Siedem method

Siedem method

Current convocation of the Sekidean Assembly has been elected using the Siedem Method

The Siedem Method is a method for allocating seats in parliaments among member states, or in party-list proportional representation systems.

Devised by a Zhoushi mathematician Чaraƌa Siedem, it is currently used to allocate seats in the Assembly of the Sekidean Parliament.

Motives

See also: Sekidean Parliament, Sekidean Assembly, Sekidean Union, and Inner Sekidean Union

Logo of the Assembly of the Sekidean Parliament

The Siedem Method was devised in early 1990's, when the early Sekidean Parliament was established. The motives behind this method are, that it serves to assign seats to countries and parties on a regional basis, ensuring, that each country has notable representation in the join parliament, while it still does keep a sense of proportionality. Given the number of coefficients, especially the S_Σ, S_R and Π_Ω, modifying the method allows to update it without the need to change it completely.

This method was designed specifically as a compromise between perfect proportionality per population and per country, creating an equilibrium between smaller and larger states of the Inner Sekidean Union. Its method ensures, that while the more populous countries have more MPs, average voter of a larger country has lesser voting power than the one of a smaller one.

Usage of the method

District allocation

Seats are assigned based on the formula:

x_S = ⌊P_C × (S_Σ - S_R × M) ÷ P₀⌋ + S_R

where:

x_S is the number of assigned seats to the district

P_C is the voter pool of the district in question

S_Σ is the number of total seats available (in ISUA currently set to 500)

S_R is the number of reserved seats (in ISUA currently set to 15)

M is the number of districts (in ISUA currently 9) and P₀ is the total voter pool of the parliament.

Assigned section

Each districts is reserved a said value of seats, marked as S_R, which the district is guaranteed to gain, even if nobody lived in the said district. In the Sekidean Assembly, the number is currently set to 15, meaning that each district gets a baseline of 15 mandates, while the rest is distributed proportionally. Given, that there are currently 9 districts (member states) sending representatives to the Sekidean Assembly, a total of S_R × M is set aside from the distribution (in the ISUA currently 135)

Proprotional section

After all the reserved seats are removed from the total S_Σ, the rest is distributed to the districts using the formula x_P = ⌊P_C × (S_Σ - S_R × M) ÷ P₀⌋, where x_P is the number of seats given to each constituency via proportional representation. The resulting x_S = x_P + S_R is the number of seats assigned to the district after summing up the assigned/reserved and proportional sections of the seat assignment.

Underhang allocation

Due to the implementation of the floor function, some seats remain unclaimed out of the total of S_Σ, if you add up all the claimed seats. Those underhang seats are distributed using special ranking procedure. Districts are given ranks from 1 to n, based on the coefficient, Q_S for which it is set, that Q_S = x_S ÷ P_C, with the highest Q_S being ranked as "1", second highest as "2" etc.

After all the districts have been ranked, the seats are assigned by adding one seat to each district, starting at the district ranked as "1" and going down, until the overhang seats run out. Each districts resulting number x is the final number, that decides how many deputies the district elects on election day.

This method ensures, that those seats are assigned to underrepresented districts, at least partially levelling the artificially created disproportionality created by the section of reserved seats.

Seat allocation

The elections are done using the party-list proportional representation. If there is an electoral threshold, it is applied already in the first scrutinia.

First scrutinia

After votes in each district are morphed into percent points (marked as Π_P). Those percentages, if they are bigger than the threshold ( Π_Ω, currently set at 4%), are then used in latter calculations. Sum of all percentages, that passed the electoral threshold, are marked as Π_E. Seats are the distributed using the formula:

R_P = ⌊(Π_E × x) ÷ Π_E⌋

Usually between 92% and 97% of the seats are distributed in the first scrutinia, with the rest being transferred to a second scrutinia for parliament-wide arrangement.

Second scrutinia

When all the R_P have been summed up for each district, the remaining seats, marked as R_R, are summed up nationwide, marked as R_S. Those underhang seats are then given in descending order from the party with most seats to the one with the least, eventually looping from the least to the most again. Multiple rounds of assigning can be done before the second scrutinia seats run out. Those seats for each party are marked as R_Π.

After the alliances are set, it is decided, which district the candidates are elected from using the R_R. Districts are ranked using the R_R, from the lowest to the highest, and parties are ranked using the R_Π, from the highest to the lowest. Then, district ranked first in R_R gets one additional mandate for a party with the highest R_Π (unless the party scored under the electoral threshold in the region). Then, the district ranked second recieves one additional mandate for the party with the highest R_Π (note: R_Π decreases with adding of mandates). After R_R reaches 0 in a district, the district is removed from the list of second scrutinia adding mandates. If R_Π reaches 0, the party is removed from the distribution of overhang seats from then on.

It applies, that Σ(R_Π) = Σ(R_R), so the last unassigned party mandate is assigned to the last country mandate, effectively filling all the mandates, while keeping both the vote and district proportionallity as set by the criteria.