It's not that there's a like or dislike of risk. Preference orderings are either (locally) convex or concave. Risk aversion is just that, a preference ordering

It's not that there's a like or dislike of risk. Preference orderings are either (locally) convex or concave. Risk aversion is just that, a preference ordering over mean/variance bundles. There was an econ textbook that gave a memorable example of a (qualified) exception to convexity: ice-cream and olives. Usually I'll want to have ice cream and olives in my fridge, but I don't want them at once! - so pure ice-cream would be prefered to a mix of them at my plate, right now. Risk aversion does not imply, on its own, that you don't want risk at all. It implies that you want some mix of risky and non-risky assets; while concavity towards risk would imply you want either one or the other. The problem with making risk aversion/convexity work with lotteries and such is that the price you're supposed to pay for lotteries is off your utility surface. But: since lottery tickets and small bets are relatively small in the context of your budget, one can figure that the mispricing in your overall mean/variance bundle is small, and that the emotion of betting may be the case of not wanting to optimize for a grey wall, an optimal mixture. Finally, re: universal formulae, I think you'd profit from reading Elie Ayache's _The Blank Swan_.