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WeightedVotingModelsfortheHathiTrustConstitutionalConvention

byJuliaLovett

I. IntroductionandScopeInMarch2011,theHathiTrustDigitalLibrarypartnerinstitutionswillmeetforaConstitutionalConvention(CC).Atthismeeting,thepartnerswilleitherdevelopanewgovernancemodelforHathiTrustorarticulateasetofquestionstoframeapost‐Conventiondiscussionofanewgovernancemodel.Questionsmightinclude:Whatshouldthegoverningboardsbe,andhowshouldtheybeconstituted?Whichinstitutionsshouldhaverepresentativepower,andhowmanyrepresentativesshouldtherebeperinstitution?ShouldHathiTrusthaveanewhostinstitutionand,ifso,whatcriteriashouldbeusedtoselectanewhostinstitution?ThesedecisionswillhavealargeimpactonthefutureofHathiTrust,andshouldbearrivedatthroughamethodthataccuratelyreflectsvaryinglevelsofinstitutionalinvestmentintheproject.Thebestwaytoensurefairdecision‐makinginasituationwherevotersareinherentlyunequalistoestablishaweightedvotingsystem(seeBarrettandNewcombe,1968).Tothispurpose,thispaperexploresthefollowingquestions:

• Howisvotingpowercalculatedinaweightedvotingsystem?• Whatfactorsandprinciplesshouldinformallocationofvotingpower?• HowdothesemodelsapplytoHathiTrust?

Thefirstquestionisthemoststraightforwardonetoanswer,drawingfromscholarlyliteratureaboutapriorivotingpower,asubsetofgeneralvotingtheoryandsocialchoicetheory.Votingpowertheorycanbeappliedto“anycollectivebodythatmakesyes‐or‐nodecisionsbyvote.”(FelsenthalandMachover,1998)Theclassificationapriorireferstovotingpowerthatis“determinedwithouttakingintoconsiderationvoters’priorbiasregardingthebillvotedupon,orthedegreeofaffinity(forexample,ideologicalproximity)betweenvoters.”(FelsenthalandMachover1998)Inotherwords,thesystemsthattheoristshaveusedtodeterminevotingpowerdependontheassumptionthateverypossiblecombinationofvotesinacommitteeisequallylikelytooccur.Inreality,ofcourse,notallcombinationsareequallylikely.Certainscholarsstronglyobjecttothefactthatapriorimethodsexcludeexternalfactorssuchasvoters’pastbiasesandaffiliations(seeGelmanetal.,2004;Margolis,2004;Albert,2003).ThisobjectiondoesnotseemtopresentaproblemforHathiTrust.Suchbiasesandaffiliations,iftheyexist,wouldbeimpossibletoquantifywithouttheexistenceofanyvotingpriortotheCC.

Votingpowertheory’srestrictiontobinary(twooption)decisionsisnecessaryforanumberofreasons.Firstandforemost,amethodofcalculatingweightedvotingpowerforasysteminvolvingmanyoptionsorcomplicatedvotingprocedureshasnotbeenwidelystudied.Manyvotingtheoristshavedetailedprocedureswithmorethantwochoicesandperhapsmorethanoneresult(Black,1998;Dummett,1984;Tideman,2006;Brams,1983),butthesestudiesusuallyassumethatconstituentshaveequalvotes.Inaddition,suchstudiesoftenfocusonelectionsandlarge‐scalevotingprocesses,asopposedto

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votingincommittees.FelsenthalandMachover(1998)explicitlynotethesetrendsintheliterature,describingthemeasurementofvotingpoweras“orthogonaltotheconcernsofthegeneraltheoryofvoting.”(5)ThemostimportantaspectofavotingmodelfortheHathiTrustCCisthateachpartnerinstitutionhasalevelofinfluencecommensuratewithitsdegreeofinvestmentinHathiTrust.Givenexistingmethodsofcalculatingvotingpower,thesurestresultscanbedrawnfrombinaryvoting.Inaddition,votingtheoryoftenassumesthatasimplemajority(morethanhalf)willberequiredforadecisiontopass.Itispossible,ofcourse,forthequota—thenumberofvotesrequiredtopassadecision—toberaisedhigherthanasimplemajority.Severalstudieshavebeenmadeoftheeffectofvariousquotasonrealvotingbodies(Leech,2003;DreyerandSchotter,1980).Forthesakeofsimplicity,thispaperwilldiscussvotingtheorybasedonasimplemajority.

Themoredifficultquestionstoanswerarethesecondandthirdintheabovelist:Whatfactorsandprinciplesshouldinformallocationofvotingpower?HowcanthesemodelsbeappliedtoHathiTrust?Whereasmethodsofcalculatingvotingpowerhavebeenwidelycitedandacceptedbymanytheorists,thereisnostraightforwardmethoddetailinghowtofairlyallocatesuchpower.Theweightingfactorsseemtodependontheorganization,andcouldincludeprinciplesoffairness,monetarycontributions,andadesiretobalancelargerandsmallerpowers.CasestudiesofvotinginrealorganizationssuchastheUnitedNations,InternationalMonetaryFund,andEuropeanUnionCouncilofMinisters,couldprovidesuggestionsforHathiTrust.

II. VotingPowerTheory

Therearetwowidelyacceptedandcitedmethodsforcalculatingapriorivotingpower.OnewasoutlinedbyPenrose(1946)andlaterarrivedatindependentlybyBanzhaf(1965).TheothermethodwasfirstproposedbyShapleyandShubik(1954).Furthermore,Leech(2003)hasdemonstratedhowtousethesemethodstoworkbackwardsandcalculatevotingweightbasedonpredeterminedvotingpower,accordingtotheBanzhafmethod.Therearealsosomeminormethodsthathavenotbeenwidelyadoptedandwillnotbediscussedinthispaper(seeFelsenthalandMachover,2004).

Thehistoryofvotingpowertheoryhasbeencharacterizedbyfitsandstarts,asmanyscholarshaveundertakentheproblemofmeasuringapriorivotingpowerwhileapparentlyunawareofpriorworkinthesubject.BanzhafindependentlyarrivedatthesamesystemasPenrose,inignoranceofthelatter’s1946paper.Coleman(1971)approachedtheproblemunawareofbothShapley‐ShubikandBanzhaf.(FelsenthalandMachover,1998)Onlyrelativelyrecentlyhasthefieldcometogetherinacoherentway.

InboththeUnitedStatesandEurope,interestinvotingpowertheoryhassurgedwithchangesindecisionrulesoflargevotingbodies.Forexample,intheEuropeanUnion,manytheoristsarguedfororagainsttheuseofaprioripowermeasuresasaguideforthere‐weightingofvotesintheCouncilofMinistersin2001(PajalaandWidgren,2004).IntheUnitedStates,thetopicofvotingpowerenjoyedthegreatestpopularityinthe1960’swhenmanyscholarsadvocatedapplyingweightedvotingtostatelegislatures.(FelsenthalandMachover,2004;Leech,2003)ItwasduringthiscontroversythatJohnBanzhaffirstarguedagainstequatingvotingweightwithvotingpower.

