EXAMPLE 14 Using the d’Hondt Method
We will use the d’Hondt method to apportion the first 30 seats in the parliament of Example 9 (page 584), based on the data from the first election. The calculations are presented in Table 14.14, a d’Hondt table. There is a column in the table for each party. The first entry in each column is the number of votes that the party received—the party’s initial priority number. Running down each column, the entries are the number of votes for the parties divided by 2, 3, 4, and so on. When a seat is awarded, the priority number for the party that receives the seat is crossed out because it has been used. The next seat goes to the party with the highest priority that has not been crossed out.
| Apportioned | Whigs | Tories | Liberals | Centrists |
|---|---|---|---|---|
| 1 | #1 5,525,381 | #3 3,470,152 | #2 3,864,226 | 201,203 |
| 2 | #4 2,762,691 | #7 1,735,076 | #5 1,932,113 | 100,602 |
| 3 | #6 1,841,794 | #10 1,156,717? | #9 1,288,075 | 67,068 |
| 4 | #8 1,381,345 | #14 867,538 | #12 966,057 | 50,301 |
| 5 | #11 1,105,076 | #17 694,030 | #16 772,845 | 40,241 |
| 6 | #13 920,897 | #21 578,359 | #19 644,038 | 33,534 |
| 7 | #15 789,340 | #25 495,736 | #23 552,032 | 28,743 |
| 8 | #18 690,673 | #28 433,769 | #26 483,028 | 25,150 |
| 9 | #20 613,931 | 385,572 | #29 429,358 | 22,356 |
| 10 | #22 552,538 | 347,015 | 386,423 | 20,120 |
| 11 | #24 502,307 | 315,468 | 351,293 | 18,291 |
| 12 | #27 460,448 | 289,179 | 322,019 | 16,767 |
| 13 | #30 425,029 | 266,935 | 297,248 | 15,477 |
| 14 | 394,670 | 247,868 | 276,016 | 14,372 |
At any stage of the d’Hondt process, we can see how many seats have been assigned to a party: it is the number of entries in its column that have been crossed out. if a party has been assigned seats so far, the first remaining entry in its column is its population divided by .
As shown in the table, the Whigs get the first seat. The first priority number is marked #1 and gets crossed out because it has been used. The greatest remaining priority number is for the Liberals, who get the second seat. As seats are awarded, the priority numbers are numbered in sequence and crossed out, in decreasing order. The number of seats awarded to each party is equal to the number of numbers crossed out in its column. Of the first 30 seats, the Whigs get 13, the Tories get 8, the Liberals get 9, and the Centrists get none.