Fred has an argument with the "Everyone Wins" scholarship committee. There are 7 scholarships to distribute among four schools, and Fred feels that the apportionment of scholarships per school is unfair (he is a student at school D listed below). The committee used Hamilton's method of apportionment to distribute the scholarships based on number of students attending each school and Fred feels there is a "more fair" method.

Learning Outcomes:

Upon completion of this lab you will be able to:

1.Apportion items using Alexander Hamilton's Method

2.Apportion items using Thomas Jefferson's Method

3.Apportion items using Daniel Webster's Method

4.Apportion items using John Quincy Adams' Method

5.Discuss whether an apportionment method has a paradox such as the Alabama Paradox, the Population Paradox, and the New-States Paradox

Procedure:

School

A

B

C

D

Total

# Students

752

101

99

98

1050

You are Fred's friend and you want to help him prove his point. You volunteer to use Hamilton's method, Jefferson's method, Webster's method and Adams' method of apportionment to determine which method is the "most fair".

1) a) List the apportionment for each method.

b) Considering all four methods of apportionment, which method do you feel is the "fairest"? How would you determine what is "most fair"?

c) In the next year, the population of Fred's school (and the other schools too) has changed. The studentpopulation of each school is now listed in the table below.Using Hamilton's method of apportionment,

how does the apportionment change from the previous year's apportionment? Is this a "fair"

apportionment? Explain your reasoning in depth and with complete sentences.

School

A

B

C

D

Total

# Students

753

377

96

97

1323

d) The selection committee made an error in omitting a fifth school, school E which has 126 students. Now the

selection committee must add 5 scholarships and re-apportion the scholarships amongst the five schools.

List the new apportionments using Hamilton's method. Is this new apportionment "fair"? How can

"fairness" be determined in this situation? Explain your reasoning in depth and with complete sentences.

e) Summarize what you have learned as a result of this lab in one or two paragraphs. Address points such as:

Is there a "best" apportionment method? Is this method ALWAYS better? Why or why not?

Is there an apportionment method you prefer over all others? Why?

Should new apportionment methods continue to be developed or do you feel current methods are sufficient (see the discussion assignment or research online)? Explain your views.