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

Abstract
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)
Keywords Probabilistic causality  Conjunctive forks  Interactive forks  Multi-causal forks  Markov condition  Bayesian networks  Causal factors  Heart disease
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Wesley C. Salmon (1980). Causality: Production and Propagation. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:49 - 69.
DM Hausman & J. Woodward (1999). Independence, Invariance and the Causal Markov Condition. British Journal for the Philosophy of Science 50 (4):521-583.
Daniel Steel (2005). Indeterminism and the Causal Markov Condition. British Journal for the Philosophy of Science 56 (1):3-26.
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