1. 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

2. What happens to p5 as we lower s?10 p5 8
.690
← s →
p5 bumped by 1 when s reaches 0.667
.667

3. What happens to p4 as we lower s?
p4 bumped up at these two s values 23
22 p4 21
.682
.652 10 p5 8
.667
← s →
.690

4. What happens to p3 as we lower s?39
38 p3 37
.684
.667 23
22 p4 21
.682
.652 10 p5 8
.667
← s →
.690

5. What happens to p2 as we lower s?52
51 p2 50
.673
.686 39
38 p3 37
.684
.667 23
22 p4 21
.682
.652 10 p5 8
.667
← s →
.690

6. What happens to p1 as we lower s?83
82 p1 81
.675
.683 52
51 p2 50
.673
.686 39
38 p3 37
.684
.667 23
22 p4 21
.682
.652 10 p5 8
.667
← s →
.690

7. Since we need 3 more seats, the first three that are bumped up get the seats83
82 p1 81
.675
.683 52
51 p2 50
.673
.686 39
38 p3 37
.684
.667 23
22 p4 21
.682
.652 10 p5 8
.667
← s →
.690

8. 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 6 8
197
200

9. Need a quick way to determine these divisor values83
82 p1 81
.675
.683 52
51 p2 50
.673
.686 39
38 p3 37
.684
.667 23
22 p4 21
.682
.652 10 p5 8
.667
← s →
.690

10. p1, with population 56, gets a bump to 82 when s = 56/8283
82 p1=56 81
.675
.683 52
51 p2=35 50
.673
.686 39
38 p3=26 37
.684
.667 23
22 p4=15 21
.682
.652 10
p5=6 8
.667
← s →
.690

11. p1, with population 56, gets a bump to 82 when s = 56/8283
82 p1 81
.675
82 p1=56
56/82 52
51 p2 50
.673
51 p2=35
.686 39
38 p3 37
.684
.667
38 p3=26 23
22 p4 21
.682
.652
22 p4=15 10 p5 8
p5=6
.667
← s →
.690

12. p1, with population 56, gets a bump to 83 when s = 56/8381
56/82
56/83
82 p1=56 52
51 p2 50
.673
51 p2=35
.686 39
38 p3 37
.684
.667
38 p3=26 23
22 p4 21
.682
.652
22 p4=15 10 p5 8
p5=6
.667
← s →
.690

13. p2, with population 35, gets a bump to 51 when s = 35/5183
82 p1 81
56/82
56/83
82 p1=56 52
51 p2 50
.673
51 p2=35
35/51 39
38 p3 37
.684
.667
38 p3=26 23
22 p4 21
.682
.652
22 p4=15 10 p5 8
p5=6
.667
← s →
.690

14. and so on… 83
82 p1 81
56/82
56/83
82 p1=56 52
51 p2 50
35/51
35/52
51 p2=35 39
38 p3 37
26/38
26/39
38 p3=26 23
22 p4 21
15/22
15/23
22 p4=15 10 p5 8
p5=8
6/9
← s →
.690

15. For a population pi with house seats ni, the divisor needed to get to ni+1 seats is
And so on …

16. In some cases, some populations get 2 seats before other can get 1
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

17. p1 bumped twice before p3, p4 bumped once
Again, need 3 seats, so the first three bumps get the seats
10.11
9.97
10.05
9.57
9.43
9.25
10.12
← s → 71
70 p1 69 21
20 p2 19 p3 6 p4 3
p1 bumped twice before p3, p4 bumped once

18. Again, need 3 seats, so the first three bumps get the seats
10.11
9.97
10.05
9.57
9.43
9.25
10.12
← s → 71
70 p1 69 21
20 p2 19 p3 6 p4 3
In fact…

19. p1 would be bumped many times before p3, p471
70 p1 69 21
20 p2 19 p3 6 p4 3
10.11
9.97
10.05
9.57
9.43
9.25
10.12
← s → 72 73
9.83
9.69
p1 would be bumped many times before p3, p4

20. Final Result p1 bumped twice to 71 p2 bumped to 20 pi Initial Final
708 69 71
201 19 20 66 6 37 3 97
100

21. Another example with four states, where p = 1000, h=100 and s = 10pi
ni = floor(pi/s)
949 94 18 1 17 16
Total: 97

22. In this case p1 is the only one that is bumped… 98 97
9.68
96 p1 95 94 p2 1 p3 p4
9.78
9.89
9.99 9
8.5 8
← s → 10
In this case p1 is the only one that is bumped

23. Final Result p1 bumped three times to 97 pi Initial Final 949 94 97 1817 16
100