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A quota-capped divisor method is an apportionment method where we begin by assigning every state its lower quota of seats. Then, we add seats one-by-one to the state with the highest votes-per-seat average, so long as adding an additional seat does not result in the state exceeding its upper quota. [ 30 ]
Huntington-Hill uses a continuity correction as a compromise, given by taking the geometric mean of both divisors, i.e.: [4] A n = P n ( n + 1 ) {\displaystyle A_{n}={\frac {P}{\sqrt {n(n+1)}}}} where P is the population of the state, and n is the number of seats it currently holds before the possible allocation of the next seat.
An apportionment method always encourages schisms if the coalition receives at most + seats (in other words, it is merge-proof - two parties cannot gain a seat by merging). Among the divisor methods: [7]: Thm.9.1, 9.2, 9.3 Jefferson's method is the unique split-proof divisor method;
For illustration, continue with the above example of four parties. The advantage ratios of the four parties are 1.2 for A, 1.1 for B, 1 for C, and 0 for D. The reciprocal of the largest advantage ratio is 1/1.15 = 0.87 = 1 − π *. The residuals as shares of the total vote are 0% for A, 2.2% for B, 2.2% for C, and 8.7% for party D.
Initially, for each region a regional divisor is chosen using the highest averages method for the votes allocated to each regional party list in this region. For each party a party divisor is initialized with 1. Effectively, the objective of the iterative process is to modify the regional divisors and party divisors so that
The number of allocated seats for a given region increases from s to s + 1 exactly when the divisor equals the population of the region divided by s + 1/2, so at each step the next region to get a seat will be the one with the largest value of this quotient. That means that this successive adjustment method for implementing Webster's method ...
The goal is to find an apportionment method is a vector of integers , …, with = =, called an apportionment of , where is the number of seats allocated to party i. An apportionment method is a multi-valued function M ( t , h ) {\displaystyle M(\mathbf {t} ,h)} , which takes as input a vector of entitlements and a house-size, and returns as ...
The Hare quota was devised by Thomas Hare, one of the first to work out a complete STV system. In 1868, Henry Richmond Droop (1831–1884) invented the Droop quota as an alternative to the Hare quota. The Hare quota today is rarely used with STV due to fact that Droop is considered more fair to both large parties and small parties.