When causation does not imply correlation: robust violations of the Faithfulness axiom

TL;DR

This paper reveals that the Faithfulness assumption in causal analysis is fundamentally violated in control systems, which are common in social sciences, due to their inherent ability to maintain variables constant despite external influences.

Contribution

It demonstrates that control systems can violate the Faithfulness axiom in a robust manner, challenging the applicability of standard causal inference methods.

Findings

Control systems can show zero correlation between causally connected variables.

They can exhibit high correlations between variables with no direct causal link.

These correlation patterns are robust to parameter changes.

Abstract

We demonstrate that the Faithfulness property that is assumed in much causal analysis is robustly violated for a large class of systems of a type that occurs throughout the life and social sciences: control systems. These systems exhibit correlations indistinguishable from zero between variables that are strongly causally connected, and can show very high correlations between variables that have no direct causal connection, only a connection via causal links between uncorrelated variables. Their patterns of correlation are robust, in that they remain unchanged when their parameters are varied. The violation of Faithfulness is fundamental to what a control system does: hold some variable constant despite the disturbing influences on it. No method of causal analysis that requires Faithfulness is applicable to such systems.