Complexity of Law the Exploration of Indonesian Legislation Network

7/24/2019 Complexity of Law the Exploration of Indonesian Legislation Network

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ComplexityofLaw:TheExplorationof

IndonesianLegislationNetwork

ArdianMaulana

[[email protected]]

Dept.ComputationalSociology

BandungFeInstitute

HokkySitungkir

[[email protected]]

Dept.ComputationalSociology

BandungFeInstitute

Abstract

Thepaperutilizes citationnetwork for legaland lawproducts.By focusingon theweakly connected

componentsinthenetwork,weshowedthesmallworldnetworktopologyastheindegreecumulative

distribution functionexhibitingpower law.This factexpresses thecomplexcharacteristics in the legal

system

in

Indonesia.

Furthermore,

the

centrality

measures

of

the

citation

among

legal

and

law

products

isbroughtasitpresentsthedominationoflawonIndonesianpoliticalandregionalgovernment.

Keywords:legalproducts,law,citationnetwork,smallworldtopology,powerlaw


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I. Introduction

Inbroaddefinition, law isthecollectionofrulesneededtoregulatesocialsystem. Stateenforcesthe

lawthroughsetofinstitutionsthatassurelegalsecuritywithinsociety. Theenterpriseofwrittenrules

andlegalinstitutionshapesthefaceofsocietybyassuringthelegalsecuritywithinsociety.

However,regardlessofitsfunction,lawcouldbeseensimplyasaproductoflegalsystem,collectionofagent,peopleand institutionthat isconferredpowertomakeregulation. Inthissystem,socialactors,

whicharenaturallyheterogeneous,interactwithandadapttoeachotheraccordingtolawmakingrule,

and in turnemerge thechainof legalproduct.Legalsystemalsoshares thecharacteristicofcomplex

systemlikeanyothersocialsystem.Consequently,wecouldexpectthatallofthepropertiesofcomplex

systemsarethereatworkinthelegalsystem[1].

Analytical implementation of complexity in legal system opens the opportunities to better

understandinghow legal systemorganizesandevolvesover time. By incorporating thisapproach to

studylegalsystem,somepreviousworksshowthattheweboflegalproducthassmallworldstructure

which is indicatedbythepresenceofhighlyconnectedhubsthatconnectseparatedclusterof legal

products [2, 3]. Furthermore, largenumberofnodeswith very few links,and a smallbut significant

numberofnodeswithsomany linksshare thestatisticalcharacteristicsofcomplexnetwork including

theexistenceofpowerlaw.

Modeling legal system as network of legal product becomes an alternative approach to unravel the

complexitiesoflegalsystem.Inthepastdecade,thisapproachhasbeenextendedtothemostdiverse

contexts, from communication systems to railroads, from the spreading of viruses to social

communication[4]. In thispaper,ourcorpus isthecollectionof legislationproducts in Indonesia.We

constructthenetworkoflegalcitationsinwhichtheverticesrepresentingthelegislationsandcitationof

legislationbyanotherdefinetheedgesofnetwork.

Webeginbyexplainingthewayofthecitationnetworkisconstructed.Thisisfollowedbyanalyzingthe

topologycharacteristics related to thesmallworldpropertyandstatisticalpropertiesof thenetwork.

Wealsoextendtheanalysisbyextractingthekindoflegalauthoritythatemergesfromthenetworkby

usingHITScentralitymethod.Thepaperendswithsomeconcludingremarksfocusingontheresultthat

obtainedinthisresearch.

II. Constructingthecitationnetworkoflegislation

Legislation isakindof rule that isenactedby legislature.According to thehierarchyof regulation in

Indonesia,legislationisplacedasthesecondhighestlegalauthorityafterconstitutionguaranteeingits

importanceasthesourceoflaw.For65years(19452010),Indonesianlegalsystemalreadyhavearound

1929legislationsorotherlegalproductsofthesamelevel,comprising1454Act(Undangundang),175

Emergency Act (Undangundang Darurat), and the remaining legislation originating from the

GovernmentRegulationinLieuofLaw(174PeraturanPenggantiUndangundang),PresidentialDecision

(37UUpnps.),andPresidentialRegulation (94UUprps.) [5].Someof these legislationsareno longer

rulingsinceithasbeenamendedorsupplementedbylegislationsthereafter.


