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The design of mechanisms for group decision making, addressing questions about how apartment mates should choose rooms and share the rent, how a government should select and pay its suppliers, how a town should elect a mayor, or how students and college ought to be matches to one another. The first three weeks include classic papers by two Nobel-prize winning scholars about matching students and about government procurement. We will ask questions such as: What are the provable properties of these mechanisms? Is it possible for individuals or groups to manipulate the mechanisms for their own advantage? The remaining weeks focus on group decisions that are guided by "voting" mechanisms, showing the inherent trade-offs and proving theorems about the incompatibility among some simple, desirable properties of mechanisms. The ideas treated in this class are being used today to design new mechanisms for voting, matching, auctions and other applications, based on an awareness of the formal properties that the mechanisms may have.