Psychological and Normative Theories of Causal Power and the Probabilities of Causes

Abstract: This paper (1)shows that the best supported current psychological theory (Cheng, 1997) of how human subjects judge the causal power or influence of variations in presence or absence of one feature on another, given data on their covariation, tacitly uses a Bayes network which is either a noisy or gate (for causes that promote the effect) or a noisy and gate (for causes that inhibit the effect); (2)generalizes Chengs theory to arbitrary acyclic networks of noisy or and noisy and gates; (3)gives various sufficient conditions for the estimation of the parameters in such networks when there are independent, unobserved causes; (4)distinguishes direct causal influence of one feature on another (influence along a path with one edge) from total influence (influence along all paths from one variable to another) and gives sufficient conditions for estimating each when there are unobserved causes of the outcome variable; (5)describes the relation between Cheng models and a simplified version of the Rubin framework for representing causal relations.