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A. PenroseandBanzhaf

Inhisseminalarticle“WeightedVotingDoesn’tWork:AMathematicalAnalysis,”JohnBanzhaf(1965)arguesthat“votingpowerisnotproportionaltothenumberofvotesalegislatormaycast.”(318)Inotherwords,agreatervotingweightdoesnotautomaticallytranslateintogreaterpower.Banzhafcraftedthisargumentinresponsetowidespreadsuggestionsatthetimethatweightedvoting,inwhichlegislativerepresentativeswouldholdvotingweightsproportionaltothepopulationoftheirrespectivedistricts,couldbeimplementedasanalternativetoreapportioningthelegislativeseats.Theresultingdistributionofpower,proponentsargued,wouldbethesameineithercase.

Banzhafdemonstratesthefallacyofequatingweightwithpowerthroughaseriesofexamplesandmathematicalreasoning.Heasserts,“itwouldbemoreeffectivetothinkofvotingpowerastheabilityofalegislator,byhisvote,toaffectthepassageordefeatofameasure.”(318)Alegislator’spowerliesinthechancethathisindividualvotewillswingthecollectivevote.Thosechancesareindeedhighlydependentontherelativevotingweightsinthecommittee,butnotinapredictableorintuitiveway.Banzhafpresentsthefollowingtable(p.339)asonerealexamplewhereseeminglyappropriatevotingweightsresultinradicallyinappropriatepowerdistribution:

Inordertotallythenumbersinthelastcolumn,Banzhafhastakenallthepossiblecombinationofvotesandlookedatthecombinationswherethelegislatorcouldswingthevote.Heassumesthatasimplemajority(morethanhalf)willcausethebilltopass.ThemostsurprisingresultisthatNorthHempstead,withapopulationof213,225and21weightedvotes,canneverbethepivotalvoteandthereforeeffectivelyhasnovotingpower.

Banzhaf’sargumentechoestheworkofL.S.Penrose(1946),whosearticle“TheElementaryStatisticsofMajorityVoting”firstundertookaseriousstudyofapriorivotingpower.Penrosewrites,“thepoweroftheindividualvotecanbemeasuredbytheamountbywhichhischanceofbeingonthewinningsideexceedsonehalf.”(53)ParaphrasedbyFelsenthalandMachover(2004),Penrose’sbasicargument(thesameasBanzhaf’s)isthat“themorepowerfulavoteris,themoreoftenwilltheoutcomegotheways/hevotes.”(3)Banzhaf,whowasapparentlyunawareofPenrose’swork,explainsthissameconceptwithasimplemathematicalargument:

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Moreexplicitly,inacasewherethereareNlegislators,eachactingindependentlyandeachcapableofinfluencingtheoutcomeonlybymeansofhisvotes,theratioofthepoweroflegislatorXtothepoweroflegislatorYisthesameastheratioofthenumberofpossiblevotingcombinationsoftheentirelegislatureinwhichXcanaltertheoutcomebychanginghisvotetothenumberofcombinationsinwhichYcanaltertheoutcomebychanginghisvote.(331)

WhilePenroseframedhisargumentaroundtheabsoluteprobabilityofavoter’ssuccess,Banzhafwasmoreinterestedinrepresentingrelativepower.Thefollowingtable(p.342)showshismethodoflistingallpossiblevotingcombinationsandtallying“combinationsinwhicheachlegislatorcastsadecisivevote:”

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Again,therearesomesurprisingresults:VoterL,withaweightofone,hasjustasmuchrealvotingpowerasJandK,whoeachhaveaweightofthree.InordertodeterminetherelativevotingpowerofH,I,J,K,andL,onewoulddivideanindividual’svotingpowerbythetotalamountofvotingpowerintheassembly.Essentially,thiscalculationresultsintheindividualvoter’sshareofthetotalavailablevoting

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power.Convertingthenumberstopercentages,sothattheentireweightaddsupto1,resultsinwhatistermedtheBanzhafIndex(FelsenthalandMachover,2004,p.5).FelsenthalandMachover(2004,p.6)demonstrateBanzhafIndexvaluesfortheEuropeanUnionCouncilofMinistersinthefollowingtable:

IftheHathiTrustpartnersaccepttheBanzhafIndexasameasureofrelativevotingpower,suchanindexwouldbesimpletocomputeforanygivenvotingweights.Themoredifficultpartwouldbeworkingbackwardstofindvotingweight,givenapredeterminedpowerdistribution.Leech(2003)pointsout,“Therehavebeenmanystudiesofthedistributionofaprioripowerinactualvotingbodieswherethedecisionruleandallocationofvotestovotingmembersisgivenbutrelativelyfewwheretheapproachhasbeenusedasatoolfordesigningweightedvotingsystems.”Inthissamepaper,LeechdemonstrateshowtousetheBanzhafindextodesignavotingsystem.Thesecalculationsarepossiblewithsomemathematicalwork,discussedinmoredetailinthesectionbelow,“DeterminingWeightforaGivenBanzhafPowerAllocation.”

B. ShapleyandShubikTheShapley‐Shubik(1954)methodistheotherwidelyacceptedsystemofdeterminingvotingpower.Atfirstglance,thismethodseemstoreplicateBanzhaf’sapproach.ShapleyandShubikstate,“Ourdefinitionofthepowerofanindividualmemberdependsonthechancehehasofbeingcriticaltothe

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successofawinningcoalition.”(787)This“chanceofbeingcritical”isimportantinBanzhaf’smethodaswell.ButtheirconceptofvotingpowerbeginstosoundabitdifferentfromBanzhaf’s:“Itispossibletobuyvotesinmostcorporationsbypurchasingcommonstock.Iftheirpoliciesareentirelycontrolledbysimplemajorityvotes,thenthereisnomorepowertobegainedafteronesharemorethan50%hasbeenacquired.”(788)WhereasPenroseandBanzhafbothdescribedvoterpowerasthepowertoinfluenceadecision,Shapley‐Shubikdescribevoterpowerasashareinanexpectedpayoff.Thereisafundamentalconceptualdifferencebetweenthetwomethods;whereastheBanzhafmethodisbasedonprobability,theShapley‐Shubikmethodisbasedongametheory.

FelsenthalandMachover(1998,2004)stronglyarguethispointabouttheconceptualdifferencesbetweenthetwomethods.ShapleyandShubik’sviewofpower,theyargue,“isthatpassageordefeatofthebillismerelytheostensibleandproximateoutcomeofadivision.Therealandultimateoutcomeisthedistributionofafixedpurse(theprizeofpower)amongthevictorsinthecasewhereabillispassed.”(10)VotersaccordingtoPenroseandBanzhafarepolicy‐seeking;votersaccordingtoShapleyandShubikareoffice‐seeking.(FelsenthalandMachover2004,p.11)Theideaofvotermotivationissomethingthatcomesupofteninthegeneraltheoryofvoting(seeColeman,1971;Dummett,1984).Thispaperwillnotexplicitlydetailthosearguments,butithelpstobeawarethatcertainideasaboutvotermotivationunderlieboththePenrose‐BanzhafandShapley‐Shubikmethods.IndecidingonamethodofcalculatingvotingpowerintheHathiTrustCC,thepartnersshouldconsiderwhichnotionofvotermotivationfitswithHathiTrust.Mostlikely,thepartnerswillallbeinterestedinwhatisbestforHathiTrust,andthereforecouldberegardedaspolicy‐seekingratherthanoffice‐seeking.

