DistributiveDecisionsinEducation:
Goals,Trade‐OffsandFeasibilityConstraints
KennethShoresandSusannaLoeb
Abstract
Educators,policymakersandcitizensfacequestionsofhowtoallocatescarceresourcesin
thepursuitofcompetinggoalsforchildrenandyouth.Ourgoalinthispaperistoprovide
decisionmakerswithaframeworkforconsideringallocativeproblemsineducation,
explicitlyhighlightingtheimplicationsofrelevantfeasibilityconstraints.Weassumethat
thedecisionmakercaresaboutchildren’spresentandfuturewelfareandthatshegives
prioritytochildrenwhosewelfareislower.Wehighlightfourespeciallyrelevant
constraints:scarcityofresources,buy‐infromcommunitymembers,high‐stakes
consequencesofskilldevelopment,andmeasurementofdesiredoutcomes.Usingfour
casestoillustratecommonsituationsdecisionmakersface,weshowthattheframework
providesbothsomeunderstandingofthedistributivedecisionsthataremadeinpractice
andsomestructureforthinkingabouthowtooptimizedecisionsinnon‐idealsettings.
Keywords
Education,Equality,FeasibilityConstraints,Optimization,Flourishing,Welfare,Non‐Ideal
Theory
Authors’Biographies
KennethShoresisa5thyearPhDstudentinStanford’sGraduateSchoolofEducationanda
formereducator.
SusannaLoebistheBarnettFamilyProfessorofEducationandDirectoroftheCenterfor
EducationPolicyAnalysisatStanfordUniversity.
Introduction
Teachers,schoolleadersandpolicymakersfacequestionsofhowtoallocatescarce
resourcesinthepursuitofcompetinggoalsforchildrenandyouth.Ateachermaywantall
ofherstudentstolearnasmuchaspossible,butmightsacrificesomelearningofhermost
advancedstudentsinordertohelpherlowestachievingstudentscatchup,atleast
partially.Alegislatororlawyermaywishtopasslegislationthatprovidesmoreresources
tostudentslivinginpoverty,knowingthatthisreallocationcouldresultinfewerresources
forotherstudents,eventhoughshevaluesresourcesfortheseotherstudentsaswell.
Trade‐offsliketheseresultfromscarcityandotherfeasibilityconstraintsthat,attimes,go
unrecognized.Ourgoalinthispaperistoprovideeducators,policymakersandcitizens
withaframeworkforconsideringallocativeproblemsineducation,explicitlyhighlighting
theimplicationsofrelevantfeasibilityconstraints.
Akeyelementofourframeworkisthesetofgoals,bothdistalandproximal,thatreflect
valuesdecisionmakersholdforstudents.Distalgoalsaretheultimateaimsforstudents
(e.g.,goodjobopportunities),whileproximalgoalsaretheoutcomesthatcanbemeasured
immediatelyinordertoinformcurrentdecisionsandarethoseonwhichschoolshavethe
mostinfluence(e.g.,achievementonstandardizedtests).Someproximalgoalsarechosen
becausetheyarepredictorsofdistalgoals,whichcannotbemeasuredintheshortrun,and
somearechosenbecausetheyareofimmediateimportance.Inadditiontospecifyingthese
goals,policymakersmustidentifythefeasibilityconstraintsaffectingschools’capacitiesto
realizethosegoals.Theimprecisionofmeasuringthegoalsforstudentsisonefeasibility
constraint,butitisnottheonlyonethateducationdecisionmakerscommonlyface.
Inwhatfollows,wedescribeasetofgoalsthataneducationalpolicymakercouldhopeto
realizethroughschooling.Wethenidentifyfourfeasibilityconstraintsthataffectdecision
makers’choicesthatultimatelymaylimithowsuccessfullytheycanaccomplishthose
goals.Werefertothiscombinationofgoalsandconstraintsasa“framework.”
Inordertodemonstratetheusefulnessofthisframework,wepresentfourstylizedcases
thathighlightthekindsofallocativeproblemspolicymakersface.Thesecasesareintended
tohighlightcommon,yetdifficult,allocativedecisions.Teachersandschoolleadersface
similarproblemsandcouldutilizeasimilarframeworkinclassrooms,butforclaritywe
focusatthepolicylevel.
Here,now,arethecases:
Case1:Twochildrencomefromfamilieswithverydifferentsocioeconomiccharacteristics,
oneverywealthyandtheotherverypoor.Becauseoftheirbackgrounds,thetwochildren
haveverydifferentmeasuredabilities,onewhoperformsverywellandtheotherwho
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struggles.Howmuchcompensationisowed,ifany,tothechildwhocomesfromthe
disadvantagedhousehold?
Case2:Twochildrencomefrombackgroundconditionsdescribedabove.Inthiscase,
however,thetwochildrenperformequallywellonavailablemeasuresofabilities.Doesthe
childfromthedisadvantagedhouseholdhaveclaimtoadditionalresources,andifso,why?
ShouldthischildreceivelessthanthedisadvantagedchildfromCase1?
Case3:Threedifferentchildrenfromthreedifferentfamiliesareentirelyalikewithrespectto
socialcircumstance.Despitethesesimilarities,thechildrendemonstratedifferencesin
measuredabilities.Onatraditionalstandardizedtest,thefirstandsecondchildrenscorein
the5thpercentilenationally,whilethethirdchildscoresatthe50th.Betweenthefirstand
secondchildren,oneismuchmoreexpensivetoteachthantheother.Thethirdchildwho
scoresatthe50thpercentilecostssomewhereinthemiddle.Howshouldthesedifferencesin
costsoflearningandlevelsofattainmentaffecttheallocationofresources?
