In the rest of this test we try to apportion ten seats among

In the rest of this test we try to apportion ten seats among the states A,B,C and D in the following table using the Hill Huntington procedure. Test a divisor of 951 to determine if it is a proper divisor (i-e. apportions the ten seats) for the Hill Huntington procedure. If it is not a proper divisor. do you need to go higher or lower to find a proper divisor? Test a divisor of 953 to determine if it is a proper divisor (i.e. apportions the ten seats) for the Hill Huntington procedure. If it is not a proper divisor. do you need to go higher or lower to find a proper divisor? Find a proper divisor for the Hill Huntington procedure and use it to apportion the ten seats. Has the quota rule been violated? Explain

Solution

I will try to find out the solution. First of all, i will consider the Hill-Huntington method

Total population = 10000,

seats to be apportioned =10,

Standard Divisor = total population/ seats to be apportioned

SD =10000/10= 1000,

Standard Quota =SQ = State population/ SD,

SQ_A = 5963/1000=5.963,

SQ_B = 1347 /1000 =1.347,

SQ_C = 1346/1000 =1.346,

SQ_D = 1344/1000 =1.344

Upper Quota = UQ

Lower Quota = LQ

UQ_A= 6, LQ_A=5, _____________Geometric_mean =G_M_A =sqrt(UQ_A*LQ_A)=sqrt(30)=5.4772

UQ_B=2, LQ_B=1_____________________________G_M_B =sqrt(2)=1.4142

UQ_C=2, LQ_C=1____________________________ G_M_C =sqrt(2)=1.4142

UQ_D=2, LQ_D=1____________________________G_M_D =sqrt(2)=1.4142

Therefore

State A = 6 seats

State B = 1 seats

State C = 1 seats

State D = 1 seats

total seats 9 < seats to be apportioned  =10,

_______________________________________________

Now let us consider a Modified divisor 951

Modified Divisor =MD = 951;

SQ_A = 5963/951=6.2702_____________________U_Q_A=7, L_Q_A=6,__________G_M_A= 6.4807

SQ_B = 1347 /951 =1.4164____________________U_Q_B=2, L_Q_A=1___________G_M_B =1.4142

SQ_C = 1346/951 = 1.4154____________________U_Q_C=2, L_Q_C=1___________G_M_C =1.4142

SQ_D = 1344/951 = 1.4132____________________U_Q_D=2. L_Q_D=1___________G_M_D =1.4142

then,

State A = 6 seats

State B = 2 seats

State C = 2 seats

State D = 1 seats

total seats 11 > seats to be apportioned  =10,

______________________________________________

Now, let us consider the modified divisor 953

Modified Divisor =MD = 953;

SQ_A = 5963/953 = 6.2571 _____________________U_Q_A=7, L_Q_A=6,__________G_M_A= 6.4807

SQ_B = 1347 /953 = 1.4134 ____________________U_Q_B=2, L_Q_A=1___________G_M_B =1.4142

SQ_C = 1346/953 = 1.4124 ____________________U_Q_C=2, L_Q_C=1___________G_M_C =1.4142

SQ_D = 1344/953 = 1.4103 ____________________U_Q_D=2. L_Q_D=1___________G_M_D =1.4142

then,

State A = 6 seats

State B = 1 seats

State C = 1 seats

State D = 1 seats

total seats 9 < seats to be apportioned  =10,

____________________________________________

I think the modified divisor should be a number such that 951 < MD < 953. I will try MD=952.

Modified Divisor =MD = 952;

SQ_A = 5963/952 = 6.2637 _____________________U_Q_A=7, L_Q_A=6,__________G_M_A= 6.4807

SQ_B = 1347 /952 =1.4149 ____________________U_Q_B=2, L_Q_A=1___________G_M_B =1.4142

SQ_C = 1346/952 = 1.4139 ____________________U_Q_C=2, L_Q_C=1___________G_M_C =1.4142

SQ_D = 1344/952 = 1.4118 ____________________U_Q_D=2. L_Q_D=1___________G_M_D =1.4142

then,

State A = 6 seats

State B = 2 seats

State C = 1 seats

State D = 1 seats

total seats 10 = seats to be apportioned  =10,