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Notes for Session 5, Part B


Note 3

In this part, you consider the fairness of different allocations: Which allocation is the most fair? Which allocation is the least fair?

These questions ask for more than a distinction between fair and unfair -- they suggest that there are degrees of unfairness. Come up with your own method for measuring degrees of fairness. Part of the point of this lesson is to realize that statistical measures are invented by people.

If you are working in a group, discuss several methods for measuring fairness.

<< back to Part B: Unfair Allocations

 

Note 4

Excesses and deficits show how far a stack is above or below the mean. Excesses and deficits also show how many moves are required to transform an allocation to a fair allocation. Keep in mind that the total excesses must equal the total deficits. This is the defining characteristic of the mean: It is the balance point for all the deviations from the mean.

In Problems B4 and B5, you investigate an algorithm to determine the number of moves required to transform an unfair allocation to a fair one. Then you think about how the number of moves required corresponds to the fairness of the allocation. In other words, how does the number of moves measure the degree of unfairness of an allocation?

<< back to Part B: Unfair Allocations

 

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