Prerationality as Avoiding Predictably Regrettable Consequences

Following previous work on consequentialist decision theory, we consider an unrestricted domain of finite decision trees, including continuation subtrees, with: 1) decision nodes where the decision-maker must act; 2) chance nodes where a ?roulette lottery? with strictly positive probabilities that are defined a priori is resolved; 3) event nodes where a ?horse lottery? is resolved. A complete family of binary conditional base relations over Anscombe-Aumann lottery consequences is defined to be ?prerational? just in case there exists a behaviour rule that is defined throughout the tree domain which is explicable as avoiding, under all predictable circumstances, regrettable consequences. It is shown that a family of base relations is prerational if and only if: 1) each relation is complete and transitive; 2) each relation satisfies the independence axiom of expected utility theory; 3) the entire family satisfies a strict form of Anscombe and Aumann?s extension of Savage?s sure-thing principle. Assuming that the base relations satisfy non-triviality and a generalized form of state independence that holds even when consequence domains are state dependent, prerationality combined with continuity on Marschak triangles is equivalent to representation by a class of refined subjective expected utility functions that excludes zero probabilities.