 In the Reichenbach-Suppes definition of causation, the inequality \(\PP(E_{t'} \mid C_t) \gt \PP(E_{t'} \mid {\nsim}C_t)\) is necessary, but not sufficient, for causation. It is not sufficient, because it may hold in cases where \(C_t\) and \(E_{t'}\) share a common cause. Unfortunately, common causes can also give rise to cases where this inequality is not necessary for causation either. Suppose, for example, that smoking is highly correlated with living in the country: those who live in the country are much more likely to smoke as well. Smoking is a cause of lung cancer, but suppose that city pollution is an even stronger cause of lung cancer. Then it may be that smokers are, over all, less likely to suffer from lung cancer than non-smokers. Letting C represent smoking, B living in the country, and E lung cancer, \(\PP(E \mid C) \lt \PP(E \mid {\nsim}C)\). Note, however, that if we conditionalize on whether one lives in the country or in the city, this inequality is reversed: \(\PP(E \mid C \amp B) \gt \PP(E \mid {\nsim}C \amp B)\), and \(\PP(E \mid C \amp{\nsim}B) \gt \PP(E \mid {\nsim}C \amp{\nsim}B)\). Such reversals of probabilistic inequalities are instances of “Simpson’s Paradox”. The problem that Simpson’s paradox creates for probabilistic theories of causation was pointed out by Nancy Cartwright (1979) and Brian Skyrms (1980) at about the same time.