Mathematics of Social Choice: Voting, Compensation, and Division
Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.
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adjusted winner method approval voting assigned assume beatpath method beats Borda scores cake consisting cake division Chapter chocolate component choosers compensation amounts compensation arrangement Condorcet candidate Condorcet criterion Condorcet-fair considers denote dictatorship dominating set elimination method envy envy-free equal equitable division example Exercise fair division fair share first-place votes fraction head-to-head competition IIC criterion Lemma losing spoiler majority criterion margins of victory marriage condition marriage theorem mathematical mathematical induction method of pairwise minimal share monotonic natural numbers non-Smith candidate objective improvement pairwise comparison graph Pareto-efficient Pareto-optimal payout preference schedule priori Smith-fair Borda Proof proportional allocation Proposition prove ranking method recursive referee retroactive disqualification rhubarb component runoff method satisfies the unanimity second component sequential comparison share a cake single-winner method Smith candidate Smith set Smith-fair Borda count societal ranking sole winner strawberry component Suppose theorem threshold division U.S. presidents unanimity criterion unmatched beatpath winner selection method winning bidder