Comparisons: Sainte-Laguë ~ Maps 1

Two-Party Sainte-Laguë Party-List Maps

Two-party maps contain all the possible election outcomes for a given number of winners in a two-party election. The maps for two parties A and B contesting up to six vacancies in closed Sainte-Laguë Party-List elections are shown below. Recall that the actual per-unit tally shares for A and B are represented by the appropriate point along the line. The domain boundaries of an optimally proportional voting (OPV) system are indicated by the dotted markers underneath the line. These optimal boundaries are necessarily midway between the dots that represent perfect proportionality between the outcome seat share ratio (as stated underneath the dot) and the tally share ratio (point on the line) as defined by the voters.

The boundaries for the Sainte-Laguë domains are determined by the various two-way critical ties that may occur in elections with W winners. For the specific details of how party stick diagrams are used to deduce the position of these boundaries, please refer to the Map Construction appendix for the Two-Party Sainte-Laguë Method Maps page.

At least for two parties, it is clear from the above maps that the Sainte-Laguë method is an optimally proportional voting (OPV) system. Let the length of an inner domain be one unit. The length of each end domain is therefore a half-unit. Starting at either end, the domain boundaries occur at intervals of 1/2, 3/2, 5/2 units and so on from that end. Notice that the numerator sequence is 1, 3, 5 and so on. It is no co-incidence that these numbers are also the divisors used in the Sainte-Laguë method. In fact, this sequence of divisors was deliberately chosen so that optimum proportionality would inherently be achieved. It makes no difference how many seats are available, the outcome is always optimal for two competing parties.

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