View source for Jorken method

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{|class="infobox" style="background-color:#F8F8EF; vertical-align:center"
!style="font-family:Arial Unicode MS; font-size:1.5em; text-align:center" colspan=2|Jorken method
|-
|colspan=2|[[File:JorkenMethodMandateCalculation.svg|link=|180px]]
|-
|colspan=2|[[File:JorkenMethodFunctionSumation.svg|link=|180px]]
|}
[[File:ZhoushiSenate.svg|thumb|300px|Current convocation of the [[National Senate of Zhousheng]] has been elected using the Jorken Method]]
The '''Jorken method''' is a method for allocating seats in parliaments among member states, or in [[wikipedia:Party-list proportional representation|party-list]] systems. It is devised in a way, that seats assigned reach a dedicated [[wikipedia:Asymptote|asymptote]], requiring an existence of [[wikipedia:Coalition government|coalition government]] in order to gain a majority in a house elected in that way.

Devised by a [[Renia|Renish]] mathematician [[Ƈestꭈ Jorken]], it is currently used to allocate seats in the [[National Senate of Zhousheng|National Senate]] of the [[Congress of Zhousheng]].

==Motives==
{{See also|Congress of Zhousheng|National Senate of Zhousheng|Zhousheng|2001 Zhoushi protests}}
[[File:ZhoushiSenateLogo.png|thumb|200px|Logo of the [[National Senate of Zhousheng|National Senate]] of the [[Congress of Zhousheng]]]]
The Jorken method, originally devised as a test concept of using a mixed electoral system, was first put into test after the [[2001 Zhoushi protests]] led to the [[2002 Zhoushi legislative election|2002 snap election]]. The method was chosen to replace the former [[wikipedia:Instant-runoff voting|instant-runoff]] method used in the [[National Senate of Zhousheng]], and merging the 99 single-mandate constituencies into a single 99 mandate large constituency.

==Equation==
*'''''s<sub>Σ</sub>'''''{{efn|Labelling used in the proposal written by Ƈestꭈ Jorken back in 2001. [[wikipedia:Sigma|Letter Sigma (Σ)]] was chosen to represent the symbol of [[wikipedia:Summation|a sum]]}} - total number of mandates available - currently set to 99
*'''''s<sub>Ψ</sub>'''''{{efn|Labelling used in the proposal written by Ƈestꭈ Jorken back in 2001. [[wikipedia:Psi|Letter Psi (Ψ)]] was chosen because it is similar to the letter ⲯ of [[Belgorian language|Belgorian]], meaning V for "Vєlikosꞇ", "Greatness" in [[wikipedia:English language|Common]]}} - maximal number of mandates one party/alliance can recieve - currently set to 49
*'''''s<sub>i</sub>''''' - number of mandates a party ''i'' recieves - can span any intiger between 0 and 49
*'''''Π<sub>i</sub>''''' - fraction of votes a party ''i'' recieved (on the scale from 0 and 1) - can span any number on the interval ⟨0;1⟩
*'''''a''''' - variable a for setting a function

The seats are assigned using the function:
:[[File:JorkenMethodMandateCalculation.svg|link=|170px]]{{efn|Where [[File:JorkenMethodFunctionEquation.svg|link=|70px]] applies}}
Where ''a'' is a variable that is defined in a way, that it belongs to the interval (0;∞){{efn|Interval {{math|a∈(0;∞)}} is equivalent to the interval of all positive real numbers {{math|a∈ℝ<sup>+</sup>}}}}, which is defined in a way, that the following equation holds true:
:[[File:JorkenMethodFunctionSumation.svg|link=|170px]]
<!--[[File:JorkenMethodFunctionEquation.svg|link=|170px]]
TBA-->