Beyondhavingconceptualdifferences,theBanzhafandShapley‐Shubikmethodssometimesproducedifferentnumericalresultswhenappliedtothesamesetofvoterweights.ThedifferencescanbeseeninthistablefromLaneandBerg(1999),detailingvotingpowersinGermany(p.314)accordingtothePenrosemeasure(BI),BanzhafIndex(Banzhafnorm.),andShapley‐ShubikIndex(SSI):

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OnepotentialdrawbackofusingtheShapley‐ShubikIndexisthatitismuchmoredifficulttocalculatethantheBanzhafIndex.InShapleyandShubik’soriginalarticle(1954),aftergivinganexampleofanindividualvoter’spowerinacertainsituation,theystate:“Thecalculationofthisvalueandthefollowing[values]isquitecomplicated,andweshallnotgiveithere.”(789)PerhapsthesimplestexplanationisgivenbyDixon(1983,p.298),whowrites:

Thismeasurereflectsthepriorprobabilitythatanindividualwillcastthedecidingvoteonanyissuebybeingthelastmembertojoinaminimalwinningcoalition...Todeterminetheexpectationthatanindividualwillpivot,onemustconsiderallofthepossiblesequences(n!inannmembervotingbody)inwhichaminimalwinningcoalitionmightform.Foranymemberi,theShapley‐Shubikpowerindex,φ,maybedefinedas

φ=(totalpivotsfori)/n!

TheShapley‐ShubikIndextakesintoaccountthe“possiblesequences,”theorderinwhichvotesoccur.Again,thispointstoaconceptualdifferenceaswellasamethodologicaldifferencebetweentheShapley‐ShubikmethodandtheBanzhafmethod:WhereasBanzhaffocusesoncombinationsofvotes,

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theShapley‐Shubikmethodfocusesonpossiblesequencesofvotes.Thepivotalmember,accordingtoShapley‐Shubik,isthelastmemberwhosevoteformsa“minimalwinningcoalition,”renderingthesubsequentvotesmeaningless.Again,forHathiTrust,thepartnersshoulddecidewhichmethodofpowerdeterminationfitsHathiTrust’svotingscheme.Ifvoteswillbecastsimultaneouslyratherthansequentially,thentheBanzhafIndexmakesmoresensethantheShapley‐ShubikIndex.

C. DeterminingWeightforaGivenBanzhafPowerAllocation

Calculatingtheweightsforagivenpowerallocationrequiresacomputerandaprogramtorunthenecessaryalgorithm.InLeech’s2003paper,“PowerIndicesasanAidtoInstitutionalDesign:TheGeneralisedApportionmentProblem,”heexplainsastep‐by‐stepapproachtocalculatingvotingweightsbasedonagivenBanzhafIndexofpowervalues.Essentially,hismethodreliesontrialanderror,startingwithanarbitraryguessofweightsandthenrepeatingtheguessesatcertainintervalsuntilhittingontheclosestpossiblematch.Keepinmindthat,asLeechexplains,thereisnooneuniqueweightdistributionforeveryuniquepowerindex.Usinghisalgorithm,itispossibletofindanextremelycloseapproximation,withafewimportantlimitations:Ingeneral,themorevotersthereare,themorepossiblepowerdistributionsthereare,andtheeasieritistofindweightstomatchagivenpowerallocation.Forexample,Leechdemonstratesthatwith3voters,foranycombinationofweights,thereareonlyfourpossiblepowerallocations.Upto5voters,therearestillrelativelyfewresultingpowerallocations.

LuckilyforHathiTrust,bythetimeoftheCCtherewilllikelybeatleastsevenpartners,andtheweightscanbecalculatedtocloselyapproximatemostpowerallocations.Inthespreadsheetattachedtothisdocument,eachexampleHathiTrustpowerallocationcorrespondstoacertainweightdistribution,andtheseweightsarebasedonLeech’smethod.CreditforthisworkisduetoDanielKneezel,aUniversityofMichiganPhDstudentinmathematics,whodesignedaprogramtorunLeech’salgorithm.(ForamoredetailedexplanationofthisspreadsheetandspecificrecommendationsforHathiTrust,seethelastsectionofthisdocument.)

III. PrinciplestoGuideVotingPowerAllocation

Apriorivotingpowertheoryservesanextremelyusefulpurpose:itenablesthecalculationofvotingpowerbasedonunequalvotingweights.Itdoesnot,however,makethejobofdecidinghowtoallocatevotingpoweranyeasier.Manyscholars,whethertheyincorporateformalvotingpowertheoryornot,havetackledtheproblemofhowtoallocatevotingpowerinorganizationswithdiverseconstituents.Severalgeneralprinciplescanbegleanedfromthesestudies,asbasiccriteriatoguidethedistributionofvotingpower.

BarrettandNewcombe(1968)completedanextensivestudyofvariousweightedvotingformulasandhowtheymightapplytotheUnitedNations.Theauthorsneatlylayoutfourprinciplesthatavotingmodelshouldsatisfy:“Decision‐makingbyvotingisasocialinventiondesignedtosatisfyseveraltypesofdemands:Thoseofjustice(orequity),thoseofwisdomoreffectiveness,thoseofreflectingandformalizingactualpowerrelationships,andthoseofacceptabilitytotheparticipants.”(2)Corresponding

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tothese“typesofdemands”areseveralreasonsthatweightedvoting,ratherthanequalvoting,isnecessaryincertainsituations.Thefollowingtableofprinciples(“typesofdemands”),withcorrespondingreasonsforweightedvoting,isadaptedfromBarrettandNewcombe’sexplanationonp.1‐5.

TypesofDemands ReasonsforWeightedVotingEquity • Somemayhaveagreaterfinancialstake

• Somemaybemoreaffectedbythedecisions

• Somemayhavegreaterseniorityrights• Somemayrepresentlargerorganizations

Effectiveness • Somemaybeinabetterpositiontocarryoutthedecisions

• Somemaybebetterinformedabouttheissues

Reflectingandformalizingpowerrelationships • Somemayhavemorepersonalpowerthanothers,andwewishtoformalizethispowerratherthanhavingitexercisedinformallybyinfluencingthevotesofothers

Acceptabilitytoparticipants • Noexplicitreasons;weightedvotingis“acceptable”whenitreachesacompromisebetweenequityandpower

Lookingatthesedemandsandreasons,itiseasytoseethatmanyofthemapplytotheHathiTrustpartnership.ThespecificpermutationsofthefactorsastheyrelatetoHathiTrustwillbediscussedintheRecommendationssectionofthisdocument.Itisimportanttofirstunderstandtheprinciplesthemselves,thereasonsforthoseprinciples,andhowrealorganizationsattempttosatisfythoseprinciplesthroughweightedvotingschemes.

