Exposing some points of interest about non-exposed points of desirability

We study the representation of sets desirable gambles by probability mass functions. Sets are a very general uncertainty model, that may be non-Archimedean, and therefore not representable set Recently, Cozman (2018) has shown imposing additional requirement even convexity on guarantees they Already more 20 years earlier, Seidenfeld et al. (1995) gave an axiomatisation binary preferences—on horse lotteries, rather than gambles—that also leads to unique in terms To reach this goal, use two devices, which we will call ‘SSK–Archimedeanity’ ‘SSK–extension’. In paper, make arguments explicit language gambles, show how their ideas imply allow for conservative reasoning with evenly convex deriving equivalence between SSK–Archimedean natural extension, SSK–extension, extension.