View source for Siedem method

{{Region icon Anteria}}{{WIP}}
The '''Siedem Method''' is a method for allocating seats in parliaments among member states, or in [[wikipedia:Party-list proportional representation|party-list]] [[wikipedia:Proportional representation|proportional representation]] systems.
Devised by a [[Zhousheng|Zhoushi]] mathematician [[Чaraƌa Siedem]], it is currently used to allocate seats in the [[Sekidean Assembly|Assembly]] of the [[Sekidean Parliament]].

==Motives==
[[File:SekideanAssemblyLogo.png|thumb|300px|Logo of the [[Sekidean Assembly|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 {{math|S<sub>Σ</sub>}} and {{math|S<sub>R</sub>}}, 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:

:{{math|x<sub>S</sub> {{=}} ⌊P<sub>C</sub> × (S<sub>Σ</sub> - S<sub>R</sub> × M) ÷ P<sub>0</sub>⌋ + S<sub>R</sub>}}

where:

* {{math|x<sub>S</sub>}} is the number of assigned seats to the district
* {{math|P<sub>C</sub>}} is the voter pool of the district in question
* {{math|S<sub>Σ</sub>}} is the number of total seats available (in [[Sekidean Assembly|ISUA]] currently set to 500)
* {{math|S<sub>R</sub>}} is the number of [[#Assigned section|reserved seats]] (in [[Sekidean Assembly|ISUA]] currently set to 15)
* {{math|M}} is the number of districts (in [[Sekidean Assembly|ISUA]] currently 9) and {{math|P<sub>0</sub>}} is the total voter pool of the parliament.

====Assigned section====
Each districts is reserved a said value of seats, marked as {{math|S<sub>R</sub>}}, 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 {{math|S<sub>R</sub> × M}} is set aside from the distribution (in the [[Sekidean Assembly|ISUA]] currently 135)

====Proprotional section====
After all the reserved seats are removed from the total {{math|S<sub>Σ</sub>}}, the rest is distributed to the districts using the formula {{math|x<sub>P</sub> {{=}} ⌊P<sub>C</sub> × (S<sub>Σ</sub> - S<sub>R</sub> × M) ÷ P<sub>0</sub>⌋}}, where {{math|x<sub>P</sub>}} is the number of seats given to each constituency via proportional representation. The resulting {{math|x<sub>S</sub> {{=}} x<sub>P</sub> + S<sub>R</sub>}} 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 [[wikipedia:Floor and ceiling functions|floor function]], some seats remain unclaimed out of the total of {{math|S<sub>Σ</sub>}}, if you add up all the claimed seats. Those [[wikipedia:Underhang seat|underhang seats]] are distributed using special ranking procedure. Districts are given ranks from 1 to {{math|n}}, based on the coefficient, {{math|Q}} for which it is set, that {{math|Q {{=}} x ÷ P<sub>C</sub>}}, with the highest {{math|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 {{math|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 [[wikipedia:Party-list proportional representation|party-list proportional representation]]. If there is an [[wikipedia:Electoral threshold|electoral threshold]], it is applied already in the first scrutinia.

====First scrutinia====
After votes in each district are morphed into percent points (marked as {{math|Π<sub>P</sub>}}). 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 {{math|Π<sub>E</sub>}}. Seats are the distributed using the formula:

:{{math|R<sub>P</sub> {{=}} ⌊(Π<sub>E</sub> × {{math|x}}) ÷ Π<sub>E</sub>⌋}}

====Second scrutinia====
TBA

{{Template:Sekidean info pages}}
{{Template:Anteria info pages}}