A. Equity

Theprincipleofequityisintuitive.Inasituationwhereeveryvoterhasanequalsay,themeansofsatisfyingtheprincipleofequityissimple:eachpersonshouldhaveonevote.Manytheoristsarguethatinrealinternationalorganizations,whosemembersrepresentthecitizensoftheirrespectivecountries,theidealvotingpowerallocationwillequalizethepowerofthosecitizensthroughweightedvotingintheorganization.Ifeachmemberoftherepresentativeboardgetsonevote,thenthecitizensoflargercountriesactuallyhavelesspowerthanthecitizensofsmallercountries.Likewise,BanzhafandShapley‐Shubikhaveproventhatgivinglargercountriesagreatervotingweightdoesnotresultintheappropriateallocationseither.Itwasthisprincipleoffairnessofrepresentation,andtheconcernthatentiregroupsofcitizensmightnothaveanyactualvotingpower,thatdroveBanzhaftocreatetheBanzhafIndex.Acountry’spopulation,therefore,isoftensuggestedasamainfactorindeterminingvotingpower.

HathiTrustisnotarepresentativebody,andcannotrelyonthedemocraticprincipleofone‐person‐one‐vote.Thereareotherfactors,though,thatarebeing“represented”bythevotingmembersof

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HathiTrust.Thesecouldincludethenumberofvolumescontributedtotherepository.Thegreaternumberofvolumesaninstitutionhascontributed,thegreatertheinstitution’sstakeinHathiTrustandthegreatertheamountofmaterialthatisbeingrepresentedfromthatinstitution’scollection.

B. Effectiveness

Theprincipleofvotereffectivenessisperhapsthemostdifficulttoquantify,andyetitseemsrelevanttoanyorganizationinwhichmembershavevaryingdegreesofexperience.InHathiTrust,certainmemberinstitutionshavemoreintimatefamiliaritywiththegovernanceofHathiTrustsimplybyhavingworkedontheprojectatagranularlevelonadailybasis.Ifanynew,non‐foundingpartnersjoinHathiTrustbeforetheCC,certainlythosenewpartnershavelessexpertisethanthecurrentpartners,aswellaslesscapabilitytoeffectivelyactondecisionmaking.BarrettandNewcombeclassifytheabilitytoactondecisionsaspartoftheeffectivenessprinciple.Voterswhoarewiseandexperiencedareprobablymoreinvolvedintheissuesathand,andthereforebetterpoisedtocarryoutdecisions.ThiscorrelationiscertainlytrueinHathiTrust,wherethememberswhohavemoreexperiencealsohavemoreexistingtiestotheprojectandgreaterabilitytocarryoutdecisions.

C. Power

Inanyorganization,somemembershavemorerealpowerthanothers.BarrettandNewcombeexplainthatthereareseveraltypesofinformalpoweramembermightpossess.Forexample,certainmembersmaybemorecharismaticthanothers.Certainmembersmayhavemorepoliticalpower.ThefactisthatcertaininstitutionsinHThavemorerealpowerthanothers.Alongwithacommitmenttohostthephysicalinfrastructure,MichiganandIndianahavemadedeepercommitments(e.g.theMichiganlegalorientation,alargerfinancialcommitmentbyeachuniversity,andIU’stechnologicalinvestments)thatpartnerswouldbechallengedtofindatanotherinstitution.

Theneedtopreventstrongermembersfromdominatingdecision‐making,whilestillensuringthatsmallerpowershaveavoice,isacentralneedthatweightedvotingattemptstosolve.Intheir2006article“ReformingtheIMF’sWeightedVotingSystem,”RapkinandStrand(2006)arguethatreformstotheIMF’svotingregimemustanswera“fundamentalproblemthatisboththeoreticalandpractical:howbesttoreconciletheprincipleofsovereignequalitywiththefactofwidepowerasymmetriesamongmembers.”(p.2)IntheIMF,variousmembersdohavemorerealpowerthanothers,andtherearecertainvotingmeasuresthatattempttoformalizethatpower.TheUnitedStates,forcertaintypesofdecisions,“retainstheonlysingle‐countryvetoovermajorIMFdecisions,includinganydecisionthatwouldreduceitsvotingpowerandincreaseordecreasethatofothercountries.”(p.12)Vetopowerisoneoptionincaseswhereonemembersimplyhasmorerealpowerthanalloftheothermembersputtogether.Itcanbeharmful,however;RapkinandStrandalsopointoutthattheU.S.’svetopowerfosters“perceptionsofsystemicunfairness”(p.2)andinfluencesdecisionsevenwhenitisnotexplicitlyexercised.

Whetheranorganizationgrantscertainmembersvetopowerornot,thefactremainsthatmorepowerfulmembersofanorganizationwillnotacceptavotingmodelinwhichtheyarenotgrantedenoughpower.Neitherwillthelesspowerfulmembershaveconfidenceinamodelthatgrantsthem

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verylittleornopower.Theprincipleofpower,therefore,ishighlyinterrelatedwiththeprincipleofacceptability.

D. Acceptability

Acceptability,accordingtoBarrettandNewcombe(amongothers),representsacompromisebetweentheprinciplesofpowerandequity.Anacceptableschemewillrepresenttheinterestsofboththestrongerandweakerparties.Acceptabilityisarguablythemostimportantprinciplethataweightedvotingmodelshouldsatisfy,simplybecauseavotingmodelthatisnotacceptabletovoterswillnotwork.Newcombe,Wert,andNewcombe(1971)alsoechothisfocusonacceptabilityintheirlaterstudyofpossibleUNformulas:

Onlyaworldbodythathastheconfidenceofasmanymember‐nationsaspossible,EastandWest,richandpoor,largeandsmall,willbeabletoobtainthepowersitneeds.The‘balancing’neededtogaintheconfidenceofmemberstatesisadifficultmatter.Preciselythisbalancingisthepurposeofanyweighted‐votingscheme....Themaincriterioninevaluatingaweighted‐votingformulaisacceptability,noteitherabstractjusticeortheoreticalreasoning.”(452)

Theirastuteobservationisagoodonetokeepinmind,andwillmostlikelybethedrivingprinciplebehindselectingavotingprocedureforanyorganization.Inthelongterm,novotingprocedurewillworkifitdoesnotinspiretheconfidenceoftheconstituents.

ManyofthevoteallocationformulasproposedbyBarrettandNewcombe,andlaterdiscussedbyDixon(1983),inrelationtotheUnitedNations,aimatsomesortofcompromisebetweenthefactorsofequityandpower.Thefactorofacountry’spopulationcorrelatestothedemandsofequity,whilethefactorofGDPcorrespondsto“aroughindicationofastate’spower.”(Dixon,1983)Thesefunctionsincludetakingdirectnumbers,logarithms,squareroots,andothervariationsoneachcountry’srespectiveGDPandpopulation.Interestingly,Dixonalsodebatestheacceptabilityofapriorivotingtheoryitself,asthepointofhisstudyistoapplytheBanzhafIndextoeachformula.Hepointsoutthatifaweightedvotingsystemisdesignedspecificallytomeettheneedsofagivenpowerallocation,thevotingweightsnecessarytogenerateagivenpowerdistributionwillseemsoarbitrarytovotersastorenderthemunacceptable.

