**Proceedings of Symposia in Applied Mathematics**

Volume: 33;
1985;
170 pp;
Softcover

MSC: Primary 90;

**Print ISBN: 978-0-8218-0094-2
Product Code: PSAPM/33**

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

**Electronic ISBN: 978-0-8218-9248-0
Product Code: PSAPM/33.E**

List Price: $41.00

AMS Member Price: $32.80

MAA Member Price: $36.90

# Fair Allocation

Share this page *Edited by *
*H. Peyton Young*

This collection of six papers provides a valuable source of material
on the real-world 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 real-world social problems.