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Figure1showsthegrowthoflegislationinIndonesiasince1945.Thisfigureclearlyshowsthepresence

ofthreephasesalongthedynamicoflegislationgrowthwhichinterestinglyareinaccordwiththethree

phases of Indonesian political order. This indicates that the political situation has strong influence

towardthedynamicofIndonesianlaw.

Gambar1:TimeseriesofIndonesianlegislationthatproducedduringtheperiodof 19452010:a.total;b.Based

onthelegislationtype(biru:UU;merah:UUprp;green:Uudrt;orange:UUpnps;Black:UUprps.

The hierarchicalnatureof Indonesian legal system necessitates each legalproduct a legalbasisof a

higherlevel,bycitingotherlegalproductlegitimizing itsexistence.Thisruleof lawmakingdefinesthe

connection between legalproducts and emerge thenetworkof legal citation among legislation. The

legalbasisoflegislationcanbeeitherthearticlesofconstitutionorregulationofthesamelevel,suchas

precedinglegislation(ti),GovernmentRegulationinLieuofLaw( ),PresidentialRegulation( ),

PresidentialDecision( ),GovernmentRegulation1( ).

WerepresentsthecitationnetworkofIndonesianlegislationasdirectedacyclicgraphG V, Ewhere

VdenotedasthesetofverticesandEassetofarc[6,7]. Eachvertex(v)inVrepresentlegislation(t)

and other legal product that is cited byv, such as Government Regulation in Lieu of Law (s),

Presidential Decision (r), Presidential Regulation (q), and Government Regulation (p), where

V p, q, r, s, t.Herewe ignorethearticleofConstitutionasonetypeofvertexofthegraph.For

anylegislationt,thereisanarchfrom ttov(e E)ifandonlyiftcitesv.

Thediversityoflegislation inrelationtoitslegalsubjectmadeourlegalcitationnetworkfailtoforma

closedgraph.Herewefocusonthelargestweaklyconnectedcomponentwhichcontains1276vertices

and3609edges,asshown inFigure2.Totalnumberoftheedgesmeansadensityof0.004,signifying

thatthenetworkisrelativelysparse.

1Inprincipal,thelegislationshouldonlyciteotherlegalproductsthathavehigherorsamelevellegalposition. However,this

ruleisnotfullyrealizedinpracticeespeciallyforthelegislationwrittenintheearlytimesofRepublicIndonesia.


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Figure2:weaklyconnectedcomponentsofcitationnetworkofIndonesianlegislation

III. Analysis

In this part, we reveal the topological properties of citation network of Indonesian legislation by

conductingsomemeasurement,asfollows:

a. Smallworldtopologyandscalefreenetwork

Smallworldpropertyisastructuralattributeofnetworkthathasbeenfoundinmanyrealphenomena.

Thispropertyiscommonlyassociatedtothepresenceofarelativelysmallnumberofhighlyconnected

nodes in the network that integrate the separated nodes.Networkwith smallworld topologyhas a

highdensityclustered structure but the distance between the vertices is very low. This could be

identifiedbymeasuringclusteringcoefficient(C)andcharacteristicpathlengthoftheobservednetwork

(d)[8].

Clusteringcoefficientdealingwiththelocaldensityofnetworkisdefinedasproportionoflinksbetween

verticeswithinitsneighborhooddividedbythenumberoflinksthatcouldpossiblyexistbetweenthem.

Thisisformallywrittenasfollow:

1 ;

2

( 1)i

N

i ij jk

j k j ki i

C e ek k

(1)

inwhich, clustering coefficientof theobservednetwork is themeanof clustering coefficientofeach

vertexwithinnetwork,thatis

1

1 N

i

i

C CN

(2)


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Characteristic path length isdefinedasaverage shorthestpath lengthofeach vertex towardothers

vertexwithinnetwork.Thismetricisformallywrittenasfollow:

min

1

1( , )

N

i

j

d i jN

(3)

where ( , ) min( )iji j d ,theminimumpath lengthbetweenvertices.Thereby, thecharacteristicpath

lengthofnetworkis

1

1 N

i

i

d dN

(4)

Theproblemistheequations14abovecouldnotstraightlybeappliedtoourcitationnetworkbecause

thenetworkisrepresentedasdirectedgraphwithoutclosedloop[9].Therefore,tomeasurethesmall

worldproperties

oflegal

citation

network,

we

should

treat

the

citation

network

inits

undirected

form.

Inthisway,directionalrelationshipbetweenverticesisonlyconsideredasanindicationofaconnection

betweenlegalproducts.

