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The two names for these methods—highest averages and divisors—reflect two different ways of thinking about them, and their two independent inventions. However, both procedures are equivalent and give the same answer. [1] Divisor methods are based on rounding rules, defined using a signpost sequence post(k), where k ≤ post(k) ≤ k+1.
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 is denoted by a multivalued function (,); a particular -solution is a single-valued function (,) which selects a single apportionment from (,). A partial apportionment method is an apportionment method for specific fixed values of n {\displaystyle n} and h {\displaystyle h} ; it is a multivalued function M ∗ ( t ...
Jefferson's method uses a quota (called a divisor), as in the largest remainder method. The divisor is chosen as necessary so that the resulting quotients, disregarding any fractional remainders, sum to the required total; in other words, pick a number so that there is no need to examine the remainders. Any number in one range of quotas will ...
[1] [4] [5] [6] While favoring large parties reduces political fragmentation, this can be achieved with electoral thresholds as well. The Sainte-Laguë method shows fewer apportionment paradoxes compared to largest remainder methods [ 7 ] such as the Hare quota and other highest averages methods such as d'Hondt method .
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers ...
Biproportional apportionment is a proportional representation method to allocate seats in proportion to two separate characteristics. That is, for two different partitions each part receives the proportional number of seats within the total number of seats.
When using the Hare quota, this rule is called Hamilton's method, and is the third-most common apportionment rule worldwide (after Jefferson's method and Webster's method). [ 1 ] Despite their intuitive definition, quota methods are generally disfavored by social choice theorists as a result of apportionment paradoxes .