Bread Prices and Sea Levels: Why Probabilistic Causal Models Need to Be Monotonic

Hoffmann-Kolss, Vera (2024). Bread Prices and Sea Levels: Why Probabilistic Causal Models Need to Be Monotonic. Philosophical Studies Springer 10.1007/s11098-024-02112-y

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A key challenge for probabilistic causal models is to distinguish non-causal probabilistic dependencies from true causal relations. To accomplish this task, causal models are usually required to satisfy several constraints. Two prominent constraints are the causal Markov condition and the faithfulness condition. However, other requirements are also needed. One of these additional requirements is the causal sufficiency condition, according to which models must not omit any direct common causes of the variables they contain. In this paper, I argue that the causal sufficiency condition is problematic: (1) it is incompatible with the requirement that the variables in a model must not stand in non-causal necessary dependence relations, such as mathematical or conceptual relations, or relations described in terms of supervenience or grounding, (2) it is either trivial or leads to an infinite regress, and (3) if models are only required to be causally sufficient, they cannot deal with cases where variables are probabilistically related by accident, such as Sober's example of the relationship between bread prices in England and the sea level in Venice. I show that these problems can be avoided if causal models are required to be monotonic in the following sense: the causal relations occurring in a model M would not disappear if further variables were added to M. I give a definition of this monotonicity condition and conclude that causal models should be required to be monotonic rather than causally sufficient.

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