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{|class="wikitable<!-- sortable-->" style="text-align:center"
The '''Anthony apportionment method''' is the first of the three [[Anthony methods]] used in the electoral system of the [[Parthenian Economic Union]]. It is used to [[wikipedia:Apportionment|apportion]] mandates within the [[Parthenian Parliament]] and representatives of the [[Parthenian Convention]], ensuring the representation of each member states' population based on the principle of [[wikipedia:Degressive proportionality|degressive proportionality]].
!rowspan=2|State !!rowspan=2|Population !!colspan=2|Scrutinium 1+2 seats !!colspan=2|Reminder
|-
![[Parthenian Parliament|Parliament]] !![[Parthenian Convention|Convention]] !![[Parthenian Parliament|Parliament]] !![[Parthenian Convention|Convention]]
|-
|style="text-align:left"|{{flag|Angland}} ||{{formatnum:{{PopAnglandNum}}}}
|{{formatnum:{{#expr:floor(({{PopAnglandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}


|{{formatnum:{{#expr:floor(({{PopAnglandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}
==Functionality==
The main equation for the apportionment is following:


|{{formatnum:{{#expr:({{PopAnglandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}}-floor(({{PopAnglandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}  
{{math|S(x)<nowiki>=</nowiki>⌊(p<sup>λ</sup>(x):∑(i<nowiki>=</nowiki>1→n)p<sup>λ</sup>(i))·(S<sub>Σ</sub>-(S(P)+S<sub>1</sub>·n))⌋+S<sub>1</sub>}}


|{{formatnum:{{#expr:({{PopAnglandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}}-floor(({{PopAnglandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}


|-
*{{math|S<sub>Σ</sub>}} is the total number of seats to be apportioned (currently, {{math|S<sub>Σ</sub><nowiki>=</nowiki>{{ParthenianParliament-SΣ}}}})
|style="text-align:left"|{{flag|Bogmia}} ||{{formatnum:{{PopBogmiaNum}}}}  
*{{math|S(P)}} is the number of seats reserved for the Parthenian-wide constituency (currently, {{math|S(P)<nowiki>=</nowiki>{{ParthenianParliament-SP}}}})
|{{formatnum:{{#expr:floor(({{PopBogmiaNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}  
*{{math|S<sub>1</sub>}} is considered to be a [[#Reserved minimum|reserved minimum of seats]] (currently, {{math|S<sub>1</sub><nowiki>=</nowiki>{{ParthenianParliament-S1}}}})
*{{math|p(x)}} is the population of the country {{math|x}}
*{{math|n}} is the [[:Category:Countries in the Parthenian Economic Union|number of member states]] as of the time of apportionment (currently, {{math|n<nowiki>=</nowiki>{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}})
*{{math|λ}} is the [[#Leveling constant|leveling constant]] (currently, {{math|λ<nowiki>=</nowiki>{{#expr:{{ParthenianParliament-λ}}}}}})


|{{formatnum:{{#expr:floor(({{PopBogmiaNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}
===Reserved minimum===
The reserved minimum {S<sub>1</sub> is the minimum of seats one nation can recieve. Currently, the number is set to {{formatnum:{{#expr:{{ParthenianParliament-S1}}}}}}, ensuring that even a nation with a minimum of people living in it recieves at least a single mandate during the apportionment.


|{{formatnum:{{#expr:({{PopBogmiaNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})-floor(({{PopBogmiaNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}  
===Secondary apportionment===
Secondary apportionment is the main process of apportionment, between {{formatnum:{{#expr:{{ParthenianParliament-SΣ}}-({{ParthenianParliament-S1}}*{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}+{{ParthenianParliament-SP}}+{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}-1)}}}} and {{formatnum:{{#expr:{{ParthenianParliament-SΣ}}-({{ParthenianParliament-S1}}*{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}+{{ParthenianParliament-SP}})}}}} mandates are apportioned in it.


|{{formatnum:{{#expr:({{PopBogmiaNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})-floor(({{PopBogmiaNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}
Those mandates are distributed based on the principle of degressive proportionality based on the application of the [[#Leveling constant|leveling constant]] on member state's population in a way of  a modified [[wikipedia:Penrose method]]. The sum of mandates apportioned to a member state through the reserved minimum and the secondary apportionment constitutes the number of mandates the member state recieves in the institution, disregarding the [[#Compensatory seats|compensatory seats]].