Onepossiblecompromisebetweenweightedvotingandequalvoting,whichisRapkinandStrand’s(2006)mostimportantrecommendationtotheIMF,isthesystemofvotingbydoublemajority.The“CountandAccount”(doublemajority)votingscheme,asdescribedbelowbyO’NeillandPeleg(2000),representsamorestableandconsistentcompromisebetweenweightedvotingandequalrepresentation:

Votingbycountandaccounttakesintoconsiderationbothsizeandequalityanddoessoinasimpleway.Votesarecountedtwice,firstwitheachpartyweightedequally,andthenwitheachweightedbyitsfinancialcontributionorsomeotherobjectivemeasure.Aproposalpassesifitgetsamajorityinbothways.Theruleformalizestheideathatanorganizationshouldactonlywhenithasthesupportofboththegeneralmembershipandtheimportantmembers.(3)

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Onethingtobeawareofisthatthecountandaccountschemeis“necessarilymoreconservativethanusingastraightmajorityoftheaccountweightsalone,sincetwocriteriahavetobesatisfiedratherthanoneandfewerresolutionsgetpassed.Thiscanbeseeneitherasadisadvantageofthemethod.”(O’NeillandPeleg8)Itisalsopossibletoapplyvotingpowerindexestothedoublemajoritymethod;Turnovec(1997)hasdonesoinhisusefulstudyofvotingintheEuropeanUnion.Thedoublemajoritymethodisonepossiblewaytoincreaseacceptability.ItcouldbeparticularlyusefulasatechniqueforHathiTrust.

IV. RecommendationsforaHathiTrustVotingModel

Drawingfromtheprevioussections’discussionsofapriorivotingpowertheoryaswellascasestudiesofvotingpowerallocation,thissectionwillproposerecommendedvotingmodelsforHathiTrust.Recommendationsfallintotwodifferentcategories:basicrecommendations,andspecificrecommendations.Whereasbasicrecommendationshavetodowiththeassumptionsandscaffoldingofthevotingmodel,specificrecommendationswillentailanumberofdifferentformulasthatcouldworkforHathiTrust.

TodesignavotingmodelthatworksforHathiTrust,wemustask:

• Whichofthefourprinciples—equity,effectiveness,power,andacceptability—arerelevanttoHathiTrustattheConstitutionalConvention?

• Howcantheprinciplesbesatisfiedthroughaweightedvotingmodel,andwhatfactorsareavailabletoinformthemodel?

Toanswerthefirstquestion,itishelpfultoturntoexistingHathiTrustdocumentation,particularlytheMissionandGoals,FAQ,andFunctionalObjectivesontheHathiTrustwebsite(http://www.hathitrust.org/).Acrossallofthedocumentation,thereisastrongfocusoncollaboration,co‐ownership,andopenness.TheMissionandGoalsexplainHathiTrust’scorevalues,statingthattheorganizationisa“collaborationofthethirteenuniversitiesoftheCommitteeonInstitutionalCooperationandtheUniversityofCaliforniasystemtoestablisharepositoryfortheseuniversitiestoarchiveandsharetheirdigitizedcollections.Partnershipisopentoallwhosharethisgrandvision.”Atthesametime,theHathiTrustdocumentationmakesreferencestothefactthatdespitethisunityofvision,partnerswillretaintheirindividuality.Forexample,HathiTrustwillbe“co‐ownedandmanagedbyanumberofacademicinstitutions”andwillstriveto“dramaticallyimproveaccesstothesematerialsinwaysthat,firstandforemost,meettheneedsoftheco‐owninginstitutions.”Thesestatementssuggestatoncecollectiveownership,collectivemanagement,andcollectiveneeds,butalsoindividualownership,individualmanagement,andindividualneeds.ItissafetosaythatHathiTrustisacollaborativeorganizationwithacohesivevisionthatisnonethelesscomprisedofindividualanddistinctconstituents.OneofthechallengesindesigningavotingmodelwillberecognizingthefundamentalvalueofeachHathiTrustinstitution,whileallowingfordifferencesinpowerandinfluence.

ItisalsoclearfromtheHathiTrustdocumentationthatthefoundingpartnersofHathiTrustdeserveagreatdealofcreditfortheirhardworkontheprojectthusfar.UndertheFAQ“Who’stakingthelead?”

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thefollowingstatementemphasizesthecommitmentandexpertiseofthecurrentpartners:“TheUniversityofMichigan,IndianaUniversity,theUniversityofVirginia,andtheUniversityofCaliforniasystem,allhighlyregardedfortheirexpertiseintheareasofinformationtechnology,digitallibraries,andprojectmanagement,areleadingthepartnershipeffortthroughtheirexpertiseandfinancialcommitment.AllmembersoftheCICarefoundingpartners.”Recognizingpowerdifferencesamongthepartnerssuggeststhattheprinciplesofbothequityandpowerneedtobesatisfiedbyaweightedvotingsystem.Currently,therearefivepartners:

• UniversityofMichigan• IndianaUniversity• CaliforniaDigitalLibrary(includesalltheUniversityofCaliforniainstitutions)• CommitteeonInstitutionalCooperation(excludingMichiganandIndiana)

o MichiganStateUniversityo NorthwesternUniversityo TheOhioStateUniversityo PennStateUniversityo PurdueUniversityo TheUniversityofChicagoo UniversityofIllinoiso UniversityofIllinoisatChicagoo TheUniversityofIowao UniversityofMinnesotao UniversityofWisconsin‐Madison

• UniversityofVirginia

Inaddition,ColumbiaUniversityandYaleUniversitymayalsobejoiningtheranksofHathiTrustrelativelysoon.Amongthepartners,thefollowingfactorscontributetotheirdifferencesincommitmenttoHathiTrust:

• Financialcontributions• Projectednumberofvolumesinrepository• Lengthofcommitment(sinceJanuary2008)• Repositoryadministratorstatus

o UniversityofMichigan,IndianaUniversity• Founderstatus

o UniversityofMichigan,IndianaUniversity,CommitteeonInstitutionalCooperation,UniversityofCalifornia

Toillustratetherelationshipofthesefactorstoprinciples,or“typesofdemands,”thefollowingtablemimicstheprevioustablewhileaddingineachfactorandwhereitwouldcorrelatetoaprinciple:

TypesofDemands HathiTrustReasonsforWeightedVoting

HathiTrustWeightingFactors

Equity • Somehaveagreaterfinancialstake

• Somearemoreaffectedbythedecisionsduetogreaterinvestmentofresourcesand

• Financialcontribution• Numberofvolumes

contributed(projected)• Lengthofcommitment,

startinginJanuary2008• Founderstatus

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Inthistable,severalofthefactorsoverlap;thatis,theyfulfillseveraldifferentprinciples.Theprincipleofeffectivenessistheonlyonethatdoesnothaveanyuniquefactors.Itissafetosaythatequity,power,andacceptabilityarethedemandsthatwilldeterminetheHathiTrustCCvotingmodel.Effectivenessiscertainlyimportant,butanyvotingmodelthatsatisfiestheotherthreeprincipleswillautomaticallysatisfytheprincipleofeffectivenessaswell.

A. GeneralRecommendations

TherecommendationsforHathiTrust’svotingmodelcanbedividedintogeneralrecommendations,pertainingtotheoverarchingstructureofthemodel,andspecificrecommendationspertainingtothemorecomplicatedsubsetofquestionsaboutpowerallocationandvotingweight.ThosemorecomplicatedquestionswillbediscussedinSectionB.ThefollowingsetofrecommendationsappliestothebasicarchitectureofaHathiTrustvotingpowerscheme.Itgoeswithoutsayingthattheyaremeanttosatisfytheprinciplesofequity,power,andacceptability,aswellasappropriatelyreflectthefactors.

