A, B, and C arc dividing 4 items from an inheritance using the method of sealed
ID: 3142702 • Letter: A
Question
A, B, and C arc dividing 4 items from an inheritance using the method of sealed bids. Their bids are below. The Bandana Republic is a small country consisting of four states: A: state A has a population of 3, 310,000 B: state B has a population of 2, 670,000 C: state C has a population of 1, 330,000 D: state D has a population of 690,000 Suppose that there are 160 seats (representatives) in the Bandana Congress to be apportioned among the four states based on their respective populations a. Find the standard divisor. b. Find each state's standard quota. e. Find the apportionment of the Bandana Republic Congress under the Hamilton's method using 160 seats. d. If MD = 49, 300 find the apportionment using Jefferson's method. e. If MD = 50,000 find the apportionment using Webster's method.Explanation / Answer
(1)
Given table calculated as below:
i.e., Total Value = (Dresser + Desk + Vanity + Tapestry)
Item value = Sum of all highest bids of each player
i.e., for player A
Item value = 220
for player B
Item value = 360
for player C
Item value = 300+550 = 850
A receives the desk and $140 in cash.
B receives the dresser only.
C receives the vanity and tapestry, but has to pay $380.
= (140+0-380)/3
= 80
Hence, summary table as below:
A
B
C
Dresser
200
360
350
Desk
220
200
210
Vanity
210
220
300
Tapestry
450
300
550
Total Value
1080
1080
1410
Fair Share
360
360
470
Item value
220
360
850
Money owed or owes
140
0
-380
Share of surplus money
80
80
80
Final settlement
220
80
-300
(2)
Given that,
State A has a population of 3,310,000
State B has a population of 2,670,000
State C has a population of 1,330,000
State D has a population of 690,000
Thus, total population = 3,310,000 + 2,670,000 + 1,330,000 + 690,000 = 8,000,000
and Total Seats = 160
(A)
Standard Divisor
The Standard Divisor is the average number of people per seat over the entire population.
Standard Divisor (SD) = (Total Population) / (Total number of seats)
Standard Divisor (SD) = 8,000,000 / 160
Standard Divisor (SD) = 50,000
(B)
Standard Quota
The Standard Quota is the fraction of the total number of seats a state would be entitled to if the seats were not indivisible.
Standard Quota (SQ) = (State Population) / (Standard Divisor)
thus, Standard Quota (SQ) of State A = (State A Population) / (Standard Divisor)
= (3,310,000) / (50,000)
= 66.2
Standard Quota (SQ) of State B = (State B Population) / (Standard Divisor)
= (2,670,000) / (50,000)
= 53.4
Standard Quota (SQ) of State C = (State C Population) / (Standard Divisor)
= (1,330,000) / (50,000)
= 26.6
Standard Quota (SQ) of State D = (State D Population) / (Standard Divisor)
= (690,000) / (50,000)
= 13.8
Hence, Standard Quota (SQ) of State A = 66.3
Standard Quota (SQ) of State B = 53.4
Standard Quota (SQ) of State C = 26.6
Standard Quota (SQ) of State D = 13.8
(C)
Hamilton’s Apportionment Method:
Step1. Calculate each state’s standard quota.
Step2. Give to each state its lower quota.
Step3. Give the surplus seats to the state with the largest fractional parts until there are no more surplus seats.
State
Population
Standard Divisor
Standard Quota
Lower Quota
Upper Quota
Fractional Parts
Surplus
Hamilton's Apportionment
A
3310000
50000
66.2
66
67
0.2
66
B
2670000
50000
53.4
53
54
0.4
53
C
1330000
50000
26.6
26
27
0.6
Second
27
D
690000
50000
13.8
13
14
0.8
First
14
Total
8000000
200000
160
158
162
2
2
160
Here difference between standard quota and lower quota is 2 seats. So, the surplus seats to the state with the first two largest fractional parts, i.e., State D and State C surplus one – one seat in our lower quota.
A
B
C
Dresser
200
360
350
Desk
220
200
210
Vanity
210
220
300
Tapestry
450
300
550
Total Value
1080
1080
1410
Fair Share
360
360
470
Item value
220
360
850
Money owed or owes
140
0
-380
Share of surplus money
80
80
80
Final settlement
220
80
-300
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