Fairness and Equity (8/10/99)

Prepared by:

Joseph Malkevitch
Mathematics and Computing Department
York College (CUNY)
Jamaica, New York 11451-0001

Email: malkevitch@york.cuny.edu

Sample Course Outline

Major topics

(The topics below are not disjoint from each other and are in no particular order.)

1. Theories of Justice

a. Aristotle

b. Bentham (Utilitarianism)

c. Rawls

2. Game Theory

a. Cooperative games

b. Uncooperative games

c. 2-person games

d. n-person games

e. Zero-sum games

f. Matrix games

g. Equilibrium concepts

h. Solution concepts

i. Shapley value

ii. Stable sets

iii. Core

iv. Nucleolus

v. Bargaining set

j. Contributions of John Nash

k. Nobel Memorial Prizes for work related to game theory and fairness and equity.

3. Election and Voting Methods

a. Arrow's Theorem

b. Sophisticated voting

c. Borda vs. Condorcet methods

d. Empirical studies of voting

e. Fairness of setting up districts to achieve racial goals

f. Ballot types

i. Ordinal

ii. Cardinal

iii. Approval

g. Approval voting

h. Voting systems actually in use

4. Weighted Voting

a. Existence of powerless players in weight proportional to population situations

b. Different power indices

i. Shapley-Shubik

ii. Banzhaf

iii. Deegan-Packel

iv. Johnson

c. Real world examples

i. European union

ii. Electoral college

iii. Proposed system to amend Canadian Federal Constitution

d. Axiomatic approaches to weighted voting

5. Apportionment

a. European parliamentary systems

b. US House of Representatives

i. Recent Supreme Court Cases

c. Non-political instances

d. Shape of election districts (gerrymandering)

e. Methods

i. Hamilton

ii. Adams

iii. Webster (St. Laguë)

iv. D'Hondt (Jefferson)

v. Hill-Huntington

vi. Dean

vii. Methods based on voting power

6. Proportional Representation

a. The single transferable vote

b. Other apportionment systems

c. Role of district size

d. Variable size legislature

e. Mixed list and single seat system

f. Historic examples of proportional representation

7. Fair Division

a. Divisible goods

b. Indivisible goods

c. Proportional share

d. Envy and envy free

e. Limitations and strengths of divide and choose

f. Steinhaus procedure

g. Efficiency (Pareto optimality)

8. Intellectual Property Protection for New Technology

a. What can be copyrighted and how the copyright system works

b. What can be patented and how the patent system works

c. Trade secret protection for intellectual property

d. Has software created problems for the traditional methods of protecting intellectual property?

e. Patenting surgery, cell lines, and DNA sequences.

9. Standards

a. Sometimes a large company can destroy a smaller company's superior product (which may be patent protected) by using its size to promote an inferior product

b. International attempts to promote product standards

10. Common-Pool Resources

a. Renewable resources

i. Fish

ii. Grazing

iii. Table water

iv. River water

v. Forests

b. Non-renewable resources

i. Oil

ii. Deep ocean resources

c. Access to public lands

11. Ranking Systems

a. Chess

b. Bridge

c. High school and professional football teams

d. Tennis players

e. Seeding systems

12. Organ Transplant Programs

a. Heart transplants

b. Kidney transplants

c. Lung transplants

13. Vaccination Programs and Drug Development

a. Reimbursement for adverse reactions to vaccines

b. Development of drugs for rare diseases

14. Auctions

a. English

b. Dutch

c. Auction of portions of the electromagnetic spectrum for new phone and communications technology

d. Vickrey auctions

15. Bargaining and Negotiating

a. Labor/management negotiation

b. Treaty negotiations

c. Trade negotiations

d. Mediation

e. Arbitration

16. Optimization Issues Incidental To Fairness

a. Tradeoffs between efficiency and fairness

17. Measuring Fairness

a. Income inequality

i. Gini Index

ii. Lorenz Curve

b. Construction of index numbers

18. Taxes

a. Regressive taxes

b. Flat tax

c. Equal sacrifice taxation

d. Taxation as a bankruptcy model

19. Fairness in Health Care

a. Access to health care

b. Transplant equity

c. Settlement of class action suits

i. Breast implants

ii. Hemophiliacs who got AIDS

iii. Vaccination suits

d. Assigning medical residents to hospitals

e. Drug and vaccine development policy

20. Bankruptcy Models

a. Solution methods

i. Proportionality

ii. Maimonides method

iii. Contested garment rule (Talmudic rule)

iv. Shapley value

b. Fairness axioms for bankruptcy

i. Consistency

ii. Monotonicity

21. Fairness in Scheduling

a. Fairness in scheduling sports events

b. Fairness in access to time sharing systems

c. Fairness in scheduling planes, trains and urban transportation

Potential audience

Accounting and Business Majors

Biology Majors

Economics Majors

Mathematics Majors

Philosophy Majors

Political Science Majors

Sociology and Anthropology Majors

Psychology Majors

Mathematics Majors


This work was prepared with partial support from the National Science Foundation (Grant Number: DUE9555401) to the Long Island Consortium for Interconnected Learning (administered by SUNY at Stony Brook, Alan Tucker, Director).

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