• Implementadoublemajorityvotingsystemofbothweightedandequalvotes,requiringamajorityofbothtypesofvotesinorderforadecisiontopass

• Fortheweightedvotes,setasimplemajority(50%quota)• Fortheequalvotes,themajoritycanbesetatasimplemajorityorhigherdependingonthe

importanceofthedecision• Forespeciallyimportantdecisions,itwouldalsobewisetorequireamajorityorunanimityof

theHathiTrustfoundinginstitutions:UM,UC,CIC,andIU

Equity • Somehaveagreaterfinancialstake

• Somearemoreaffectedbythedecisionsduetogreaterinvestmentofresourcesandcontributionofvolumes

• Somehavemadealongercommitmentand/ororarefoundingmembers

• Financialcontribution• Numberofvolumes

contributed(projected)• Lengthofcommitment,

startinginJanuary2008• Founderstatus

EffectivenessofVoters • SomeareHathiTrustadministrators

• SomehavebeenmoreinvolvedthanothersinshapingHathiTrust,andaremoreinformedabouttheissues

• Administratorstatus• Lengthofcommitment,

startinginJanuary2008

Power • SomeareHathiTrustadministratorsand/orfoundingmembers,andthereforehavemorerealinfluenceoverdecisions

• Administratorstatus• Founderstatus

Acceptability • GiventhepowerasymmetriesinHathiTrust,aweightedvotingschememakessense

• Compromisebetweenfactorsofpowerandequity

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• HathiTrustadministrators,UMandIU,shouldeachhaveaninstitutionalveto• Sticktobinary(twooptions,oryes/no)voting,whichwillenabletheapplicationofapriori

votingpowertheorytotheweightedvotes• Determineavotingpowerallocationbasedonanappropriateformulaandfactors,andthen

calculatethevoterweightsaccordingtotheBanzhafIndexusingLeech’s(2003)method(seeSectionBandattachedspreadsheet)

o Recommendedpowerallocationformula:

VotingPower=(squarerootofvolumes)+(squarerootoffinancialcontribution)

Mostoftheserecommendationsareself‐explanatory,orhavebeenjustifiedelsewhereinthedocumentalready.ThedoublemajorityvotingmodeleffectivelyreflectsthetensionevidentintheHathiTrustmissionstatementbetweeninstitutionalequalityandpowerdifferences.Itfulfillstheprincipleofacceptabilitybecauseitachievesinexecutionwhatitpromisesintheory.Itisalsoanextremelyusefulmodel,asitissimpleandyetadaptabletodifferenttypesofdecision‐making.Thisadaptabilitymakesitlikelytobeanacceptablescheme.Asnotedabove,theequalvotesportionoftheschemecanbeeasilymanipulatedintermsofitsquotaandalsothesubsetsoftypesofvoters.Forimportantdecisions—movingtheHathiTrusthostinstitution,forexample—itmakessensetorequirenotonlyamajorityofvoters,butahighermajoritythanusualandperhapsamajorityoffoundingmemberinstitutions.

ImplementinganinstitutionalvetofortheHathiTrustadministratorsislikelytobethemostcontroversialoftheserecommendations,butitmakessensebothpracticallyandtheoretically.TheUniversityofMichiganandIndianaUniversityhavebothmadetremendouscommitmentsofadministrativeresourcesandlegalresponsibilitytoHathiTrust.

Asfortheweightedvotingportionofthescheme,thequotaislessflexible.Thequotashouldbesetat50%because,withahigherquota,itissimplymoredifficulttofindweightsthataccuratelyreflectagivenpowerallocation(seeLeech2003).Sincethegoalofweightedvotingistoachieveanaccurateallocationofpower,itmakessensetouseaquotathatachievesthisaccuracy.Theadherencetobinaryvotesisalsomeanttosatisfytheneedforaccuratevotingweights,asonlybinaryvotingcanbeanalyzedusingapriorimethods.

TherecommendationofusingtheBanzhafIndex,asopposedtotheShapley‐ShubikIndexofcalculatingvotingpower,isbasedonthetwomethods’verydifferentconceptionsofvotermotivationandprocedure.TheBanzhafIndexassumesthatvotersaredisinterestedparties(policy‐seeking)ratherthanseekersoftheirownadvancement.TheHathiTrustpartnerscertainlyhavetheproject’sbestinterestsatheart,andthereforetheBanzhafconceptionofmotivationismoreappropriate.TheShapley‐ShubikIndexisalsobasedonsequenceofvotes,whichseemsirrelevanttoHathiTrust.VotesattheHathiTrustCCshouldbetakensimultaneously.Asforthevotingweightsthemselves,thereareanumberofdifferentformulasthatcanbeusedtoallocatepower,butsomeworkbettertoaccuratelyreflectinstitutionalcontributionsandachieveabalanceofpowerandequity.

B. SpecificRecommendations:PowerAllocationandVotingWeights

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Thefollowingrecommendationsrefertothefirstpointofthebasicrecommendations:“Determineavotingpowerallocationbasedonanappropriateformulaandfactors,andthencalculatethevoterweightsaccordingtotheBanzhafIndexusingLeech’s(2003)method.”Theattachedspreadsheetillustratesseveraldifferentpowerallocationsaccordingtoformulas,aswellastheweightsdeterminedbyLeech’salgorithmdiscussedabove.Asfounderstatusandadministratorstatushavealreadybeenaccountedforthroughotherrecommendations,theseformulasarederivedfromthequantifiablefactorsoffinancialcontributionsandnumberofvolumescontributedtoHathiTrust.

Thereareseveralpossiblepowerallocationsthatcouldwork,andthissectionwillproposefourformulas.Asmentionedintheprevioussection,Dixon(1983),drawingfromNewcombe,Wert,andNewcombe(1971)aswellasBarrettandNewcombe(1968),proposedseveralformulasthatpurporttosatisfytheprinciplesofequityandpower(andthusachieveacceptability)bytakingeitherdirectproportionsorsimplemathematicalderivationsofbothpopulationandGDP.Recallthatpopulationsatisfiestheprincipleofequity,whileGDPequatestopower.

Theformulasareasfollows:

1. Population+GDP2. PopulationxsquarerootofGDPpercapita3. Logpopulation+logGDP

Thefirstformulaobviouslydirectlycorrelatestothetwofactorsinvolved,simplytotalingthetwo.Thethirdformulauses“theapplicationoflogarithmsasawaytodiscountextremevalues,”(p.300)whilethesecond“compensatesforpopulationdifferencesbydistributingvotesaccordingtotheproductofpopulationandthesquarerootofGDPpercapita.”(p.300)OutofDixon’sfifteenformulas,thesearethethreethatusemultiplefactorsandalsousemathematicalfunctionstospecificallymitigatetheinequalitiesoftherawnumbers.TheyseemappropriateandtranslatabletoHathiTrust’sneeds.(Notethattheseformulaswereoriginallyproposedasformulasforweight,butwhattheyaretrulymeanttosignifyispower.Itissafetousethemtoallocatepowerratherthanweight.)