==Example of usage==
There are 6 parties running. They recieve the following number of votes:
{|class="wikitable<!-- sortable-->" style="text-align:center"
!colspan=2|Party ||% of votes ||Π<sub>i</sub>
|-
|style="border-right:none; text-align:center;background:#F00"| ||style="border-left:none;text-align: left;"|'''PARTY A''' ||17.55% ||0.1755
|-
|style="border-right:none; text-align:center;background:#FF0"| ||style="border-left:none;text-align: left;"|'''PARTY B''' ||3.22% ||0.0322
|-
|style="border-right:none; text-align:center;background:#008000"| ||style="border-left:none;text-align: left;"|'''PARTY C''' ||47.80% ||0.4780
|-
|style="border-right:none; text-align:center;background:#0FF"| ||style="border-left:none;text-align: left;"|'''PARTY D''' ||19.12% ||0.1912
|-
|style="border-right:none; text-align:center;background:#00F"| ||style="border-left:none;text-align: left;"|'''PARTY E''' ||9.55% ||0.0955
|-
|style="border-right:none; text-align:center;background:#F0F"| ||style="border-left:none;text-align: left;"|'''PARTY F''' ||2.11% ||0.0211
|-class="sortbottom"
|style="border-left:none;text-align: left;" colspan=2|'''''Invalid''''' ||0.65% ||0.0065
|}

The [[wikipedia:Electoral threshold|electoral threshold]] is currently set to 3.5%. That means, that PARTY B and PARTY F are automatically disqualified from membership in the house. Following this disqualification, the function ''a'' is calculated, so the sum of all seats is equal to ''s<sub>Σ</sub>'' (set to 99) using the party ceiling ''s<sub>Ψ</sub>'' (set to 49). In this case, the constant ''a = 0.47''. The final set of seats is therefore:
{|class="wikitable<!-- sortable-->" style="text-align:center"
!colspan=2|Party ||% of votes ||Π<sub>i</sub> ||s<sub>i</sub> ||class=unsortable|Scheme
|-
|style="border-right:none; text-align:center;background:#F00"| ||style="border-left:none;text-align: left;"|'''PARTY A''' ||17.55% ||0.1755 ||'''23
|rowspan=7|[[File:JorkenMethodExampleParliament.svg|300px]]
|-
|style="border-right:none; text-align:center;background:#FF0"| ||style="border-left:none;text-align: left;"|'''PARTY B''' ||style="background:#FEE7E6"|3.22% ||style="background:#FEE7E6"|0.0322 ||style="background:#FEE7E6"|'''0
|-
|style="border-right:none; text-align:center;background:#008000"| ||style="border-left:none;text-align: left;"|'''PARTY C''' ||47.80% ||0.4780 ||'''35
|-
|style="border-right:none; text-align:center;background:#0FF"| ||style="border-left:none;text-align: left;"|'''PARTY D''' ||19.12% ||0.1912 ||'''24
|-
|style="border-right:none; text-align:center;background:#00F"| ||style="border-left:none;text-align: left;"|'''PARTY E''' ||9.55% ||0.0955 ||'''17
|-
|style="border-right:none; text-align:center;background:#F0F"| ||style="border-left:none;text-align: left;"|'''PARTY F''' ||style="background:#FEE7E6"|2.11% ||style="background:#FEE7E6"|0.0211 ||style="background:#FEE7E6"|'''0
|-class="sortbottom"
|style="border-left:none;text-align: left;" colspan=2|'''''Invalid''''' ||0.65% ||0.0065 ||—
|}

