Measuring Causal Invariance Formally

Entropy (Basel). 2021 May 30;23(6):690. doi: 10.3390/e23060690.

Abstract

Invariance is one of several dimensions of causal relationships within the interventionist account. The more invariant a relationship between two variables, the more the relationship should be considered paradigmatically causal. In this paper, I propose two formal measures to estimate invariance, illustrated by a simple example. I then discuss the notion of invariance for causal relationships between non-nominal (i.e., ordinal and quantitative) variables, for which Information theory, and hence the formalism proposed here, is not well suited. Finally, I propose how invariance could be qualified for such variables.

Keywords: causal specificity; causation; information theory; invariance.