WhileHathiTrustmembersdonothaveeitherpopulationorGDP,therearecertainfactorsinHathiTrustthatsatisfytheprinciplesofbothequityandpower,respectively,andcouldbesubstitutedintheformulas.Theprincipleofequity,forHathiTrust,couldberoughlyfulfilledbyafactorofthenumberofvolumescontributedtotherepository.Theprincipleofpower,meanwhile,couldbesignifiedbyfinancialcontribution.Substitutingthesefactorsfortheoriginalones,wehave:

1. Numberofvolumes+financialcontribution2. Numberofvolumesxsquarerootoffinancialcontribution3. Log(numberofvolumes)+log(financialcontribution)

Totheseformulascanbeaddedafourthformulathatdoesnotappearintheliteraturebutreflectssomeofthereasoningbehindthe2ndand3rdformulaabove,andturnsouttobebetterforHathiTrust’sneeds:

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4. Squarerootofvolumes+squarerootoffinancialcontribution

ThisformulawillbetherecommendedformulaforHathiTrust,butletusexplorehowthefourformulascompare.

First,herearetheprojectedestimatedvaluesforeachHathiTrustinstitution’sfinancialcontributionandvolumescontributed,asofMarch2011.Thesenumbersaremerelyguessesatthispoint,andcanbeadjustedinthefuture:

Institution Financialcontribution Volumes

UniversityofMichigan 2,155,404 5,000,000IndianaUniversity1 900,000 600,000CommitteeonInstitutionalCooperation 1,650,000 1,000,000UniversityofCalifornia 1,244,142 3,000,000UniversityofVirginia 72,000 500,000ColumbiaUniversity 72,000 500,000YaleUniversity 40,000 30,000TOTALS 6133546 10,630,000

Itismoreequitabletousetheseprojectedamounts,ratherthancurrentamounts.Someinstitutionshavemorevolumescurrentlyintherepositorysimplybecausetheyweretherefirst.Inaddition,asexplainedpreviously,Leech’salgorithmofcalculatingvotingweightforagivenpowerdistributionworksfarbetterongroupsofmorethanfivevoters.

Theattachedspreadsheetshowsdifferentpowerandweightvaluesofthesefourformulas,accordingtotheinstitution.Thepowervalueswerecalculatedaccordingtotheformulas,whiletheweightswerecalculatedseparatelyusingLeech’salgorithm.Notethatchangingtheinputvaluesofvolumesorfinancialcontributionswillreadjustthepowervalues,butwillnotre‐calculatetheweights.Lookingatthevaluesthatresultfromeachoftheseformulas,itisimmediatelyapparentthatcertainformulascompensatefornumericalextremesbetterthanothers,andthatsuchcompensationisanextremelyimportantcriteriaforselectingapowerallocationformula.

Informula1,theUniversityofMichiganhas43%ofthetotalpower,whileYaleUniversityreceivesonly0.42%ofthepower.Suchanextremedifferencewouldmostlikelybeconsideredunacceptableandunfairbyallofthepartners,andcertainlybyYale.Thefollowingtablegivestheformula1powerandweightvalues:

Formula1:(financialcontribution)+(volumes)

1TogenerateIU’svotingpower,IU’svolumeestimateshavebeenseparatedfromthetotalCICvolumes.

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Institution Power RelativePower2 RelativeWeights3UniversityofMichigan 7,155,404 42.68% 41.73%IndianaUniversity 1,500,000 8.95% 7.81%CommitteeonInstitutionalCooperation 2,650,000 15.81% 15.60%UniversityofCalifornia 4,244,142 25.32% 26.73%UniversityofVirginia 572,000 3.41% 3.87%ColumbiaUniversity 572,000 3.41% 3.87%YaleUniversity 70,000 0.42% 0.37%TOTALS 16,763,546 100% 100%

Onepositiveaspectofformula1isthatthepowerratiosareveryclosetotheweightratios.Thisstrongcorrelationmakestheweightsmoreintuitiveandthereforemoreacceptable.Still,thewildlyunevenpowerallocationmakesthisformulalessthanideal.

Formula2resultsinevengreaterhighsandlowsofpowervalues,andsomeoftheweightsgeneratedasaresultoftheseextremesarezeroornegativevalues.Obviously,negativeweightvaluesareuselessfromapracticalandtheoreticalstandpoint.Herearethevaluesresultingfromformula2:

Formula2:volumesxsquarerootof(financialcontribution)Institution Power RelativePower RelativeWeightsUniversityofMichigan 7,340,647,110 57.28% 50.08%IndianaUniversity 569,209,979 4.44% 0.00%CommitteeonInstitutionalCooperation 1,284,523,258 10.02% 0.06%UniversityofCalifornia 3,346,233,405 26.11% 50.01%UniversityofVirginia 134,164,079 1.05% ‐0.07%ColumbiaUniversity 134,164,079 1.05% ‐0.07%YaleUniversity 6,000,000 0.05% ‐0.01%TOTALS 12,814,941,909 100% 100.00%

Note,also,thatthepowervaluesandweightvaluesaccordingtothisformulaarequitedifferent.Arelativepowerof10.02%yieldsaweightof0.06%,whichseemscounterintuitiveevenifitismathematicallycorrect.

UnlikeFormulas1and2,whichresultinextremehighsandlowofpowerallocations,Formula3attemptstoalleviatetheseextremesbytakingthelogarithmofeachfactor.Theresultingpowerallocationisperhapsnotdiverseenough,withallofthepercentageslyingveryclosetogether:

2RelativePowerrepresentstheinstitution’spowerdividedbythetotalpowerofallinstitutions.3RelativeWeightsrepresenttheclosestpossiblematchofweightratios,accordingtoLeech’salgorithm,thatyieldthedesiredpowerallocation.Anyweightsthatmaintainthegivenratioswillresultinthesamepowerallocation.Thesimplestwaytomaintaintheratioswouldbetoallocatevotesasintegerstotaling100.

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Formula3:log(financialcontribution)+log(volumes)Institution Power RelativePower RelativeWeightsUniversityofMichigan 13.03 16.34% 17.51%IndianaUniversity 11.73 14.71% 14.96%CommitteeonInstitutionalCooperation 12.22 15.32% 15.91%UniversityofCalifornia 12.57 15.77% 16.61%UniversityofVirginia 10.56 13.24% 12.64%ColumbiaUniversity 10.56 13.24% 12.64%YaleUniversity 9.08 11.39% 9.73%TOTALS 79.75 100.00% 100%

Sofar,twoofthethreeformulashaveresultedintoomanyextremevalues,andthethirdyieldsapowerallocationthatistooevengiventhevariationinpartnercommitmentstoHathiTrust.Evidently,aswiththeoverallvotingmodeldesign,itisdifficultwiththeseformulastoachieveamiddlegroundbetweenextremeinequalityandcompleteequality.The4thformula,derivedinresponsetothisneedforamiddleground,seemstoachievethenecessarybalance.Thosevaluesareasfollows:

Formula4:squarerootof(financialcontribution)+squarerootof(volumes)Institution Power RelativePower RelativeWeightsUniversityofMichigan 3,704 28.75% 28.30%IndianaUniversity 1,723 13.38% 13.98%CommitteeonInstitutionalCooperation 2,285 17.73% 17.84%UniversityofCalifornia 2,847 22.10% 21.69%UniversityofVirginia 975 7.57% 7.70%ColumbiaUniversity 975 7.57% 7.70%YaleUniversity 373 2.90% 2.78%TOTALS 12,884 100% 100%

Takingthesquarerootofeachfactor,andthentotalingthem,mitigatestheproblemofextremes,butnotasthoroughlyastakingthelogarithm.Itseemstorepresentanacceptabledistributionofpower,andinaddition,thecorrespondingweightsareextremelyclosetotheactualpowerdistribution.Theclosenessofweightandpowerservestomakethisformulamoreacceptableandintuitive.ThefinalrecommendationforHathiTrust,therefore,istouseformula#4toallocatepower,equatingvotingpowerwiththesumofsquarerootsofaninstitution’sfinancialcontributionandnumberofvolumescontributed.Thisweightedvotingformulawillserveasacorecomponentofalargerdoublemajorityscheme,satisfyingtheprinciplesofbothequalityandpowerdisparitiesinHathiTrust.Toseehowthisproposedvotingmodelwouldplayoutinrealdecision‐making,letusexamineafewpotentialscenarios.

