Suppose 36 representatives are to be divided amongst 6districts with populations

Question

Suppose 36 representatives are to be divided amongst 6districts with populations 27744, 25178, 19947, 14614, 9225, 3292, . Find the appointment according to the methods of Largest Fractors (LF), Greatest Divisions (GD) Major Fractors (MF) and Equal Proportions (EP). The constitution says each of the 50 states must get at least one representative. Given that 435 seats are to be distributed amongst the 50 states, show that for some set of state populations there is no way to distribute the representatives to satisfy the constitution and the lower and upper quota properties.

Explanation / Answer

36 representives in 6 places with population (27744,25178,19947,14614,9225,3292)

Total Population : 100000

for place 1) No of representatives are =(27744/100000)*36 = 9.98

for place 2) No of representatives are = (25178/100000)*36 = 9.06

for place 3) No of representatives are = (19947/100000)*0.36 = 7.18

for place 4) No of representatives are = 5.26

for place 5) No of representatives are = 3.32

for place 6) No of representatives are = 1.185

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