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

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 and S_R, modifying the method allows to update it without the need to change it completely.

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 for which it is set, that Q = x ÷ P_C, with the highest Q 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, 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⌋

Second scrutinia

TBA