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Learning Math Home
Session 5, Part B: Unfair Allocations
Session5 Part A Part B Part C Part D Part E Homework
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Session 5 Materials:

Session 5, Part B:
Unfair Allocations (25 minutes)

In This Part: Fair and Unfair Allocations | Measuring the Degree of Fairness
Looking at Excesses and Deficits

The average for a set of data corresponds to the equal-shares allocation or fair allocation of the data. For example, suppose that each of 9 people has several dollars and altogether they have $45. The mean of $5 represents the number of dollars each of the 9 people would get if they combined all their money and then redistributed it fairly (i.e., equally).

As seen in Problem A3, the fair allocation of 45 coins into 9 stacks is to place 5 coins in each stack, as follows:

Here is a second allocation of the 45 coins, which is almost fair:

The above allocation is almost fair because most stacks have 5 coins, and the others have close to 5. But, the following allocation of 45 coins doesn't seem fair at all:

Problem B1


Look at these five allocations:

Allocation A

Allocation B

Allocation C

Allocation D

Allocation E

Rank the five allocations on their "fairness," from most fair to least fair. Also, explain how you decided on the level of "unfairness" in an allocation.

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Although there are many different ways to think about "unfairness," one way is to consider the number of exchanges that would have to take place in order to achieve a fair allocation.    Close Tip

Next > Part B (Continued): Measuring the Degree of Fairness

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