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C. PotentialVotingScenarios

Althoughwecanonlyguessatconfigurationsofvoterpreferencesforanygivenquestion,itisworthwhiletolookathowthevoteswouldplayoutforafewhypotheticalsituations.AttheCC,thepartnerswillrespondtorecommendationsfromtheHathiTrustthree‐yearreview.ImaginethatoneoftheserecommendationspertainstowhetherornottheHathiTrustmodelshouldcontinuetocombinepreservationandaccess.The3‐yearreviewrecommendsthatHathiTrustcontinuetoembracetheconceptofa“lightarchive,”enablingbothpreservationandaccess.NowimaginethatofthepartnersexceptfortheUniversityofMichigansupporttherecommendation.TheUniversityofMichiganopposesthismeasureandsupportsconvertingHathiTrustintoa“darkarchive”onthegroundsthatitismoreeconomicalandlesscomplex.Accordingtoformula4,theweightedvoteswouldplayoutasfollows:

Institution Weights(Integers) Maintain“lightarchive”?UniversityofMichigan 28.3 NOIndianaUniversity 14.0 YESCommitteeonInstitutionalCooperation 17.8 YESUniversityofCalifornia 21.7 YESUniversityofVirginia 7.7 YESColumbiaUniversity 7.7 YESYaleUniversity 2.8 YESTOTALS/OUTCOME 100.0 YESNUMBEROFYES n/a 71.7NUMBEROFNO n/a 28.3

Tomakethetablemorereadable,theweightshavebeenturnedintopositivenumberstotaling100,roundedofftothenearesttenth.WithallofthepartnersexceptforUniversityofMichigancominginat71.7%ofthevote,theirpreferencetokeepthelightarchivemodelwillpassintheweightedvotingphase.

Accordingtotheothercomponentsoftherecommendedvotingmodel,thereisalsothedoublemajorityrequirementtobeconsidered,aswellasthefactthatMichiganhasavetopower.Thisscenarioalsoeasilypassesaccordingtotheunweightedvotescomponentofthedoublemajority,withsixoutofsevenmembersinagreement.Italsohappens,though,thattheonememberindisagreementhasvetopower.ThefactthattheUniversityofMichiganpossesstheabilitytovetodoesnotautomaticallymeanthatUMwouldexercisethatpower.Inthishypotheticalsituation,Michiganwouldhavetocarefullyconsidertheopinionsoftheotherpartnersaswellasthepoliticalramificationsofopposingthecollectivemembership.IfMichigandidchoosetovetothedecision,itwouldnotautomaticallymeanthatthevotewouldgoMichigan’sway;rather,thequestionwouldrequirefurtherdiscussion,possiblealterationstotheproposal,andanothervote.

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TakingthissamehypotheticalpropositionofmaintainingHathiTrustasa“lightarchive,”nowsupposethatIndianaandCaliforniajoinMichiganinopposingthemeasureandvotingtoconvertHathiTrustintoadarkarchive.Theweightedvoteswouldlooklikethis:

Institution Weights(Integers) Maintain“lightarchive”?UniversityofMichigan 28.3 NOIndianaUniversity 14.0 NOCommitteeonInstitutionalCooperation 17.8 YESUniversityofCalifornia 21.7 NOUniversityofVirginia 7.7 YESColumbiaUniversity 7.7 YESYaleUniversity 2.8 YESTOTALS/OUTCOME 100.0 NONUMBEROFYES n/a 36.0NUMBEROFNO n/a 64.0

Inthisscenario,the“no’s”gettheweightedvotewitha64%majority.Buttakingintoconsiderationthedoublemajorityrule,the“yes”voteshavefouroutthesevenunweightedvotes.Themeasureneitherpassesnorfails,andthepartnersgobacktodiscussion.Inasituationlikethisone,wherethereareconflictingoutcomesbetweentheweightedandunweightedvotes,itisclearthathavingadoublemajorityrulemakespassingadecisionmoredifficult.Thiscouldbeseeninapositivelight—anopportunityforthepartnerstohavefurtherdiscussionandperhapsmodifytheproposal—orinanegativelight,asanobstructiontodecision‐making.

Thereareaninfinitenumberofscenariostobeconsidered,andtothispurpose,theattachedspreadsheetincludesa“votecalculator”basedonformula4.

V. Conclusion

Torevisittheinitialgoalsputforthinthisdocument,thequestionsthatthisdocumentsetouttoanswerwere:

• Howisvotingpowercalculatedinaweightedvotingsystem?• Whatfactorsandprinciplesshouldinformallocationofvotingpower?• HowdothesemodelsapplytoHathiTrust?

Thesethreequestionswereansweredthroughanexplorationofapriorivotingpowertheory,anexaminationofthebasicprinciplesthatvarioustheoristshavesuggested,andfinally,adetailedsetofrecommendationsforHathiTrustalongwithseveralpotentialscenariosandtheiroutcomesaccordingtotherecommendedvotingmodel.Thatrecommendedmodel,whichinvolvesthreecomponents—weightedvotes,unweightedvotes,andinstitutionalvetopower—attemptstosatisfytheprinciplesofequity,power,andacceptabilitydetailedbytheoristsandalsoevidentinHathiTrust’sonlinedocumentationoftheproject’smission.

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ThegoalofthisdocumenthasbeennotonlytorecommendaspecificvotingmodelforHathiTrustasitiscomprisedintheforeseeablefuture,butalsotooutlineflexibleapproachesandformulasthatcanbeadaptedasthemembershipandcontributingfactors(financialcontributionandnumberofvolumes)change.Forexample,ifthehostinstitutionchanges,itmaynolongerbepracticaltogivetheUniversityofMichiganvetopower.Intheweightedvotingcomponent,itmightmakemoresensetouseadifferentformulaforpowerallocationifthefactorschange;formula3,forinstance,equalizespowertoomuchinthecurrentconfiguration.Withmoreextremedifferencesincontributingfactors(financialcontributionsandnumberofvolumes),formula3mightworktooffsetthosedifferences.Inaddition,theexecutivecommitteemaywishtoconsiderdifferentbreakdownsofthemembership,suchasbreakingtheCICandUCintotheirrespectivememberinstitutionstobeuniqueHathiTrustpartners.AstheHathiTrustDigitalLibrarywillcertainlyevolveinunexpectedways,itsdecision‐makingprocessesshouldalsoevolvetosupportthosechanges.

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