Sainte-Laguë Method

The Saine-Laguë method (also known as Webster method or divisor method with standard rounding) is a greater average method for assign seats in systems of proportional representation by electoral lists. The higher average methods are characterized by dividing the total votes obtained by the different parties through different divisors, producing sequences of decreasing quotients for each party and assigning seats to the highest averages. It is named after the French mathematician André Sainte-Laguë (1882-1950).

Proportional representation systems attempt to assign seats to lists in proportion to the number of votes received. In general, it is not possible to achieve exact proportionality, since it is not possible to assign a decimal number of seats. Of the methods commonly used for the proportional conversion of votes into seats, the Sainte-Laguë method is one of those that achieves greater proportionality.

The Sainte-Laguë method is applied in Germany, New Zealand, Norway, Sweden, Denmark, Bosnia and Herzegovina, Latvia, Kosovo, in the German states of Hamburg and Bremen, and in Ecuador for legislative elections.

Distribution

After counting all the votes, successive quotients are calculated for each electoral list. The formula for quotients is

${displaystyle quotient={frac {V}{2s+1}}}}}$

where:

• V represents the total number of votes received by the list.
• s represents the number of seats that each list has taken at the moment, initially 0 for each list.

The number of votes received by each list is successively divided by each of the values given by the formula 2s+1 when s is equal to 0, 1, 2, 3, etc.; which means dividing by 1, 3, 5, 7, etc. (i.e. the sequence of odd numbers). The allocation of seats is done by ordering the quotients from highest to lowest and assigning each one a seat until they are exhausted. Unlike other systems, the total number of votes does not intervene in the calculation.

Modified Sainte-Laguë Method

There is a variation of the Sainte-Laguë method well used and known as the Modified Sainte-Laguë Method, which consists of modifying the initial formula of each list (i.e., when ${displaystyle s=0}$, the party has not obtained any seat yet) so that the initial quotient is:

${displaystyle quotient;inicial={frac {V}{1.4}}}}$

and once each list obtains the first seat, I would use the standard method formula:

${displaystyle quotient={frac {V}{2s+1}}}}}$

Therefore the sequence of divisors would be: 1.4, 3, 5, 7 and the successive odd numbers.

Examples

Pure Sainte-Laguë Method

Modified Sainte-Laguë Method