DEGRESSIVE PROPORTIONALITY IN THE EUROPEAN PARLIAMENT

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1 M A T H E M A T I C A L E C O N O M I C S No. 7(4) 20 DEGRESSIVE PROPORTIONALITY IN THE EUROPEAN PARLIAMENT Katarzya Cegełka Abstract. The dvso of madates to the Europea Parlamet has posed dffcultes sce the begg of ts operato. The troducto of the degressve proportoalty prcple to legal acts tesfed further dscusso o ths subject. The researchers propose dfferet solutos the form of algorthms or fuctos wth whch t s possble to determe the composto of the Europea Parlamet. Keywords: degressve proportoalty, dvsble goods, apportomet problem, Europea Parlamet, Europea Uo. JEL Classfcato: D39.. Itroducto The dvso of goods s oe of the oldest problems of ay kd of commuty. It cocers, ter ala, the separato of objects that caot be dvded to smaller parts. Ths stuato occurs the case of the dstrbuto of parlametary madates. Over hudreds of years varous methods of determg the composto of the uts represetg a partcular commuty have bee developed. These clude the kow method of Hamlto ad the dvsor methods of Jefferso, Adams ad Webster (Cegełka et al., 200a). However, they are based o proportoal dstrbuto, the use of whch s ot possble the case of the Europea Parlamet. Ths results from the large dversty of the Member States terms of the umber of ctzes, based o whch seats are allocated. For ths reaso, the composto of the Europea Parlamet s determed by the prcple of degressve proportoalty (Cegełka et al., 200b). Katarzya Cegełka Departmet of Mathematcs, Wrocław Uversty of Ecoomcs, Komadorska Street 8/20, Wrocław, Polad. E-mal: katarzya.cegelka@ue.wroc.pl

2 32 Katarzya Cegełka 2. Degressve proportoalty legal acts Degressve proportoalty, troduced order to stadardze the rules for dstrbutg seats the Europea Parlamet was eshred Artcle, Pot 5 of the Treaty of Lsbo: The Europea Parlamet shall be composed of represetatves of the Uo s ctzes. They shall ot exceed seve hudred ad ffty umber, plus the Presdet. Represetato of ctzes shall be degressvely proportoal, wth a mmum threshold of sx members per Member State. No Member State shall be allocated more tha ety-sx seats (The Treaty of Lsbo, 200). Ths legacy pots out the total umber of madates ad the mmum ad maxmum umber of seats for each coutry. It does ot, however, clude the characterstcs of degressve proportoalty. Ths lack was supplemeted the Report of the Commttee o Costtutoal Affars ad the Europea Parlamet Resoluto. The rules cluded them specfy how to apply the prcple troduced the Lsbo Treaty. Aalyss of the cotets of these rules allows dstgushg two codtos wth whch a degressvely proportoal dvso must comply. Accordg to them, members from coutres wth a hgher populato represet a greater umber of ctzes ad do ot have fewer seats tha the less populated coutres (Cegełka et al., 200b). Deotg as umber of coutres, l populato of the coutry ad m the umber of madates of the coutry, all the codtos ca be saved as follows (Cegełka, 200): W. m 75, 6 m 96, W2. l l2 l m m2 m, l l2 l W3. l l2 l. m m2 m The frst of these s cotaed the Treaty tself the total umber of MPs does ot exceed 75, but o coutry may receve less tha 6 ad more tha 96 seats. Others stem from the rules cluded addtoal parlametary documets. The secod says that states wth smaller populatos may ot receve more seats tha states wth larger populatos. The thrd dcates that MEPs from coutres wth larger populatos represet a greater umber of ctzes tha MEPs from coutres wth a lower populato. For a detaled mathematcal aalyss of the degressve proportoalty, see Florek (20).