Tabel1showsclusteringcoeffiecientandcharacteristic pathlengthofthelegalcitationnetworkofthe

Indonesian legislation.Asacomparison,weconstructrandomgraphwhichhassimilarattributeswith

theobservednetwork.Aswecansee inTable1,clusteringcoeffiecientoftheobservednetwork isfar

greater than theassociatedrandomgraph,whilethecharacteristicpath lengthsofbothnetworksare

notmuchdifferent.This confirms that the citationnetworkof Indonesian legislationhas smallworld

properties.

Table1:topologicalpropertiesofcitationnetworkofIndonesian

legislationandtheassociatedrandomgraph

Graph C d

Citationnetwork 0.227374 5.66933 1.92

Randomnetwork 0.00356385 4.27066

Oneof themost interestingpropertieswhichareuniversallydiscovered inmany realnetworks is the

scalefreepropertiesofnetworktopology.Inscalefreenetwork,therearealargenumberofnodeswithvery few links and a small, but significant, number of nodeswith very many links. Specifically, this

networkischaracterizedbyhavingpowerlawdegreedistribution.

Here,weevaluate thevertexdegreedistributionbasedonnumberof indegree ()andoutdegree

()valueofeachvertex,asfollow:

(5)


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(6)

Figure 3a shows that the indegree distribution of our legal citation network follows powerlaw

distribution[10]:

(7)

with scaling coefficient =1.92.Thismeans that the fractionof vertexwith aparticularnumberof

connections (x) decays as once x is getting large. Number of legal products that cite the

observed legislationdefinethe indegreevalueofthe legislation.Thispattern indicateshowrelatively

fewlegislationgetthemajorityofallcitationswhilemostlegislationsarerarelyornevercited.Thehigh

concentrationofcitation insmallfractionof legislationspecifiesthose legislationsastheauthoritative

sourcesoflawreferredbymajorityoflegislations.

However,powerlawfeaturecouldnotbefound inoutdegreedistributionofcitationnetwork (Figure

3b).This isdue to the fact that legislationdocumenthas limitedspacepreventingeach legislation to

havealargenumberofoutwardcitation.

Figure3:cumulativedistributionofcitationnetworkofIndonesianlegislation:a.indegree;b.outdegree

b. Centrality

In this sectionwe apply the concept of network centrality to quantify the importance of legislation

withinnetwork.Inlegalcitationnetwork,theimportanceofadocumentiscloselyrelatedtoconceptof

legalauthority. Inoneside,alegislationthatreceivesmanycitationsfromotherlegislationlikelyplays

an important role as a source of lawwithin the legal system. Beside, a legislation that has a large

numberofoutward citations takes the role as thehub that leads toward anumberof authoritative

legislation.Thus,the importanceof legislationcanbeassociated inbothconceptofcentralitynamely,

authorityandhub.


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Formally,authorityvalueofvertexxicouldbewrittenasfollow[6]:

(8)

whilehubvalueofvertexyi,couldbewritten:

(9)

Inthematrixform,thisequationcouldbewrittenasfollows:

dan (10)

wherexandyareofthesymmetricmatricesAATdanATA.

Theabovemethod,whichcommonlyiscalledHITS2method[11],couldbeappliedtomeasurecentrality

of vertex in legal citationnetwork thathas acyclic character. Table2 shows the tenmost important

legislations, in the term of authority or hub centrality. It is interesting to know that most of this

legislationsconcernwithpolitics,autonomy,andregionalgovernment.

Table2:tenmost importantlegislations

Rank Authority Theme Hub Theme

1 UU_32_T2004 Localgovernment UU_9_T2007 Autonomy

2 UU_33_T2004 Financialrelationbetween

Central&Local

UU_4_T2007 Autonomy

3 UU_22_T2003 Politics UU_15_T2007 Autonomy

4 UU_10_T2004 Regulationmaking UU_14_T2007 Autonomy

5 UU_12_T2003 Election UU_8_T2007 Autonomy

6 perpu_3_T2005 Localgovernment UU_33_T2007 Autonomy



9 UU_21_T2001 Autonomy UU_8_T2008 Autonomy

10 UU_22_T2007 Election UU_6_T2008 Autonomy

IV. ConcludingRemarks

Inthispaper,werepresentthecorpusofIndonesianlegislationaslegalcitationnetwork.Byusingsome

measuringmethod,weshow that the topologyof thesenetworkhavesmallworldcharacteristics.On

2HypertextInducedTopicSearch


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onehand, thismeans thedistance between vertices is low, signifying the tendency of legislation to

integrate into coherent legal system, while on the other, the higher value of clustering coefficient

qualitativelyreflectsthetendencyoflegislationtoorganizeitselfsemantically,thatisaccordingtotopic

orcasetheyregulate.