|-
====Leveling constant====
|style="text-align:left"|{{flag|Monteblanco}} ||{{formatnum:{{PopMonteblancoNum}}}}
The compensatory constant λ is the fraction that describes the power to which the population of the member states is raised. Currently, this constant is equal to {{#expr:{{ParthenianParliament-λ}}}}. That means, that if there are two nations, with the populations of 27,000 and 1,000,000 inhabitants respectively (meaning that the values p<sup>λ</sup> are equal to 900 and 10,000 respectively), the small nation, despite constituting only approximately 2.63% of the population recieves 8.26% of the seats.
|{{formatnum:{{#expr:floor(({{PopMonteblancoNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}


|{{formatnum:{{#expr:floor(({{PopMonteblancoNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}
===Parthenia-wide constituency===
{{See also|Anthony voting method}}
TBA


|style="text-align:left"|{{flag|Monteblanco}} ||{{formatnum:{{PopMonteblancoNum}}}}
===Compensatory seats===
|{{formatnum:{{#expr:({{PopMonteblancoNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})-floor(({{PopMonteblancoNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}
TBA


|{{formatnum:{{#expr:({{PopMonteblancoNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}}-floor(({{PopMonteblancoNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}
==New members==
TBA


|-
==Current apportionments==
|style="text-align:left"|{{flag|Vermand}} ||{{formatnum:{{PopVermandNum}}}}
Currently, there are {{formatnum:{{#expr:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}}}
|{{formatnum:{{#expr:floor(({{PopVermandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}
{{ParthenianParliamentApportionment}}
 
|{{formatnum:{{#expr:floor(({{PopVermandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})}}}}
 
|{{formatnum:{{#expr:({{PopVermandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}}-floor(({{PopVermandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{ParthenianParliament-SP}}+{{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}
 
|{{formatnum:{{#expr:({{PopVermandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}}-floor(({{PopVermandNum}}^{{ParthenianParliament-λ}}/{{ParthenianParliament-PopλSum}})*({{ParthenianParliament-SΣ}}-({{formatnum:{{PAGESINCATEGORY:Countries in the Parthenian Economic Union}}}}*{{ParthenianParliament-S1}}))+{{ParthenianParliament-S1}})round3}}}}
 
|-
!Total ||{{formatnum:{{ParthenianEU-Pop}}}} ||{{formatnum:{{ParthenianParliament-SΣ2}}}} ||{{formatnum:{{ParthenianConvention-SΣ2}}}}
|-
|'''''Reminder || ||{{formatnum:{{#expr:{{ParthenianParliament-SΣ}}-{{ParthenianParliament-SΣ2}}-{{ParthenianParliament-SP}}}}}} ||{{formatnum:{{#expr:{{ParthenianParliament-SΩ}}-{{ParthenianConvention-SΣ2}}}}}}
|}
{{Parthenian Community}}
{{Parthenian Community}}
{{Elezia}}
{{Elezia}}

Latest revision as of 09:32, 21 May 2023

The Anthony apportionment method is the first of the three Anthony methods used in the electoral system of the Parthenian Economic Union. It is used to apportion mandates within the Parthenian Parliament and representatives of the Parthenian Convention, ensuring the representation of each member states' population based on the principle of degressive proportionality.

Functionality

The main equation for the apportionment is following:


S(x)=⌊(pλ(x):∑(i=1→n)pλ(i))·(SΣ-(S(P)+S1·n))⌋+S1


SΣ is the total number of seats to be apportioned (currently, SΣ=500)

S(P) is the number of seats reserved for the Parthenian-wide constituency (currently, S(P)=50)

S1 is considered to be a reserved minimum of seats (currently, S1=1)

p(x) is the population of the country x

n is the number of member states as of the time of apportionment (currently, n=13)

λ is the leveling constant (currently, λ=0.66666666666667)

Reserved minimum

The reserved minimum {S1 is the minimum of seats one nation can recieve. Currently, the number is set to 1, ensuring that even a nation with a minimum of people living in it recieves at least a single mandate during the apportionment.

Secondary apportionment

Secondary apportionment is the main process of apportionment, between 425 and 437 mandates are apportioned in it.

Those mandates are distributed based on the principle of degressive proportionality based on the application of the leveling constant on member state's population in a way of a modified wikipedia:Penrose method. The sum of mandates apportioned to a member state through the reserved minimum and the secondary apportionment constitutes the number of mandates the member state recieves in the institution, disregarding the compensatory seats.

Leveling constant

The compensatory constant λ is the fraction that describes the power to which the population of the member states is raised. Currently, this constant is equal to 0.66666666666667. That means, that if there are two nations, with the populations of 27,000 and 1,000,000 inhabitants respectively (meaning that the values pλ are equal to 900 and 10,000 respectively), the small nation, despite constituting only approximately 2.63% of the population recieves 8.26% of the seats.

Parthenia-wide constituency

See also: Anthony voting method

TBA

Compensatory seats

TBA

New members

TBA

Current apportionments

Currently, there are 13

[V]
State Population Seats Remainder Inhabitants per MPP
 Almagria 47,702,401 64 0.706 745,350
 Angland 49,884,032 66 0.633 755,819
 Bogmia 12,304,654 26 0.814 473,256
 Brynmor 5,156,286 15 0.456 343,752
 Charmelcia 5,466,011 16 0.029 341,626
 Eisenland 17,724,731 33 0.926 537,113
 Leciria 10,637,713 24 0.427 443,238
 Livania 63,222,442 77 0.865 821,071
 Monteblanco 7,925,465 20 0.253 396,273
 Telekia 7,891,162 20 0.197 394,558
 Vermand 68,003,293 81 0.693 839,547
Parthenian Economic Union Parthenia-at-large — 50 — 5,918,364
Total 295,918,190 492 8 —
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