jefferson method example
DESCRIPTION
Populations 56, 35, 26, 15, 6 Total population p = 138 House size h = 200 Standard divisor s = p/h = .69. Jefferson Method Example. Total: 197. ← must fill 3 seats. 10. 9 p 5. 8. p 5 bumped by 1 when s reaches 0.667. .667. ← s →. .690. What happens to p 5 as we lower s?. 23. - PowerPoint PPT PresentationTRANSCRIPT
Jefferson Method Example• Populations 56, 35, 26, 15, 6
– Total population p = 138
• House size h = 200– Standard divisor s = p/h = .69
pi pi/s ni = floor(pi/s)
56 81.159 81
35 50.725 50
26 37.681 37
15 21.739 21
6 8.696 8
Total: 197 ← must fill 3 seats
What happens to p5 as we lower s?
.667
109 p58
.690← s →
p5 bumped by 1 when s reaches 0.667
What happens to p4 as we lower s?
2322 p421
109 p58
.682.652
.667
.690← s →
p4 bumped up at these two s values
What happens to p3 as we lower s?
3938 p337
2322 p421
109 p58
.684.667
.682.652
.667
.690← s →
What happens to p2 as we lower s?
5251 p250
3938 p337
2322 p421
109 p58
.686.673
.684.667
.682.652
.667
.690← s →
What happens to p1 as we lower s?
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
.683.675
.686.673
.684.667
.682.652
.667
.690← s →
Since we need 3 more seats, the first three that are bumped up get the seats
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
.683.675
.686.673
.684.667
.682.652
.667
.690← s →
Final Result
• p2 bumped to 51
• p1 bumped to 82
• p3 bumped to 38
pi Initial Final
56 81 82
35 50 51
26 37 38
15 21 21
6 8 8
97 100
Need a quick way to determine these divisor values
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
.683.675
.686.673
.684.667
.682.652
.667
.690← s →
p1, with population 56, gets a bump to 82 when s = 56/82
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
.683.675
.686.673
.684.667
.682.652
.667
.690← s →
p1, with population 56, gets a bump to 82 when s = 56/82
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
56/82.675
.686.673
.684.667
.682.652
.667
.690← s →
p1, with population 56, gets a bump to 83 when s = 56/83
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
56/8256/83
.686.673
.684.667
.682.652
.667
.690← s →
p2, with population 35, gets a bump to 51 when s = 35/51
8382 p181
5251 p250
3938 p337
2322 p421
109 p58
56/8256/83
35/51.673
.684.667
.682.652
.667
.690← s →
and so on…8382 p181
5251 p250
3938 p337
2322 p421
109 p58
56/8256/83
35/5135/52
26/3826/39
15/2215/23
6/9
.690← s →
For a population pi with house seats ni, the divisor needed to get to ni+1 seats is
di =pi
ni + 1
To get to ni+2 seats:
di =pi
ni + 2
And so on …
In some cases, some populations get 2 seats before other can get 1. Consider the following example with four states, where p = 1012, h=100 and s = 10.12
pi ni = floor(pi/s)
708 69
201 19
66 6
37 3
Total: 97
7170 p169
2120 p219
7 p36
4 p43
10.119.97
10.059.57
9.43
9.25
10.12← s →
p1 bumped twice before p3, p4 bumped once
Again, need 3 seats, so the first three bumps get the seats
7170 p169
2120 p219
7 p36
4 p43
10.119.97
10.059.57
9.43
9.25
10.12← s →
In fact…
Again, need 3 seats, so the first three bumps get the seats
p1 would be bumped many times before p3, p4
7170 p169
2120 p219
7 p36
4 p43
10.119.97
10.059.57
9.43
9.25
10.12← s →
7273
9.839.69
Final Result
• p1 bumped twice to 71
• p2 bumped to 20
pi Initial Final
708 69 71
201 19 20
66 6 6
37 3 3
97 100
Another example with four states, where p = 1000, h=100 and s = 10
pi ni = floor(pi/s)
949 94
18 1
17 1
16 1
Total: 97
96 p19594
2 p21
2 p31
2 p41
In this case p1 is the only one that is bumped
9.999.89
9
8.5
8
10← s →
9798
9.789.68
…
Final Result
• p1 bumped three times to 97
pi Initial Final
949 94 97
18 1 1
17 1 1
16 1 1
97 100