A foundation for causal decision theory

Summary

I have argued that CDT is a good rational decision theory; its use leads to the correct recommendations in problems where V-maximization goes wrong. Objections to K-expectation CDT were mentioned in Section 2, and I claimed that they would be answered by the foundation presented above. One of the objections was simply that CDT lacks the foundation that a representation theorem provides; this objection has now been met. Of course, we really seek a good foundation. If we are convinced that the theorem does follow from the axioms, that the uniqueness portion of the theorem is as strong as we would like it to be, and that the utility rule (7) is correct, the relevant question is: Are the conditions placed on rational preference systems by the axioms understandable, plausible, and not overly restrictive? The answer is yes, qualified by the acknowledgement that there are no doubt improvements to be found. Full justification of that answer requires a general discussion of formal, idealized treatments of rational preference and representation theorems for rational decision theory. Such a discussion appears in Armendt (1983). It also requires careful assessment of Axioms (1)–(11) given above; this also appears in Armendt (1983).

The other objections to K-expectation CDT mentioned in section 2 were directed toward the problem of the selection of appropriate K-partitions. These objections have been answered by the statement of the sufficient conditions for appropriate K's given in sections 4 and 5. (Notice that a statement of interesting necessary conditions is likely to be difficult; for a particular decision problem a partition of state descriptions might by coincidence yield an accurate evaluation of action A when used in rule (6) even though the partition fails to satisfy any intuitively correct conditions for appropriate K's). Those conditions describe, as they ought, the behavior of the K propositions in the agent's preferences. And the conditions are simple enough, clear enough, that partitions which satisfy them are readily found in decision problems which require their use.