Prerationality as Avoiding Predictably Regrettable Consequences

Abstract

Following previous work on consequentialist decision theory, we consider an unrestricted domain of finite decision trees, including continuation subtrees, with: (i) decision nodes where the decision maker must make a move; (ii) chance nodes at which a "roulette lottery" with exogenously specified strictly positive probabilities is resolved; (iii) event nodes at which a "horse lottery" is resolved. A complete family of binary conditional base preference 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, consequences that are regrettable given what is feasible. Prerationality is shown to hold if and only if all conditional base preference relations are complete and transitive, while also satisfying both the independence axiom of expected utility theory and 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 refined subjective expected utility function that excludes zero probabilities.