Nontransitive models for decision making under uncertainty: A general framework and some applications Extended abstract

In a series of recent papers (Bouyssou and Pirlot, 2002, 2004a), we have proposed several conjoint measurement models that tolerate intransitive preferences. Their main characteristic is that they replace the additivity requirements used in most models designed to cope with intransitivities (e.g. the additive difference model proposed by Tversky (1969) and analyzed in Fishburn (1992) or the additive nontransitive model proposed in Fishburn (1991) and (Vind, 1991)) by a mere decomposability requirement. These models, while being nontrivial, are amenable to a simple axiomatic analysis that dispenses with any unnecessary structural requirements on the set of objects (e.g. solvability). In this paper, we show how to adapt the models proposed in Bouyssou and Pirlot (2002) and Bouyssou and Pirlot (2004a) to the case of decision making under uncertainty. As in the case of conjoint measurement, we obtain