Decomposable Choice under Uncertainty

Savage motivated his sure-thing principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, it should be preferred overall. The ability to decompose and recompose decision problems in this way has normative appeal. It does not, however, require the full separability embodied in Savage's axiom. We formulate a weaker axiom that suffices for decomposability, and show it is almost equivalent to Gul and Lantto's dynamic programming solvability property. Given probabilistic sophistication, weak decomposability is equivalent to betweenness. Without probabilistic sophistication, weak decomposability implies an implicit additive representation. Journal of Economic Literature Classification Numbers: D80, D81.