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

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