Social Choice Theory

The theory of analyzing a decision between a collection of alternatives made by a collection of  voters with separate opinions. Any choice for the entire group should reflect the desires of the individual voters to the extent possible.

Fair choice procedures usually satisfy anonymity (invariance under permutation of voters), duality (each alternative receives equal weight for a single vote), and monotonicity (a change favorable for  does not hurt ). Simple majority vote is anonymous, dual, and monotone. May's theorem states a stronger result.

REFERENCES:

Taylor, A. Mathematics and Politics: Strategy, Voting, Power, and Proof. New York: Springer-Verlag, 1995.

Young, S. C.; Taylor, A. D.; and Zwicker, W. S. "Counting Quota Systems: A Combinatorial Question from Social Choice Theory." Math. Mag. 68, 331-342, 1995.