3 Degressve proportoalty the Europea Parlamet Deftos of degressve proportoalty 3.. Strog degressve proportoalty Dffereces the populato of the Member States meat that t was decded to determe a just, comprehesble ad lastg system for the dstrbuto of seats (Lamassoure, Sever, 2007). The result of ths work was the troducto of the prcple of degressve proportoalty. The Lsbo Treaty, whch t was wrtte dow, etered to force December 2009, thus dversfcato of the EU coutres had bee place sce ts cepto. Wth several doze years of the fuctog of the Europea Parlamet, there were attempts to formulate the method of selectg ts composto. Oe of them s the algorthm set at the meetg of the Coucl of Europe 992. Ths ca be show 4 pots (Lamassoure, Sever, 2007): ) Each state receves 6 seats. 2) States wth a populato of to 25 mllo receve a madate for every 500 thousad ctzes. 3) States wth a populato of 25 to 60 mllo receve a madate for every mllo ctzes. 4) States wth a populato exceedg 60 mllo receve a madate for every 2 mllo ctzes. Ths patter was ever strctly appled. However, t dcates some sort of dvso: to assg successve madates to a creasg umber of represeted ctzes. It turs out that ths type of dvso s always cosstet wth the prcple of degressve proportoalty. Degressvely proportoal dvso wll, therefore, also be the dvso that meets the followg codtos: W. m 75, 6 m 96, W2. l l2 l m m2 m, l 2 W3., m 2 where l l j, m m j, whe m j m j m j m m, ad l, m,

4 34 Katarzya Cegełka whe m m m m m for = {2, 3,, }, j = 2, j j ad 0 m l. We also defe m ad l. Theorem. Each dvso meetg the codtos W, W2, W3 also meets codtos, W2, W3. Proof. Codtos W ad W2 are respectvely equal to the codtos W ad W2; therefore, t suffces to show: l l. m m Accordg to the defto of the quotet, equalty s equvalet to oe of the followg equaltes: l l l l m m m m k k k k ; m m m m k l l lk lk ; m m m mk mk. m m m m, () If m = m 2, expressos l m from equaltes () ad (2) are replaced by ad the proof s aalogous. For = {2,, }, k = {, 2,, 2}, k {, 2,, ad equalty () we have: k l l lk l. m m m m k k By assumpto m k m, equalty () s the equvalet to l l l l m m m m m m k k k k k l l whch partcular for k = mples. m m For the equalty (2) ad by defto the quotet we obta:, (2)

5 Degressve proportoalty the Europea Parlamet 35 k l l lk lk. k m m mk mk l k l l Iequalty mples k, whch results from the defto of m k m mk the quotet. l Therefore, t suffces to show that m k k defto of ad ad codto W3 sayg that l we have m k k l m. Thus: 2 2 l l m m.. Takg to accout the We have show that each dvso that satsfes the codtos W, W2, W3 also satsfes codtos W, W2, W3. Ths meas that the determato of the composto of the Europea Parlamet whch cosst allocatg more seats to Members represetg a growg umber of ctzes always geerates a degressvely proportoal dvso. The costructo of dvso that satsfes the codtos of a strog degressve proportoalty s much more dffcult tha the determato of the composto satsfyg the codtos eclosed the Europea Parlamet Resoluto. Ths problem s exacerbated wth the creasg umber of Member States. Wth the curret umber of 27 coutres, the dstrbuto already poses dffcultes that satsfy codtos W, W2, W3. Therefore, researchers have proposed modfyg the codtos of degressve proportoalty Weakeed degressve proportoalty I February 20 at the Commttee o Costtutoal Affars meetg, a group of mathematcas led by Professor Geoffrey Grmmett preseted a proposal to stadardze the composto of the Europea Parlamet the so-called Cambrdge Compromse. The scetsts proposed the method base+prop, where each State receves a certa umber of seats ( base ) ad the the remag umber of seats s dvded by oe of the classc methods of

