Probabilistic Causality and Simpson's Paradox

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Abstract
This paper discusses Simpson's paradox and the problem of positive relevance in probabilistic causality. It is argued that Cartwright's solution to Simpson's paradox fails because it ignores one crucial form of the paradox. After clarifying different forms of the paradox, it is shown that any adequate solution to the paradox must allow a cause to be both a negative cause and a positive cause of the same effect. A solution is then given that can handle the form of the paradox that Cartwright's solution ignored, and allows causes to be both a positive and a negative cause of an effect.

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