This result shows, the while the strongest and most popular party recieved the most seats, it is not proportionally as much as one could expect in completely proportional systems i.e. - the system makes sure, that the weaker parties are favoured in the [[National Senate of Zhousheng|upper house]], in contrast to the [[National Assembly of Zhousheng|lower house]], where the representation is strictly proportional.
<!--{|class="wikitable" style="text-align:center;vertical-align:center"
!Complete proportionality !!Threshhold proportionality !![[wikipedia:D'Hondt method|D'Hondt method]]  !!Jorken method
|-
|{{Pie chart
|thumb=center
|label1 = PARTY A
|value1 = 17.55
|color1 = #F00
|label2 = PARTY B
|value2 = 3.22
|color2 = #FF0
|label3 = PARTY C
|value3 = 47.80
|color3 = #008000
|label4 = PARTY D
|value4 = 19.12
|color4 = #0FF
|label5 = PARTY E
|value5 = 9.55
|color5 = #00F
|label6 = PARTY F
|value6 = 2.11
|color6 = #F0F
|label7 =
|value7 = 0.65
|color7 = grey
}}
|{{Pie chart
|thumb=center
|label1 = PARTY A
|value1 = 18.67
|color1 = #F00
|label2 = <s>PARTY B</s>
|value2 = 0
|color2 = #FF0
|label3 = <b>PARTY C</b>
|value3 = 50.84
|color3 = #008000
|label4 = PARTY D
|value4 = 20.34
|color4 = #0FF
|label5 = PARTY E
|value5 = 10.16
|color5 = #00F
|label6 = <s>PARTY F</s>
|value6 = 0
|color6 = #F0F
}}
|{{Pie chart
|thumb=center
|label1 = PARTY A
|value1 = 18.18
|color1 = #F00
|label2 = <s>PARTY B</s>
|value2 = 0
|color2 = #FF0
|label3 = <b>PARTY C</b>
|value3 = 51.52
|color3 = #008000
|label4 = PARTY D
|value4 = 20.20
|color4 = #0FF
|label5 = PARTY E
|value5 = 10.10
|color5 = #00F
|label6 = <s>PARTY F</s>
|value6 = 0
|color6 = #F0F
}}
|{{Pie chart
|thumb=center
|label1 = PARTY A
|value1 = 23.23
|color1 = #F00
|label2 = <s>PARTY B</s>
|value2 = 0
|color2 = #FF0
|label3 = PARTY C
|value3 = 35.36
|color3 = #008000
|label4 = PARTY D
|value4 = 24.24
|color4 = #0FF
|label5 = PARTY E
|value5 = 17.17
|color5 = #00F
|label6 = <s>PARTY F</s>
|value6 = 0
|color6 = #F0F
}}
|}

As a comparison, the Jorken method favours smaller parties crossing the threshhold. In our example, the change is the following:-->
{|class="wikitable<!-- sortable-->" style="text-align:center"
!colspan=2 rowspan=2|Party ||rowspan=2|% of votes ||colspan=2|[[wikipedia:D'Hondt method|D'Hondt]] ||Jorken ||rowspan=2|Difference
|-
!No threshhold ||colspan=2|3.5% electoral threshhold
|-
|style="border-right:none; text-align:center;background:#F00"| ||style="border-left:none;text-align: left;"|'''PARTY A''' ||17.55% ||17 ||18 ||23 ||'''{{Increase}} 5
|-
|style="border-right:none; text-align:center;background:#FF0"| ||style="border-left:none;text-align: left;"|'''PARTY B''' ||3.22% ||3 ||style="background:#FEE7E6"|0 ||style="background:#FEE7E6"|0 ||style="background:#FEE7E6"|'''{{Steady}} 0
|-
|style="border-right:none; text-align:center;background:#008000"| ||style="border-left:none;text-align: left;"|'''PARTY C''' ||47.80% ||49 ||51 ||35 ||'''{{Decrease}} 16
|-
|style="border-right:none; text-align:center;background:#0FF"| ||style="border-left:none;text-align: left;"|'''PARTY D''' ||19.12% ||19 ||20 ||24 ||'''{{Increase}} 4
|-
|style="border-right:none; text-align:center;background:#00F"| ||style="border-left:none;text-align: left;"|'''PARTY E''' ||9.55% ||9 ||10 ||17 ||'''{{Increase}} 7
|-
|style="border-right:none; text-align:center;background:#F0F"| ||style="border-left:none;text-align: left;"|'''PARTY F''' ||2.11% ||2 ||style="background:#FEE7E6"|0 ||style="background:#FEE7E6"|0 ||style="background:#FEE7E6"|'''{{Steady}} 0
|}

==Notes==
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{{Elezia}}
[[Category:Election method]]