Increasing the number of seats to be shared out can reduce the number a state receives.
The census clerk C. W. Seaton found it in 1880: a House of 299 seats gave Alabama eight, and a House of 300 gave it seven. The cause is the largest-remainder method, in which enlarging the total changes every state's quota and reshuffles the order of the remainders. The United States eventually abandoned the method, and Balinski and Young later proved that no apportionment rule avoids every paradox of this kind.
In practice
- A funding formula that shares grants by rounded shares gives a small department less money after the total pot grows.
- A school adds a place to every year group and one class loses a teacher.
- Standing
- Mathematically settled, and the reason apportionment rules are chosen by which paradoxes they avoid rather than by intuition. Compare Arrow's impossibility theorem.
- Subject
- Law & Politics
- Essay
- The paradoxes of democracy and the quips of partisans