Fairness and Equity: Notes 4

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451



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Who are the experts in fairness and equity questions?

Common responses are:

a. Clergy

b. Lawyers

c. Accountants

d. Philosophers

e. Economists

f. Judges

Perhaps a somewhat unexpected answer is that increasingly mathematicians are making important contributions to questions involving equity. Sometimes these contributions have been very unexpected, such as the work of Kenneth Arrow for which he won the Nobel Memorial Prize in Economics relating to the existence of "fair" decision making or voting procedures, the Saitterwaite-Gibbard Theorem about manipulability of voting systems, and the Balinski-Young Theorem about apportionment problems.

Dramatic recent insights into fairness questions has been obtained by the following people who are either mathematicians or have had extensive mathematical training:

Kenneth Arrow (Economist) Elections and social decision making methods.

John Banzhaf III (Lawyer) Power in weighted voting games.

Steven Brams (Political Scientist) Developer of approval voting and many striking examples of unexpected phenomena ("paradoxes" in voting).

Michel Balinski (Mathematician, but employed by an Econometrics Laboratory)

Hervé Moulin (Mathematician, but employed by an Economics Department)

Roth, Alvin (Economist) (Two sided markets.)

Shapley, Lloyd (Mathematician) (Game Theory)

H. P. Young (Mathematician, but employed by an Economics Department)

In economics one can divide the subject into "microeconomics" and "macroeconomics." Macro (large) problems deal with trade between countries, inflation, unemployment, monetary issues, economic development and fiscal policy. Micro (small) problems deal with consumer choice, price, production and cost, product markets, monopolistic competition, antitrust policy, labor, public choice, and market failure. Obviously, there are many areas of overlap between the two subjects.

In the area of fairness and equity issues there is a similar distinction. There are significant society issues of fairness that involve broad issues that often goes under the name of distributive justice. How should society organize itself for dealing with how it treats its citizens? If, as some claim, capitalism involves building up inequities between individuals (and hidden societal costs such as environmental damage), then society may choose to have some income or wealth transfer system so as to avoid "revolution." (Income involves short term payments for work or from investments in the form of money. Wealth involves the total monetary value of a person's possessions. A person may be wealthy because she owns land which could be sold for lots of money or have a painting that is very valuable but not have money in the bank (because she has little income) to pay for food the next day. On the other hand, a recent college graduate with an unusual mix of skills might have a high salary ($100,000 a year) but little wealth. Having large amounts of wealth in the hands of very few members of society has sometimes been the cause of revolutions. For example, some claim wealth concentration was one of the causes of the French Revolution. Voting systems are to some extent in this category because they affect the structure of society (e.g. does plurality voting discourage multiple parties?) and the way it makes decisions. Elections can also be thought of as much more of a "micro" phenomenon as well.

The other kind of fairness and equity questions are more "local." In a bankruptcy situation, where a collection of creditors have claims of different sizes on the remaining assets of a company, how should the remaining assets of the company be divided? Given the populations of each of the 50 states after a census, how many of the 435 seats in the House of Representatives should each state be given? In a divorce settlement, how should the properties of the couple be divided between the husband and wife? What is a fair tax policy for a mixed economy (e.g. a mixture of capitalism and government controls)?

Many fairness and equity questions are also of an "emotional" kind. When a famous basketball figure is accused of raping a woman, clearly there are many fairness issues that get raised. One can only hope that the fairness procedures built into the legal system of a democracy will get at the truth. In a case such as this, often only the two people involved can really know what happened.


(These questions are with regard to voting in a situation where a single winner is to be chosen. What other voting environments are you familiar with?)

1. What is involved with the design of a fair voting system in a democracy? (Remember that elections have been held in many countries that are far from being democracies.)

2. What do you think are virtues of plurality voting?

3. What do you think are the dangers of plurality voting?

4. What system of elections would you favor?