You started out by assuming a preference relation on lotteries with various properties. The completeness, transitivity, and continuity axioms talk about this preference relation. Your “standard deviation bound” axiom, however, talks about a utility function. What utility function?
You started out by assuming a preference relation on lotteries with various properties. The completeness, transitivity, and continuity axioms talk about this preference relation. Your “standard deviation bound” axiom, however, talks about a utility function. What utility function?