6 36 Katarzya Cegełka proportoal allocato ( prop ). They cocluded that the best choce s the base equal to fve madates ad dvso of the Adams dvsor method (assumg roudg fractos up to the earest whole teger) so that each Member receves a mmum 6 seats as guarateed the Treaty of Lsbo. The authors ther delberatos wet eve further. They cosdered that apart from the troducto of a algorthm developed by them there should be also a chage the defto of degressve proportoalty proposed by A. Lamassoure ad A. Sever the Report of the Commttee o Costtutoal Affars o the composto of the Europea Parlamet from 2007: [The Europea Parlamet] cosders that the prcple of degressve proportoalty meas that the rato betwee the populato ad the umber of seats of each Member State must vary relato to ther respectve populatos such a way that each Member from a more populous Member State represets more ctzes tha each Member from a less populous Member State ad coversely, but also that o less populous Member State has more seats tha a more populous Member State (Lamassoure, Sever, 2007). 2 The authors of the Compromse proposed the followg chages: [The Europea Parlamet] cosders that the prcple of degressve proportoalty meas that the rato betwee the populato ad the umber of seats of each Member State before roudg to whole umbers must vary relato to ther respectve populatos such a way that each Member from a more populous Member State represets more ctzes tha each Member from a less populous Member State ad coversely, but also that o less populous Member State has more seats tha a more populous Member State (Grmmett, 20). Professor Grmmett also refers to the theorem whch states that wth ths defto the dvso wll always be degressvely proportoal (O the apportomet ). Such a guaratee, however, occurs oly the case of the composto based o a prove algorthm. It s clear that the algorthm or fucto that assgs the umber of seats depedg o the populato a degressvely proportoal maer wll retur a degressvely proportoal dstrbuto f the results are ot chaged (rouded). 3 The weakess of the defto however, brought, beyod the facltato of accouts to the authors, o soluto. Members declare that the deal alteratve would be to agree o a udsputed mathematcal formula of degressve proportoalty that would esure a soluto ot oly for the preset revso but for future elargemets or modfcatos due to demographc chages (Lamassoure, Sever, 2007). So far, howe- 2 Whch was wrtte dow codtos W2 ad W3. 3 The authors of the varous proposals for the fucto of separatg the madates are well aware that t s the questo of the teger umber that spols degressve proportoalty.

7 Degressve proportoalty the Europea Parlamet 37 ver, they have ot accepted ay of the developed solutos. 4 The oly way of selectg the composto of the Europea Parlamet remas the tedous egotatos, as held so far. I ths case, MPs shall determe the total umber of seats; therefore a modfcato of the Lamassoure ad Sever s defto leads owhere. The troducto of chages wthout a doubt would, however, smplfy the work of the authors of the varous fuctos ad algorthms. 4. Coclusos The Europea Parlamet curretly cossts of represetatves of the ctzes of 27 coutres, whose populatos are characterzed by a large dsperso. Ths leads to the eed of seekg methods of allocatg seats whch are ot based o proportoal methods. Accordg to the Lsbo Treaty, they should, however, fulfll the codtos of degressve proportoalty. Scetsts have so far offered varous solutos le wth the assumptos. However, MPs have ot take ay of them. I addto, t appears that the terpretato of degressve proportoalty largely depeds o the terpreter. A multtude of ukows ad the lack of a determed posto o the part of MEPs meas that the problem of ufcato of the procedures for selectg the composto of the Europea Parlamet stll remas usolved. Lterature Cegełka K. (200). Dstrbuto of seats the Europea Parlamet accordace wth the prcple of degressve proportoalty. Mathematcal Ecoomcs. Vol. 6. No. 3. Cegełka K., Destrzańsk P., Łyko J., Msztal A. (200a). Dvso of seats the Europea Parlamet. Joural for Perspectves of Ecoomc, Poltcal ad Socal Itegrato. Vol. XVI. Cegełka K., Destrzańsk P., Łyko J., Msztal A. (200b). Demographc chages ad prcples of the far dvso. Iteratoal Joural of Socal Sceces ad Humaty Studes. Vol. 2. No. 2. Cegełka K., Destrzańsk P., Łyko J., Msztal A. (20). Degressve proportoalty the cotext of the composto of the Europea Parlamet. Ecoomcs. Vol. 2. No. 4. Florek J. (20). Allocato of Seats the Europea Parlamet ad a Degressve Proportoalty. 4 Members rejected, amog others, V. Ramrez-Gozalez s Parabolc method ad have ot appled so far the Cambrdge Compromse.

8 38 Katarzya Cegełka Grmmett G.R. (20). Europea apportomet va the Cambrdge Compromse. Mathematcal Socal Sceces. USep3.pdf. Accessed: Lamassoure A., Sever A. (2007). Report o the Composto of the Europea Parlamet. A6-035/2007. O the Apportomet of the Seats the Europea Parlamet: A Report by Mathematcas. Vdeo from the debate. teret/frd/vod/player;jsessod =888E0AE94B2ACAB752FA7A0C038D?category=COMMITTEE & evet Code= COMMITTEEFCO&format=wmv&byLeftMeu =research commttee&laguage=e#achor. Accessed: The Treaty of Lsbo (200). UrServ/Lex UrServ.do? ur=oj:c:200:083:full:en:pdf. Accessed: A DOC+XML+V0//EN. Accessed: