Proceedings of Symposia in Applied Mathematics 1985; 170 pp; softcover Volume: 33 ISBN10: 0821800949 ISBN13: 9780821800942 List Price: US$39 Member Price: US$31.20 Order Code: PSAPM/33
 This collection of six papers provides a valuable source of material on the realworld problem of allocating objects among competing claimants. The examples given show how mathematics, particularly the axiomatic method, can be applied to give insight into complex social problems. Originally presented as an AMS Short Course, these papers could serve as a suitable text for courses touching on game theory, decision sciences, economics, or quantitative political science. Most of the material is accessible to the mathematically mature undergraduate with a background in advanced calculus and algebra. Each article surveys the recent literature and includes statements and sketches of proofs, as well as unsolved problems which should excite student curiosity. The articles analyze the question of fair allocation via six examples: the apportionment of political representation, the measurement of income inequality, the allocation of joint costs, the levying of taxes, the design of voting laws, and the framing of auction procedures. In each of these examples fairness has a somewhat different significance, but common axiomatic threads reveal broad underlying principles. Each of the topics is concerned with norms of comparative equity for evaluating allocations or with standards of procedures for effecting them; it is this focus on normative properties which suggests that a mathematical analysis is appropriate. Though game theory provides a useful tool in many of these allocation problems, the emphasis here is on standards rather than strategy and equity rather than rationality, an approach which more accurately mirrors realworld social problems. Readership Table of Contents  M. L. Balinski and H. P. Young  The apportionment of representation
 J. E. Foster  Inequality measurement
 H. P. Young  Cost allocation
 H. P. Young  The allocation of debts and taxes
 H. Moulin  Fairness and strategy in voting
 R. J. Weber  Auctions and competitive bidding
