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Over the past two decades, several consistent procedures have been designedto infer causal conclusions from observational data. We prove that if the truecausal network might be an arbitrary, linear Gaussian network or a discreteBayes network, then every unambiguous causal conclusion produced by aconsistent method from non-experimental data is subject to reversal as thesample size increases any finite number of times. That result, called thecausal flipping theorem, extends prior results to the effect that causaldiscovery cannot be reliable on a given sample size. We argue that sincerepeated flipping of causal conclusions is unavoidable in principle forconsistent methods, the best possible discovery methods are consistent methodsthat retract their earlier conclusions no more than necessary. A series ofsimulations of various methods across a wide range of sample sizes illustratesconcretely both the theorem and the principle of comparing methods in terms ofretractions.

Causal Conclusions that Flip Repeatedly and Their Justification