Certainty and Singular Causal Judgment

In this paper, I map out broad aims, challenges, predictions, and implica- tions for the resulting intersection of singular causal judgment and metacognition that I (tentatively) call causal metacognition. First, I will overview research on sin- gular causal judgment, focusing on popular counterfactual theories that provide a formal framework for evaluating dependency relationships, as well as several compet- ing definitions of singular causal strength. Next, I will provide relevant background in the literature on metacognition for perception and decision-making, discussing major computational theories of metacognitive judgments. After covering the small amount of work on uncertainty in causal judgments, I will then argue that although singular causal judgments pose a particular problem for some theories of metacognition, coun- terfactual theories of singular causal judgment already provide testable predictions for confidence in causal judgments and can be extended to account for a wide range of patterns in confidence in singular causal judgments. Finally, I will summarize why we need a study of causal metacognition, and what empirical and theoretical advancements in that field might look like.

Biased belief updating in causal reasoning about COVID-19

In three experiments based on 977 participants, we investigated whether people would show belief bias by letting their prior beliefs on politically charged topics unduly influence their reasoning when updating beliefs based on evidence. Participants saw data from fictional studies and made judgments of how strongly COVID-19 mitigation measures influenced the number of COVID-19 cases (political problems) or a medicine influenced number of headaches (neutral problems). We predicted that liberals would overestimate and conservatives would underestimate causal strength on political problems relative to neutral problems. In Experiments 1 and 2, liberals showed this overestimation bias. Surprisingly, college-student conservatives in Experiment 2 showed the same overestimation as liberals. These findings made sense because all three groups who overestimated the strength of mitigation measures held prior beliefs that strongly favored use of these measures. In Experiment 3, conservatives’ judgments of the strength of mitigation measures after seeing evidence increased as their degree of prior support for these measures increased. Furthermore, conservatives who strongly opposed the use of mitigation measures underestimated causal strength in the political problems. These results suggest that belief bias is driven more by specific beliefs relevant to the reasoning context than to general attitudinal factors like political ideology.

Evaluating General versus Singular Causal Prevention

Most psychological studies focused on how people reason about generative causation, in which a cause produces an effect. We here study the prevention of effects both on the general and singular level. A general prevention query might ask how strongly a vaccine is expected to reduce the risk of contracting COVID-19, whereas a singular prevention query might ask whether the absence of COVID-19 in a specific vaccinated person actually resulted from this person’s vaccination. We propose a computational model answering how knowledge about the general strength of a preventive cause can be used to assess whether a preventive link is instantiated in a singular case. We also discuss how psychological models of causal strength learning relate to mathematical models of vaccination efficacy used in medical research. The results of an experimentsuggest that many, but not all people differentiate between preventive strength and singular prevention queries, in line with the formal model.

The interplay between covariation, temporal, and mechanism information in singular causation judgments

Most psychological studies on causal cognition have focused on how people make predictions from causes to effects or how they assess causal strength for general causal relationships (e.g., “smoking causes cancer”). In the past years, there has been a surge of interest in other types of causal judgments, such as diagnostic inferences or causal selection. Our focus here is on how people assess singular causation relations between cause and effect events that occurred at a particular spatiotemporal location (e.g., “Mary’s having taking this pill caused her sickness.”). The analysis of singular causation has received much attention in philosophy, but relatively few psychological studies have investigated how lay people assess these relations. Based on the power PC model of causal attribution proposed by Cheng and Novick (2005), we have developed and tested a new computational model of singular causation judgments integrating covariation, temporal, and mechanism information. We provide an overview of this research and outline important questions for future research.

Degrading Causation

When asking if lightning caused the forest fire, one might think that the lightning is more of a cause than the dry climate (i.e., it is a graded cause) or they might instead think that the lightning strike completely caused the fire while the dry conditions did not cause it at all (i.e., it is a binary cause). Psychologists and philosophers have long debated whether such judgments are graded. To address this debate, we started by reanalyzing data from four recent studies. In this context, we provide novel evidence that causal judgments are actually multimodal: although most causal judgements were binary, there was also some gradation. We then tested two competing explanations for the gradation we observed: the confidence explanation, which states that gradation distinguishes between certain and uncertain causes, and the strength explanation, which states that gradation distinguishes between strong and weak causes. Experiment 1 tested the confidence explanation and showed that gradation in causal judgments was moderated by confidence. People tended to make graded causal judgments when they were less confident, but they tended to make discrete causal judgments when they were more confident. Experiment 2 tested the causal strength explanation and showed that although causal judgments varied with factors associated with causal strength, confidence ratings were unchanged. Overall, we found that causal judgments are multimodal and that observed gradation reflects independent effects of confidence and causal strength on causal judgments.

Causal Strength

The question “When is C a cause of E?” is well-studied in philosophy—much more than the equally important issue of quantifying the causal strength between C and E. In this chapter, we transfer methods from Bayesian Confirmation Theory to the problem of explicating causal strength. We develop axiomatic foundations for a probabilistic theory of causal strength as difference-making and proceed in three steps: First, we motivate causal Bayesian networks as an adequate framework for defining and comparing measures of causal strength. Second, we demonstrate how specific causal strength measures can be derived from a set of plausible adequacy conditions (method of representation theorems). Third, we use these results to argue for a specific measure of causal strength: the difference that interventions on the cause make for the probability of the effect. An application to outcome measures in medicine and discussion of possible objections concludes the chapter.

Bayesian Philosophy of Science

“Bayesian Philosophy of Science” addresses classical topics in philosophy of science, using a single key concept—degrees of beliefs—in order to explain and to elucidate manifold aspects of scientific reasoning. The basic idea is that the value of convincing evidence, good explanations, intertheoretic reduction, and so on, can all be captured by the effect it has on our degrees of belief. This idea is elaborated as a cycle of variations about the theme of representing rational degrees of belief by means of subjective probabilities, and changing them by a particular rule (Bayesian Conditionalization). Partly, the book is committed to the Carnapian tradition of explicating essential concepts in scientific reasoning using Bayesian models (e.g., degree of confirmation, causal strength, explanatory power). Partly, it develops new solutions to old problems such as learning conditional evidence and updating on old evidence, and it models important argument schemes in science such as the No Alternatives Argument, the No Miracles Argument or Inference to the Best Explanation. Finally, it is explained how Bayesian inference in scientific applications—above all, statistics—can be squared with the demands of practitioners and how a subjective school of inference can make claims to scientific objectivity. The book integrates conceptual analysis, formal models, simulations, case studies and empirical findings in an attempt to lead the way for 21th century philosophy of science.

What Is Transferred in Causal Generalization Across Contexts?

The covariation and causal power account for causal induction make different predictions for what is transferred in causal generalization across contexts. Two experiments tested these predictions using hypothetical scenarios in which the effect of an intervention was evaluated between (Experiment 1) or within (Experiment 2) groups. Each experiment contained a manipulation of ΔP, power and their combination. Both experiments found that causal transfer was determined by ΔP rather than causal power. The overall transfer pattern supports ΔP transfer account rather than the other transfer accounts. Causal transfers based on ΔP are irrational, violating the coherence criterion of the causal power framework. The ΔP transfer is consistent with previous findings that ΔP is a main mental non-normative measure of causal strength in causal induction.