Question

A small country consists of ve states, whose populations are A : 810, 000 B : 473, 000 C : 292, 000 D : 594, 000 E : 211, 000 If the legislature has 119 seats, apportion the seats using (a) Hamilton's Method (b) Jeerson's Method (c) Webster's Method (d) Huntington-Hill Method (e) Lowndes' metho

Answer 1

A. Hamilton Method :

	Total Seats	119
	Divisor	20000
States	Population	Quota	Initial	Final
A	810000	40.50	40	40
B	473000	23.65	23	24
C	292000	14.60	14	15
D	594000	29.70	29	30
E	211000	10.55	10	10
Total	2380000	119	116	119

The Divisor is obtained by dividing the total of population by total no of seats, which is 2380000/119.

The Quota is obtained by dividing the population with the divisor. The numbers highlighted in green are added 1 seats in the final quota , which takes the final total to 119.

B. Jefferson's Method :

	Total Seats	119
	Standard Divisor	20000
	Modified Divisor	19700
States	Population	Quota	Initial	Final
A	810000	41.12	41	41
B	473000	24.01	24	24
C	292000	14.82	14	14
D	594000	30.15	30	30
E	211000	10.71	10	10
Total	2380000	120.81	119	119

The Quota is obtained by dividing the population with the standard divisor. The sum total was 116. Now , the divisor is reduced until the number of seats , that are apportioned total to 119. Thus , we get the modified divisor as 19700.

C.Webster's Method :

In this case,

	Total Seats	119
	Standard Divisor	20000
	Modified Divisor	20100
States	Population	Quota	Initial	Final
A	810000	40.30	40	40
B	473000	23.53	24	24
C	292000	14.53	15	15
D	594000	29.55	30	30
E	211000	10.50	10	10
Total	2380000	118.41	119	119

When we divided the Population by standard divisor, we got the quota, when we rounded it off, we got the sum as 121. Now , we increased the divisor to 20100. Now ,when we round off the allocated quotas, we get the total as 119.

D. Huntington-Hill Method :

	Total Seats	119
	Standard Divisor	20000
	Modified Divisor	20100
States	Population	Quota	Lower Quota	Geometric Mean	Final
A	810000	40.299	40	40.49691346	40
B	473000	23.532	23	23.49468025	24
C	292000	14.527	14	14.49137675	15
D	594000	29.552	29	29.49576241	30
E	211000	10.498	10	10.48808848	10
Total	2380000	118.41	116	118.4668213	119

Geometric Mean is obtained by the formula , where n is the lower quota.

The highest of the geometric mean and the quota is considered and they are rounded off to get the final. The sum of final is calculated. If it is more than the total seats, then the modified divisor is used and the process is repeated until we get the sum of final apportion as total seats. In this case, the final allocations are shown in the table.