Technical Evaluation and Paradoxes
The largest remainder method is the only apportionment that satisfies the quota rule; in fact, it is designed to satisfy this criterion. However, it comes at the cost of paradoxical behaviour. The Alabama paradox is exhibited when an increase in seats apportioned leads to a decrease in the number of seats allocated to a certain party. Suppose 25 seats are to be apportioned between 6 parties with votes cast in the proportions 1500:1500:900:500:500:200. The two parties with 500 votes get three seats each. Now allocate 26 seats, and it will be found that the these parties get only two seats apiece.
With 25 seats, we get:
| Party | A | B | C | D | E | F | Total |
| Votes | 1500 | 1500 | 900 | 500 | 500 | 200 | 5100 |
| Seats | 25 | ||||||
| Hare Quota | 204 | ||||||
| Quotas Received | 7.35 | 7.35 | 4.41 | 2.45 | 2.45 | 0.98 | |
| Automatic seats | 7 | 7 | 4 | 2 | 2 | 0 | 22 |
| Remainder | 0.35 | 0.35 | 0.41 | 0.45 | 0.45 | 0.98 | |
| Surplus seats | 0 | 0 | 0 | 1 | 1 | 1 | 3 |
| Total Seats | 7 | 7 | 4 | 3 | 3 | 1 | 25 |
With 26 seats, we have:
| Party | A | B | C | D | E | F | Total |
| Votes | 1500 | 1500 | 900 | 500 | 500 | 200 | 5100 |
| Seats | 26 | ||||||
| Hare Quota | 196 | ||||||
| Quotas Received | 7.65 | 7.65 | 4.59 | 2.55 | 2.55 | 1.02 | |
| Automatic seats | 7 | 7 | 4 | 2 | 2 | 1 | 23 |
| Remainder | 0.65 | 0.65 | 0.59 | 0.55 | 0.55 | 0.02 | |
| Surplus seats | 1 | 1 | 1 | 0 | 0 | 0 | 3 |
| Total Seats | 8 | 8 | 5 | 2 | 2 | 1 | 26 |
Read more about this topic: Largest Remainder Method
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