Intervention, Robustness, and Probabilistic Dependence
Daniel M. Hausman · Cambridge University Press eBooks · 1998
This chapter will be concerned with yet another asymmetry of causation. Recently, several authors have argued that there is an asymmetry of robustness or invariance . In particular, this chapter will consider three related purported asymmetries: (Asymmetry of robustness) x causes y if and only if the relationship between x and y and other variables is invariant with respect to the value of x but not with respect to the value ofy (Arntzenius 1990, pp. 90–1; Hoover 1990, 1991, 1993; Hoover and Sheffrin 1992; Hoover and Perez 1994). ( Asymmetry of parameter independence ) Suppose that S is a complete and correct specification of a causal system involving a set of variables including x and y. x causes y if and only if one can calculate from S the correct value (or the best estimate) of y but not of x , when one substitutes a changed parameter value into S (Simon 1953, p. 69; Hoover 1990, pp. 211–12; Woodward 1995, 1998). MI ( Asymmetry of modal invariance ) Suppose that S is a complete and correct specification of a causal system involving a set of variables including x and y. x causes y if and only if the value of y one calculates when one substitutes a new value of JC into S is a correct prediction or a best estimate of what the value of y would be if the value of x were set to its new value via intervention (Cartwright 1989, ch. 4; Hoover 1991, 1994; Woodward 1995, 1998; Forster 1996b). The phrase “the relationship between x and y ” is intentionally vague, because different theorists have focused on different relationships.