Furthermore,wealso show thepresenceof scalingphenomenon in indegreedistributionof citation

networkof Indonesian legislation.Thisphenomenonconfirms thatsuch legalcitationnetworkshares

thestatisticalcharacteristicsofcomplexnetwork.Moreover,thisalsoindicatestheexistenceofasmall

number of legislations that act as anchors of the system, namely the legislations that have legal

authority to be referenced by other legislations. By using centrality measure, we quantify the

importanceoftheselegislations.

V. Acknowledgement

Both authors thank Surya Research International for financial support in which period the paper is

written,peopleinBFIfordiscussionsintheroughdraftofthepaper.WealsoextendourappreciationtoRonalRantealangforhelpingindataprocessing.

VI. Reference

1. Ruhl,J.B.2008.Law'sComplexity APrimer.GeorgiaStateUniversityLawReviewSymposiumIssue,

Forthcoming; FSU College of Law, Public Law Research Paper No. 313. Available at SSRN:

http://ssrn.com/abstract=1153514

2. Mazzega.et.al.2009. The network of French legal codes. Proceedings of the 12th International

Conferenceon

Artificial

Intelligence

and

Law

3.

Boulet.et.al.2010.Network Analysis of the French Enviromental Code. Artificial intelligence

approachestothecomplexityoflegalsystems

4. Reka.A,Barabsi.2002.Statisticalmechanicsofcomplexnetworks.Rev.Mod.Phys.,Vol.74,pp.47

97.

5. http://www.depdagri.go.id/produkhukum

6.

Leicth.et.al.2007.Largescalestructureoftimeevolvingcitationnetworks.,arXiv:0706.0015v2

7.

Bommarit.et.al.2010.Distancemeasuresfordynamiccitationnetworks.PhysicaA

8. Situngkir.H.2007.SmallWorldNetworkofAthletes:GraphRepresentationoftheWorldProfessional

TennisPlayer.WorkingPaperBandungFeInstitute

9.

Liao.et.al.2010.Smallworld directed networks in thehumanbrain:MultivariateGranger causalityanalysisofrestingstatefMRI.Neuroimage.54(4):268394.

10.Clauset.et.al.2009.PowerLawDistributioninEmpiricalData.arXiv:0706.1062v2

11.Kleinberg.J.1999.AuthoritativeSourcesinaHyperlinkedEnvironment.JournaloftheACM,46(5),pp.

60432.


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VII. Appendix

UU_32_T2004 PemerintahanDaerah

UU_33_T2004 PerimbanganKeuanganantaraPemerintahPusatdanPemerintahanDaerah

UU_22_T2003 SusunandanKedudukanMPR,DPRdanDPRD

UU_10_T2004 PembentukanPeraturanPerundangUndangan

UU_12_T2003 PemilihanUmum,AnggotaDPR,DewanPerwakilanDaerah,DPRD.

perpu_3_T2005 PerubahanatasUndangundangNo.32Th.2004tentangPemerintahanDaerah.

UU_8_T2005

Penetapan Perpu No.3 Th.2005 ttg Perubahan atas UU No.32 Th.2004 ttg

PemerintahanDaerahmenjadiUndangUndang.

UU_12_T2008

Perubahan Kedua atas UndangUndang Nomor 32 Tahun 2004 tentang

PemerintahanDaerah.

UU_21_T2001 OtonomiKhususBagiProvinsiPapua

UU_22_T2007 PenyelenggaraPemilihanUmum

UU_4_T1999 Susunan&KedudukanMPR,DPR&DPRD

UUprp_10_T19

60

PejabatygMenjalankanPekerjaanJabatanPresidenjikaPresidenMangkat,Berhenti

atauBerhalangan,sedangWakilPresidenTidakAdaAtauBerhalangan.

UU_9_T1968 PerubahanPasal7"IndischeComptabilitetswet"

UU_22_T1999 PemerintahanDaerah

UU_25_T1999 PerimbanganKeuanganAntaraPemerintahPusat&Daerah


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Complexity of Law the Exploration of Indonesian Legislation Network

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