Exam Review Suggestions	

•	Be able to apply the four different apportionment methods (Hamilton method, Jefferson method, Webster method, and Hill-Huntington).
•	Be able to explain the Alabama paradox and the population paradox.	
•	Know the quota condition and the methods that violate it. 
•	Be able to find the geometric mean of two numbers.
•	Be able to find the representative share and average district size of a state given an apportionment.
  You will be given the critical divisors formulas 

Sample Problems

1) Consider the three states with the populations shown below.  Use the given method of apportionment to distribute 40 representatives to the three states.

	State	Population	
	A	58,000	
	B	44,000	
	C	18,000	
	Total	120,000

a) Hamilton

b) Webster

2. Consider the three states with the populations shown below.  Use the given method of apportionment to distribute 17 representatives to the three states.

	State	Population	
	A	251,000	
	B	150,000	
	C	35,000	
	Total	436,000

a) Jefferson

b) Huntington – Hill

3. Two new apportionment methods are being tested.  
The two tables below give the apportionments assigned by the two methods.

 Method A		Method B	
State					State				
A	65	6.5	6		A	65	6.5	6	
B	19	1.9	2		B	19	1.9	3	
C	16	1.6	2		C	16	1.6	1	

What can you tell about the two methods from the data above?  (Circle one and then explain your choice.)

a. Both methods violate the quota condition.
b. Only method A violates the quota condition.
c. Only method B violates the quota condition.
d. Neither method violates the quota condition.

4. A country has 4 states, with populations 700254, 269117, 153232 and 3295 respectively. Their legislature has 41 seats. Find out how many seats each state will get by apportioning the seats using:

a. Hamilton method.

b. Jefferson method.

c. Webster method

d. Huntington-Hill method.

5. For the result of part d in number (4):
   
a. Find the representative share for each state.

b. Find the district population for each state.

6. Describe a situation that represents the Alabama paradox. With which apportionment methods can this happen?

7. Describe a situation that represents the population paradox. With which apportionment methods can this happen?

8. What is the quota condition? Which apportionment methods can violate it?