Probabilistic Causal Levels

Abstract

According to a standard theory of probabilistic causality, causes C raise the probability of their effects E within causally homogeneous background contexts. More precisely, let K _i ’s be maximal conjunctions of factors — not including C, not-C, or effects thereof — that are causally relevant to E. Then C causes E if and only if, for each i, Pr(E/K _i &C) > Pr(E/K _i & ^~ C).¹ Alternatively, we may call this relation that of C’s being causally positive for E, and characterizations of the relations of C’s being causally negative and causally neutral for E can be obtained by substituting “<” and “=”, respectively, for “>”. Of course, the role of the idea of background contexts in the theory is to avoid getting the wrong answer in cases of the well known phenomenon of “spurious correlation”, which arises in cases of Simpson’s paradox, for example. According to the Pareto-dominance revision of the theory suggested by Skyrms (1980), C need only raise the probability of E within some background context K _i , and must not lower the probability of E in any. Although this revision is perhaps more plausible, I will confine my attention to the “always raises” version; the issues relevant to which of the two versions is more plausible are irrelevant to the issues I wish to discuss, and this will simplify my discussion.

I presented this paper to the National Science Foundation conference on Probality and Causation, Irvine, California, July 15–19, 1985. I thank Elliott Sober for helpful discussions before the meeting, and a number of those in attendance at the meeting — especially William Harper, Igal Kvart, Elizabeth Lloyd, Fred McGifford , and Wesley Salmon — for useful criticism and suggest ions, And I thank the American Council of Learned Societies for financial support.