A foundation for causal decision theory

Abstract

The primary aim of this paper is the presentation of a foundation for causal decision theory. This is worth doing because causal decision theory (CDT) is philosophically the most adequate rational decision theory now available. I will not defend that claim here by elaborate comparison of the theory with all its competitors, but by providing the foundation. This puts the theory on an equal footing with competitors for which foundations have already been given. It turns out that it will also produce a reply to the most serious objections made so far against CDT and against the particular version of CDT I will defend. 1 Causal decision theory comes in four versions: Gibbard & Harper's (1976), Skyrms' (1979), Lewis' (1981), and Sobel's (1978). The theories are in spirit very much alike, but the differences between them are philosophically significant. A good description and comparison of the four versions is given in Lewis (1981). While Lewis prefers his formulation of CDT, I prefer Skyrms', and it is for Skyrms' version that the foundation is supplied. In accordance with standard practice, this foundation consists of 1) a set of axiomatic conditions on rational preference systems, and 2) the derivation of a representation theorem which shows that for any preference system satisfying the axioms there exist a probability measure P and order-preserving utility functions U which represent the preferences, and which are related by the theory's general utility rule. The representation theorem has a uniqueness part which shows that P and U are not arbitrary: for each preference system P is uniquely determined and U is unique up to positive linear transformation. (Here I am describing the theorem presented in this paper; some representation theorems for other theories contain weaker uniqueness conditions.) I should make it clear from the beginning that the foundation I provide for the theory relies on formal results of Fishburn's in his (1973). My alterations of his formal theory are slight. I do reinterpret his theory somewhat. The application of that interpretation to causal decision theory is new.