On the Skiadas 'Conditional Preference Approach' to Choice Under Uncertainty

We compare the Skiadas approach with the standard Savage framework of choice under uncertainty. At first glance, properties of Skiadas "conditional preferences" such as coherence and disappointment seem analogous to similarly motivated notions of decomposability and disappointment aversion defined on Savage "ex ante preferences." We show, however, that coherence per se places almost no restriction on the structure of ex ante preferences. Coherence is an `external' restriction across preferences whereas notions of decomposability in the Savage framework are 'internal' to the particular preference relation. Similarly, standard notions of disappointment aversion refer to 'within act' disappointments. Skiadas's notion of disappointment aversion for families of conditional preference relations neither implies nor is implied by standard notions of disappointment aversion for ex ante preferences.