Sainte-Laguë method

The Webster/Sainte-Laguë Method is a Highest averages method used for allocating seats proportionally for representative assemblies with party list voting systems. It works like D'Hondt method, except that you use divisors 1, 3, 5, 7, ... instead of 1, 2, 3, 4, ...

In the modified Sainte-Laguë method, the first divisor is modified to 1.4. The sequence of divisors is then 1.4, 3, 5, 7, ... The modified Sainte-Laguë method is used for elections to the Danish parliament.

Allocation
After all the votes have been tallied, successive quotas are calculated for each party. The formula for the quotient is


 * $$\text{quotient} = \frac V {2s+1}$$

where:


 * V is the total number of votes that party received, and
 * s is the number of seats that have been allocated so far to that party, initially 0 for all parties.

Whichever party has the highest quotient gets the next seat allocated, and their quotient is recalculated. The process is repeated until all seats have been allocated.

The Webster/Sainte-Laguë method does not ensure that a party receiving more than half the votes will win at least half the seats; nor does its modified form.

Extensions of theory
Several cardinal PR methods reduce to Sainte-Laguë if certain divisors are used. Some of which are:


 * Sequential proportional approval voting
 * Single distributed vote
 * Reweighted Range Voting