Daisyree Dayto Guelas

BSA 1A

1. A certain school activity has six events with 245, 350, 300, 192, 274, and 414 participants,
respectively. If 52 facilitators are to be apportioned based on the number of participants. How
many facilitators should each event have?
Standard divisor (D) = 1775/52 = 34.13
a. Hamilton plan

Events Population Quotient Standard Additional No. of

Quota (a) representatives
1 245 7.18 7 0 7
2 350 10.25 10 0 10
3 300 8.79 8 1 9
4 192 5.63 5 1 6
5 274 8.03 8 0 8
6 414 12.13 12 0 12
Total 1,775 50 52

b. Jefferson plan
Let dm = 32

Events Population Quotient Standard

Quota (a)
1 245 7.66 7
2 350 10.94 10
3 300 9.38 9
4 192 6 6
5 274 8.56 8
6 414 12.94 12
Total 1,775 52

c. Adam's method
L dm = 36

Events Population Quotient Standard

Quota (a)
1 245 6.80 7
2 350 9.72 10
3 300 8.33 9
4 192 5.33 6
5 274 7.61 8
6 414 11.5 12
Total 1,775 52

d. Webster's method

Events Population Quotient Standard

Quota (a)
1 245 7.18 7
2 350 10.25 10
3 300 8.79 9
4 192 5.63 6
5 274 8.03 8
6 414 12.13 12
Total 1,775 52

e. If another facilitator is added which makes it 53 facilitators, which event deserve the additional
facilitator?
Standard Divisor = 1,775 / 53 = 33.49
For 53 representatives

Events Population Quotient Standard Additional No. of

Quota (a) representatives
1 245 7.32 7 0 7
2 350 10.45 10 1 11
3 300 8.96 8 1 9
4 192 5.73 5 1 6
5 274 8.18 8 0 8
6 414 12.36 12 0 12
Total 1,775 50 53

Summary of Apportionment for 52 & 53 representatives

Events Population Hamilton’s Hamilton’s

 Method for 52 Method for 53
representatives representatives
1 245 7 7
2 350 10 11
3 300 9 9
4 192 6 6
5 274 8 8
6 414 12 12
Total 1,775 52 53

2. Using Adam's method a certain option receives 20 representatives while using Webster's method
it receives 19 representatives, which fairness for apportionment is violated.
According to the Adams Method, there are 20 representatives who meet the Standard Quota.
Webster's Method, on the other hand, assigns 19 representatives, one less than the Standard Quota.
Since, Webster’s method allocates 1 less than the standard quota, therefore, it violates Quota Rule.

3. State A has population 10,500 with 20 representatives and State B has a population of 13,750
with 25 representatives. If one representative is added which state deserves the additional
representative using absolute unfairness of an apportionment? Which state deserves the additional
representative using Hunting - Hill Apportionment Method?

States Population Representatives Average Average

Constituency(Old) Constituency
(New)
A 10,500 20 525 500
B 13,750 25 550 529

For Possibility 1: | Average Constituency of A – Average Constituency of B |

500 – 550 = 50

For Possibility 2: | Average Constituency of A – Average Constituency of B |

525 – 529 = 4

State A’s average State B’s average Absolute Unfairness of

Constituency Constituency Apportionment

State A receives the 500 550 50

new representative
State B receives the 525 529 4
new representative

State B seem to receive and representative because it has smaller unfairness of apportionment.
4. In your own opinion briefly explain which among the apportionment method the best is.
Hamilton's Method would be my choice because it was the first and fundamental of all extant
apportionment method. It was also simple to implement and comprehend. Finally, based on my
response, I observe that regardless of the approach employed, the outcomes are all the same, so why?
If Hamilton's Method can be used, go with the more complicated option. I understand that each has its
own function, but for the purposes of this question, the Hamilton's Method is the best for me.