Should causal models always be Markovian? The case of multi-causal forks in medicine

The development of causal modelling since the 1950s has been accompanied by a number of controversies, the most striking of which concerns the Markov condition. Reichenbach's conjunctive forks did satisfy the Markov condition, while Salmon's interactive forks did not. Subsequently some experts in the field have argued that adequate causal models should always satisfy the Markov condition, while others have claimed that non-Markovian causal models are needed in some cases. This paper argues for the second position by considering the multi-causal forks, which are widespread in contemporary medicine (Section 2). A non-Markovian causal model for such forks is introduced and shown to be mathematically tractable (Sections 6, 7, and 8). The paper also gives a general discussion of the controversy about the Markov condition (Section 1), and of the related controversy about probabilistic causality (Sections 3, 4, and 5

InvestigateDiscussEstimateAggregate for structured expert judgement.

This study presents the results of an approach to the prediction of the outcomes of geopolitical events, which we term the IDEA protocol. The participants investigate the background and causal factors behind a question, predict the outcome, and discuss their thinking with others. They then make a second, private and anonymous judgement of the probability of the event, which is subsequently aggregated mathematically. The method performed well relative to both an equally weighted linear pool and a prediction market, and is relatively simple to implement. The results indicate the value of discussion for removing arbitrary linguistic uncertainty and for sharing and debating knowledge, thereby improving the judgements. Weighting individual judgements based on prior performance using Cooke’s method improved group judgements. Even though some of the results are not statistically significant, the study may not have had sufficient power to detect some important effects. Nevertheless, the results help us to formulate conjectures, which can then be investigated further

Generic versus Single-Case Causality: The Case of Autopsy

This paper addresses questions about how the levels of causality (generic and single-case causality) are related. One question is epistemological: can relationships at one level be evidence for relationships at the other level? We present three kinds of answer to this question, categorised according to whether inference is top-down, bottom-up, or the levels are independent. A second question is metaphysical: can relationships at one level be reduced to relationships at the other level? We present three kinds of answer to this second question, categorised according to whether single-case relations are reduced to generic, generic relations are reduced to single-case, or the levels are independent. We then explore causal inference in autopsy. This is an interesting case study, we argue, because it refutes all three epistemologies and all three metaphysics. We close by sketching an account of causality that survives autopsy—the epistemic theory