Binary Gambles of a Gain and a Loss: an Understudied Domain

Assume that binary rank-dependent expected utility (subjective expected utility is a special case) holds for gains and losses separately and that a commutative binary operation of joint receipt on consequences and gambles is linked to binary gambles via the rational property of segregation. This implies that utility U of joint receipt is either itself additive or is an exponential transformation of an additive representation V. For joint receipt of mixed gains and losses two hypotheses are discussed: either U or V is additive over mixed joint receipts. Both hypotheses are linked back to gambles in two different ways: a generalization of segregation and an empirically sustained but nonrational property called duplex decomposition. The additive U model yields bilinear expressions like rank-dependent expected utility. Data favor the latter. The additive V models yield nonbilinear representations of mixed gambles.