Probabilistic Measures of Causal Strength

Abstract

A number of theories of causation posit that causes raise the probability of their effects. In this chapter, we survey a number of proposals for analysing causal strength in terms of probabilities. We attempt to characterize just what each one measures, discuss the relationships between the measures, and discuss a number of properties of each measure. One encounters the notion of 'causal strength' in many contexts. In linear causal models with continuous variables, the regression coefficients (or perhaps the standardized coefficients) are naturally interpreted as causal strengths. In Newtonian mechanics, the total force acting on a body can be decomposed into component forces due to different sources. Connectionist networks are governed by a system of 'synaptic weights' that are naturally interpreted as causal strengths. And in Lewis's account of 'causation as influence' (Lewis 2000), he claims that the extent to which we regard one event as a cause of another depends upon the degree to which one event 'influences' the other. In this chapter, we examine the concept of causal strength as it arises within probabilistic approaches to causation. In particular, we are interested in attempts to measure the causal strength of one binary variable for another in probabilistic terms. Our discussion parallels similar discussions in confirmation theory, in which a number of probabilistic measures of degree of confirmational support have been proposed. Fitelson (1999) and Joyce (MS) are two recent surveys of such measures.

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