Someone I know has put forth the claim that the best way to achieve the most prosperous society — the one with the greatest total quality of life across all people — is for each individual person to give highest priority to his own well-being. One of his personal philosophical heroines called this concept “rational self-interest”. She promoted it because she thought all behavior ought to have a wholly rational basis and she could not find such a basis in putting others' well-being first. (At least, that’s what Wikipedia says.) My acquaintance says he has an even better reason to stand behind this claim: it’s been proven by famous mathematician John Nash. In fact, there's even had a name for it: a “Nash equilibrium”.
I have a couple of problems with this. For one, he’s wrong about the term. A Nash equilibrium is when no one can get a better outcome for himself by being the only person who does something different. It may or may not be the best possible overall outcome — and if it’s not, reaching a better one will take at least two people mutually agreeing to change their actions together. So Nash equilibria are actually obstacles on the road to the true global maximum. They’re pitfalls for human psychology to fall into. People are naturally averse to giving up an acceptable, already-achieved result in exchange for a better potential outcome that requires even more effort.
Number two: focusing exclusively on maximizing the total combined well-being of society doesn’t consider how bad each individual life is. If one person’s livelihood can be cut to a tenth to double that of twenty others of similar standing, the math of pure practicality says to do it. Take this to the extreme and you get the parable of Omelas.