 Several proposals retain the basic EU norm, but reject the idea that the utility function ranges only over the real numbers. Some hold that the utility function can take hyper-real values (Skala 1975, Sobel 1996). Others hold that the utility function can take surreal values (Hájek 2003, Chen &amp; Rubio 2020). These proposals allow for versions of the Continuity/Archimedean Axiom. Another alternative is to use a vector-valued (i.e., lexicographic) utility function, which rejects these axioms (see discussion in Hájek 2003).