I examined this one, too, but the continuity axiom intuitively makes sense for comparables, except possibly in cases of extreme risk aversion. I am leaning more toward abandoning the transitivity chain when the options are too far apart. Something like A > B having some uncertainty increasing with the chain length between A and B or with some other quantifiable value.
My suspicion that what has to give is the assumption of unlimited transitivity in VNM, but I never bothered to flesh out the details.
Actually, I believe it’s the continuity axiom that rules out lexicographic preferences.
I examined this one, too, but the continuity axiom intuitively makes sense for comparables, except possibly in cases of extreme risk aversion. I am leaning more toward abandoning the transitivity chain when the options are too far apart. Something like A > B having some uncertainty increasing with the chain length between A and B or with some other quantifiable value.