs to change in order to turn an actual world into a counterfactual world. Previous findings of how people reason about counterfactuals have been mixed: sometimes people ap- pear to backtrack and reevaluate the causes of a counterfactual state (e.g. Rips, 2010). At other times, people appear to treat counterfactuals like interventions that leave the past unchanged (Sloman & Lagnado, 2005). We experimentally manipulated the order in which participants were asked to consider the con- sequences of a counterfactual state. The results show that par- ticipants are more likely to backtrack when explicitly asked to consider a counterfactual’s causes. However, when directly asked about the effects of a counterfactual state, most people don’t backtrack. Keywords: counterfactuals; causality; inference; backtrack- ing. D A C (a) What actually happened B B D A C (b) Pearl’s (2000) prediction D A C (c) Hiddleston’s (2005) prediction Figure 1: If Bob had not shot, would Dan have survived? Introduction Counterfactual thoughts play an important part in our ev- eryday lives (see, e.g. Roese, 1997): if we had missed the submission deadline, you wouldn’t be reading this paper. If we hadn’t embarked on scientific careers, we would have become famous musicians. How do we evaluate the truth of such counterfactual statements? As life does not come with a rewind button, we can never know for sure. Hannes K¨urmann, the protagonist in Max Frisch’s play Biography: A Game, gets the unique chance to go back in time and play the game of life for a second time. However, despite full aware- ness of how his unhappy life will unfold and the firm belief that things could have turned out differently, K¨urmann cannot bring himself to undo his past (and consequently, his present and future). Max Frisch’s play paints a rather fatalistic picture and sug- gests that counterfactual thoughts about how our life could have turned out differently are likely to be false. If every- thing happened as it actually did up until the point of the con- sidered counterfactual, it has to turn out false. At some point, the counterfactual world has to diverge from the actual world in order to ensure the truth of the if-part (or antecedent) of a particular counterfactual statement. At least a change of mind would have been required to transform a scientist’s life into that of a rock star. Often there are a number of ways to realize the truth of a counterfactual’s antecedent and the way in which we do so can sometimes have quite dramatic consequences. Consider the following situation: Anne is the commander of a firing squad and blows a whistle to signal to Bob and Chuck that it’s time to shoot poor Dan (see Figure 1, cf. Pearl, 2000). Both Bob and Chuck shoot and Dan dies. Let us assume that the relevant causal relationships are deterministic: whenever Anne gives the signal, Bob and Chuck shoot and they never miss. Furthermore, each of Bob’s and Chuck’s shots are indi- vidually sufficient to bring about Dan’s death. What do you think: would Dan have survived if Bob had not shot? In this paper, we investigate how people evaluate counter- factual statements about simple devices that are structurally equivalent to the scenario just described. We first review the- oretical frameworks that yield competing predictions about whether certain counterfactuals are true and then summarize previous empirical work on how people reason counterfactu- ally. In a series of experiments, we test whether or not people spontaneously backtrack by manipulating the order in which participants are asked different counterfactual questions. We find that participants are more likely to backtrack when asked to explicitly consider the cause of the counterfactual’s an- tecedent and suggest that the effect of question order can be explained in terms of a local processing strategy. Theories of counterfactual conditionals Let us illustrate the differences between theories of counter- factuals via the example of the counterfactual conditional “If Bob had not shot then Dan would have survived”. According to Lewis’s (1979) account, the counterfactual conditional is true if the counterfactual world in which Bob had not shot (B = 0) and Dan would not have died (D = 0) is more similar to the actual world than any counterfactual world in which Bob had not shot (B = 0) but Dan would have died anyhow (D = 1). To generate the relevant counterfac- tual world, we are supposed to imagine a small miracle that transforms B from its original state to the considered coun- terfactual state and then let the counterfactual world unfold