A highest-averages method, also called a divisor method, is a class of methods for allocating seats in a parliament among agents such as
political parties or
federal states
A federation (also known as a federal state) is a political entity characterized by a union of partially self-governing provinces, states, or other regions under a central federal government (federalism). In a federation, the self-governi ...
. A divisor method is an
iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''n''-th approximation is derived from the pr ...
: at each iteration, the number of votes of each party is divided by its ''divisor'', which is a function of the number of seats (initially 0) currently allocated to that party. The next seat is allocated to the party whose resulting ratio is largest.
Definitions
The inputs to a divisor method are the number of seats to allocate, denoted by ''h'', and the vector of parties' entitlements, where the entitlement of party
is denoted by
(a number between 0 and 1 determining the fraction of seats to which
is entitled). Assuming all votes are counted,
is simply the number of votes received by
, divided by the total number of votes.
Procedural definition
A divisor method is parametrized by a function
, mapping each integer
to a real number (usually in the range