At first glance, morality and mathematics seem as unrelated as martyrdom and MTV. But it is possible to characterize moral notions formally and to prove theorems. Doing so does not banish controversy and cannot replace verbal argument concerning moral matters, because the abstract mathematical characterizations of moral notions require interpretation and defense. Just as there are disagreements concerning the formal definitions of rationality, so are there controversies about formal definitions of moral notions.

Over the last 75 years economists, decision theorists, and game theorists have made exciting progress not only in representing individual rationality but also in characterizing features of human interactions. This work is linked to moral philosophy. Formal models of rationality and game-theoretic studies of incentives hold out the hope of transcending some of the ancient conundrums concerning the relations between morality, rationality and self-interest discussed in Chapter 6. Concepts of “fair” or envy-free allocations, discussed in Chapter 11, facilitate the articulation of egalitarianism. Solution concepts in game theory may enrich the contractarian perspective (discussed in Chapter 12) that morality can be justified in terms of agreement. Theorems in social choice theory explore the implications of plausible axioms and test the consistency of traditional principles concerning how social policies should respond to individual interests. We face an embarrassment of riches, and we can only comment on a few of these developments.