Vaniver comments on A question about utilitarianism and selfishness. - Less Wrong Discussion
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"Stable" in game theory generally means that no party can make themselves better off unilaterally. (Consider, for example, the stable marriage problem.) Utilitarianism is the correct descriptive observation that socially maximal situations might not be locally maximal, and the dubious prescriptive claim that agents should go for the globally maximal situation because everyone's preferences are equally valuable.