Hamilton\'s Method Question: In the country of Begonia, the national assembly mu
ID: 3120607 • Letter: H
Question
Hamilton's Method Question: In the country of Begonia, the national assembly must decide how to apportion its membership across the various states.
a) A certain Begonian state has a population of 5,800,000. The total population of Begonia is 310,000,000. How large does the house size "h" have to be for the state to have a lower quota of at least 8?
b) A state has a population of 5,800,000. THe house size in Begonia is 435. How small does the total population p of Begonia have to be for the state to have a lower quota of at least 8?
c) The total population of Begonia is 310,000,000. The house size is 435. How large does the population of a state have to be for the state to have a lower quota of at least 8?
Explanation / Answer
As per Hamilton's method,
Divisor, D = (Country Population)/(Size of House)
and State Quota = (State Population) /D.
(a)
Given lower quota of Bengonian state with population of 5,800,000 is 8.
=> maximum value of D= 5800000/8 =725000
=> Minimum Size of House = 31,000,000/ 725000 = 427.58
=> Minimum size of house (h) = 428.
(b)
Given lower quota of Bengonian state with population of 5,800,000 is 8.
=> maximum value of D= 5800000/8 =725000
Also given House size = 435
=> Minimum total population of Begonia = (435* 5800000)/ 8 = 315,375,000.
=> Total minimum population of Begonia = 315,375,000.
(C)
Given Total population of Begonia = 310,000,000
House size = 435
=> D = 310000000/435 = 712643.678
=> Population of state to have atleast 8 seats = 8*D = 5701149.42
=> Population of state have to be 5,701,150
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