1. Jefferson Method Example Populations 56, 35, 26, 15, 6 –Total population p = 138 House size h = 200 –Standard divisor s = p/h =.69 pipi p i /sn i = floor(p i /s) 5681.15981 3550.72550 2637.68137 1521.73921 68.6968 Total: 197← must fill 3 seats

2. What happens to p 5 as we lower s?.667 10 9 p 5 8.690 ← s → p 5 bumped by 1 when s reaches 0.667

3. What happens to p 4 as we lower s? 23 22 p 4 21 10 9 p 5 8.682.652.667.690 ← s → p 4 bumped up at these two s values

4. What happens to p 3 as we lower s? 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8.684.667.682.652.667.690 ← s →

5. What happens to p 2 as we lower s? 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8.686.673.684.667.682.652.667.690 ← s →

6. What happens to p 1 as we lower s? 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8.683.675.686.673.684.667.682.652.667.690 ← s →

7. Since we need 3 more seats, the first three that are bumped up get the seats 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8.683.675.686.673.684.667.682.652.667.690 ← s →

8. Final Result p 2 bumped to 51 p 1 bumped to 82 p 3 bumped to 38 pipi InitialFinal 568182 355051 263738 1521 688 97100

9. Need a quick way to determine these divisor values 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8.683.675.686.673.684.667.682.652.667.690 ← s →

10. p 1, with population 56, gets a bump to 82 when s = 56/82 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8.683.675.686.673.684.667.682.652.667.690 ← s →

11. p 1, with population 56, gets a bump to 82 when s = 56/82 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 8 56/82.675.686.673.684.667.682.652.667.690 ← s →

12. p 1, with population 56, gets a bump to 83 when s = 56/83 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 856/82 56/83.686.673.684.667.682.652.667.690 ← s →

13. p 2, with population 35, gets a bump to 51 when s = 35/51 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 856/82 56/83 35/51.673.684.667.682.652.667.690 ← s →

14. and so on… 83 82 p 1 81 52 51 p 2 50 39 38 p 3 37 23 22 p 4 21 10 9 p 5 856/82 56/83 35/51 35/52 26/38 26/39 15/22 15/23 6/9.690 ← s →

15. For a population p i with house seats n i, the divisor needed to get to n i +1 seats is d i = pipi n i + 1 To get to n i +2 seats: d i = pipi n i + 2 And so on …

16. 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 pipi n i = floor(p i /s) 70869 20119 666 373 Total: 97

17. 71 70 p 1 69 21 20 p 2 19 7 p 3 6 4 p 4 3 10.11 9.97 10.05 9.57 9.43 9.25 10.12 ← s → p 1 bumped twice before p 3, p 4 bumped once Again, need 3 seats, so the first three bumps get the seats

18. 71 70 p 1 69 21 20 p 2 19 7 p 3 6 4 p 4 3 10.11 9.97 10.05 9.57 9.43 9.25 10.12 ← s → In fact… Again, need 3 seats, so the first three bumps get the seats

19. p 1 would be bumped many times before p 3, p 4 71 70 p 1 69 21 20 p 2 19 7 p 3 6 4 p 4 3 10.11 9.97 10.05 9.57 9.43 9.25 10.12 ← s → 72 73 9.83 9.69

20. Final Result p 1 bumped twice to 71 p 2 bumped to 20 pipi InitialFinal 7086971 2011920 6666 3733 97100

21. Another example with four states, where p = 1000, h=100 and s = 10 pipi n i = floor(p i /s) 94994 181 171 161 Total: 97

22. 96 p 1 95 94 2 p 2 1 2 p 3 1 2 p 4 1 In this case p 1 is the only one that is bumped 9.99 9.89 9 8.5 8 10 ← s → 97 98 9.78 9.68 …

23. Final Result p 1 bumped three times to 97 pipi InitialFinal 9499497 1811 1711 1611 97100