SIGNED ORDERS IN LINEAR AND NONLINEAR UTILITY-THEORY

Self-reflecting signed orders on a set A and its anti-set A were intr oduced previously as a way to account for negative as well as positive feelings about the inclusion of items in A in potential subsets of ch oice. The present paper extends the notion of signed orders to lotteri es on A boolean OR A, describes reflection axioms for the lottery con text, and shows how these axioms simplify utility representations for preference between lotteries. The simplified representations are then used to guide procedures for extending preferences from A boolean OR A and its lotteries to preferences between subsets of items.