Choice of Units and the Causal Markov Condition

Elliott Sober's well-known challenge to the principle of the common cause — and to its generalization, the causal Markov condition — appeals to the apparent positive correlation between two causally unconnected quantities: Venetian sea levels and British bread prices. In this paper we examine Kevin Hoover's and Daniel Steel's opposite evaluations of Sober's case. We argue that the difference in their assessments results from a difference in their choice of units and populations for statistical modeling. Our analysis suggests yet another diagnosis of Sober's counterexample: the failure of the causal Markov condition in the population chosen by Sober and Steel is due to the presence of causal relations that hold between the relevant properties across units. Such inter-unit causation is left unrepresented in causal models congenial to statistical analysis, because statistics does not deal with inter-unit relationships once the units are fixed. Accordingly, the causal Markov condition is formulated in terms of causal structures that depict intra-unit causal relations only. It is therefore worth highlighting a methodological principle for causal inference: the units should be so chosen that they do not interfere with each other, a principle that, fortunately, is often observed in practice.