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
Average state apportionment size: 

State	Population	Quota	Lower quota	Apportionment	
A	58,000	19.33	19	19	
B	44,000	14.67	14	15	
C	18,000	6.00	6	6	
Total	120,000		39	40	

b. Webster

State	Population	Quota	Tent. App.	Final App.	
A	58,000	19.33	19	19	
B	44,000	14.67	15	15	
C	18,000	6.00	6	6	
Total	120,000		40	40	
(Since the tentative apportionment gives 40 seats, the final apportionment is the same as the tentative apportionment. There is no need to add or subtract seats.)

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
Average state apportionment size: 

State	Population 	Quota 	Lower Quota 		
A	251,000	9.79	9		
B	150,000	5.85	5		
C	35,000	1.36	1		
Total	436,000		15		

The total lower quota is only 15. This means we still have 2 extra seats. The first extra seat will be given to A since this state has the highest .

State	Population 	Lower Quota 		Final App.	
A	251,000	10		10	
B	150,000	5		6	
C	35,000	1		1	
Total	436,000	16		17	

Since B has the highest , the last extra seat should be given to B.

b. Huntington – Hill

State	Population
	Quota
			Geometric mean
	Tent. App.		Final App.	
A	251,000	9.79	9	10		10	26457.257	10	
B	150,000	5.85	5	6		6	27383.755	6	
C	35,000	1.36	1	2		2	24752.495	1	
Total	436,000					18		17	

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.

Method B violates the quota condition because state B’s apportionment is 3 while its quota is 1.9. This means state B’s apportionment is not either its lower quota (1) nor its upper quota (2).
Method A does not violate the quota condition because all of the states’ apportionments are either equal to lower quotas or upper quotas.  

c is the correct choice

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.
25, 10, 6, 0

b. Jefferson method.
26, 10, 5, 0

c. Webster method
25, 10, 6, 0

d. Huntington-Hill method.
25, 10, 5, 1

5. For the result of part d in number (4),

a. Find the representative share for each state.

.0000357, .0000372, .0000326, .000305

b. Find the district population for each state.
28010.04, 26911.7, 30646.4, 3295

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

The number of seats in the house increases from a previous year, yet in the new apportionment, a state loses a seat. This can happen with the Hamilton method

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

A state whose population has decreased gains a seat in new apportionment, while a state whose population has increased loses a seat.  This can happen with the Hamilton method.

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

Every state’s apportionment should be either its upper or lower quota. All the divisor methods (Jefferson, Webster, and Hill-Huntington) can violate it.