Fairness and Equity: Notes 6

Prepared by:

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



web page:


What are the basic principles of fairness?

In order to compare two different proposed solutions of a fairness problem one needs a way to tell whether one solution is better than another. One mechanism for doing this is to employ the concept of utility that has been developed by economists, mathematicians, and psychologists. The idea of utility is that every individual, due to that individual's uniqueness, has different ways of looking at the same object. People even look at money, which is more or less homogeneous and divisible, differently. Thus, if you have a very sore back even if you are poor, you might not bend over to pick up a dime you saw in the street. On the other hand, if you saw a $100 bill you might be tempted to pick it up, your back notwithstanding! One way to think of utility is that it is the "pleasure" or "value" that an individual assigns to the object. Not all objects are such that one wants more of them. For example, pollution or garbage put on one's front lawn is a not a "good" but a "negative." When being in a situation where one has to divide something "negative" (e.g. storing radioactive waste), these problems have quite a different flavor from those where one is dividing a "good."

If you have ever been at a child's birthday party you know how complex are the ways people think of the value, say, of birthday cake. Since cakes are typically not homogenous, some may care only for the icing, others only for the flowers, others for the chocolate part, while some other child might be allergic to chocolate.

It comes as a surprise to many people but when one has inhomogenous objects, one can often divide the object into many pieces where all the people involved in the division feel they have more than their fair share!

In a general way, here are some simple principles that come into play in fairness problems.

1. Proportionality: If there are n people dividing something, then each person should feel that he/she gets at least 1/n of the object being divided in that person's utility system. (This principle goes back to the work of Aristotle, who discusses the fact that often one has no choice but to treat people unequally. Sometimes one person may have a better claim of something that is to be divided than another person. In such cases it could be unfair to give them equal amounts.)

2. Envy. If someone has been awarded a piece of a cake as part of a fair division problem, one may none the less feel that someone else's piece is bigger than the piece one got. In a situation like this one is showing envy and would want to trade pieces (places) with the other person.

3. Efficiency (Pareto Optimality). One may have a fair division situation where everyone is happy with the piece of the pie they got and is not envious of any piece that another person has, but there may be a way of dividing the pie for which all the individuals concerned will be happier with their new piece and where none will feel worse off. There are two cases to consider here: case (I) A new solution where every one is happier, case (II) A new solution where some people are better off and none of the remaining people are worse off. The first is called Pareto Optimality and the second is called Weak Pareto Optimality.

Perhaps it does not surprise you that in many situations one can not have all of these three principles hold simultaneously. You can find out more about the basic fairness principles above on the web page:


Another consideration to take into account is whether or not people are truthful in reporting their preferences when one is carrying out a fair division or voting in an election. Perhaps if you know some else's views about what is being divided and the method being used to carry out the fair division, you can take advantage of this by lying about your true preferences. Thus, in a divorce settlement, one of the members of the couple may know the other person's views about the objects being divided and try to use this knowledge to get an advantage. Of course, this approach is available to both of the individuals. Ideally, one would like to find fair division methods that encourage people to be honest because being dishonest gives them no advantage.


1. Give as many examples as you can of situations where voting/elections take place. (You may want to jog your memory by picking "institutions" or environments and seeing where voting occurs for these cases:

a. Hospital

b. College

c. Public school system

d. Sports

e. Motion picture industry

f. Courts

g. Clubs

h. Federal administrative agencies (FDA, FCC, FAA, etc.)

i. Legislature

2. When a person votes, he/she express his/her opinions on the alternative available to chose from using a ballot. What are some of the different kinds of ballots that have been invented for voters to express their opinions on the alternative being voted on?