Quota rule
Quota rule
In mathematics and political science, the quota rule describes a desired property of proportional apportionment methods. It says that the number of seats allocated to a party should be equal to their entitlement plus or minus one. The ideal number of seats for a party, called their seat entitlement, is calculated by multiplying each party's share of the vote by the total number of seats. Equivalently, it is equal to the number of votes divided by the Hare quota. For example, if a party receives 10.56% of the vote, and there are 100 seats in a parliament, the quota rule says that when all seats are allotted, the party may get either 10 or 11 seats. The most common apportionment methods (the highest averages methods) violate the quota rule in situations where upholding it would cause a population paradox, although unbiased apportionment rules like Webster's method do so only rarely.
Mathematics The entitlement for a party (the number of seats the party would ideally get) is: :<math> \frac{\text{Votes}_\text{party}}{\#\text{Votes}} \cdot \#\text{Seats} </math>
The lower frame is then the entitlement rounded down to the nearest integer while the upper frame is the entitlement rounded up. The frame rule states that the only two allocations that a party can receive should be either the lower or upper frame. For instance, although largest remainder method satisfies the quota rule, it violates the Alabama paradox and the population paradox. The theorem itself is broken up into several different proofs that cover a wide number of circumstances.
Specifically, there are two main statements that apply to the quota rule: * Any method that follows the quota rule must fail the population paradox.
The D'Hondt method, also known as the Jefferson method sometimes violates the quota rule by allocating more seats than the upper frame allowed. Since Jefferson was the first method used for Congressional apportionment in the United States, this violation led to a substantial problem where larger states often received more representatives than smaller states, which was not corrected until Webster's method was implemented in 1842. Although Webster's method can in theory violate the quota rule, such occurrences are extremely rare.