Case4:Finally,considertwochildrenfromtwodifferentfamiliesthatarealikeintheiraccess
toresources.Theparentsofthesechildrenhavedifferentrearingpractices,inwhichthefirst
familyismorehands‐off(withoutbeingnegligent)andallowsthechildtodevelopher
interestsandskillsatherownpace.Thesecondfamilyishands‐on(whilestillbeing
nurturing)andallocatesthechild’stimeintocoordinatedlearningactivities.Theeffectof
theserearingpracticesisthatthesecondchildhasgreatermeasuredabilitiesthanthefirst
child.Doesthefactthatonechildhaslowermeasuredoutcomesthantheotherwarrant
additionaleducationalresources?
Inthenextsection,wedescribeastylized,butgenerallyrealistic,worldinwhicha
policymakermakesdecisions.Thisapproximationsimplifiestheoptimizationproblemwe
describeandlimitsustothewaysinwhichschoolingcanbeusedtoaccomplishdesired
outcomesundernon‐ideal(realistic)conditions.Withthesebackgroundconditionsin
place,wepresentdistalandproximal(ultimateandintermediate)outcomesapolicymaker
islikelytoaimfor,aswellasfourreal‐worldfeasibilityconstraintsthatconfoundthe
realizationofthoseaims.Weconcludetheessaywithananalysisofthecasesabove.The
frameworkweprovideallowsustobreakthecasesintosmallerparts,includingoutcomes
ofinterest,measurement,constraintsandtrade‐offs,whicharenecessaryconditionsfor
identifyingan“allthingsconsidered”optimalpolicychoiceforrealizingthechosen
outcomes.
Thepurposeofthispaperis“descriptive”asopposedto“prescriptive,”meaningthatthe
outcomesofinterestweidentifyreflectgenerallyagreeduponvaluesandcommitments.
Theotherelementswedescribeincludemeasurementproblems,resourceandpolitical
constraintsandthetrade‐offsthatensue.Theseotherelementsreflectempiricalrealities.
Aswemakeclearlater,therewillbemanydecisionsthatneedtobemadeabout,for
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example,howmuchweighttogivetoimprovingoverallwelfareversusimprovingthe
welfareoftheleastadvantagedstudents.Wetakenopositionhereonhowpolicymakers
shouldweightdifferentdesiderata,anditisforthisreasonthatwesaythepaperisnot,or
isonlyminimally,prescriptive.
ThePositionofthePolicymakerandBackgroundAssumptions
Imagineaneducationalpolicymaker,whomwewillrefertoasAnna,whohasconsiderable
authorityoverthestate’seducationalsystem.Anna’sprimarymeansofshapingthe
educationalexperiencesofchildrenisthroughthedistributionofresources,indicatedby
perpupilexpenditures.Expendituresrepresentanall‐purposecommodity,andcanbe
convertedintothepurchaseofteachers,curricularmaterials,evaluationsystems,etc.
Annahas,moreorless,completediscretionarypoweroverspendingonschools,unless
notedotherwise.Thestatecollectsagivenamountoffundsfromtaxrevenues,andAnna
canallocatethoseresourcestowhomevershelikes.Themoneycollectedisforusein
purchasinggoodsfordirectusebyschools.Ifthatmoneyisnotspent,itwillbelost.This
assumptionmeansthatAnnawillnotberequiredtoconsiderwhetherresourcescouldbe
betterspentinnon‐schoolsettings,suchashealthcareorwelfare,evenifthoseservices
affecteducationaloutcomes.Sheisrestrictedtomakingexpendituredecisionspertaining
toschools.Whilefewpolicymakershavecompletediscretionoverspending,manydo
considerwhatdecisionstheywouldmakegivencompletediscretionandusethis
understandingwithinapoliticalprocess.
Annaknowstheschoolingsystemandthebroadercommunitywell;however,her
knowledgeabouttheeffectsofresources,theneedsofstudentsandtheresponsesof
individualstopolicychoicesisimperfect.Annamustmakeherbestguessattheeffectsof
policieseventhoughherinformationisincomplete.
Annaalsohasverylittleinfluenceoutsideofschools.Sheassumesthatsocietalconditions
are,atleastinthenearterm,moreorlessfixed.Sheknowsthatasaresultofthese
conditions,achild’seducationislikelytosubstantiallyaffectherlifeprospects.
ThedescriptionofAnnathatweprovideisstylizedbutconformstosomeofthemore
relevantrealitieswewishtoconsider.Wegiveherdiscretionarypoweroverspending
becauseitallowsustosimplifytheprocessthroughwhichpolicymakerssecurefundsfor
differentstudents.Theotherbackgroundcharacteristicsaremorefundamentaltothe
decision‐makingprocessandarethereforeincluded.Here,then,wehavethepositionofthe
policymakerandsomebackgroundassumptions.Wenowturntothekindsofoutcomesa
policymakerinthissituationwouldliketoproduce.
DesiredOutcomes
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Here,wedescribeAnna’sgoals.Thesegoalsreflectbasicnormativecommitmentsto
children’spresentandfuturewelfare,combinedwithapreferenceforimprovingthe
welfareoftheleastadvantaged.Welfare(whichforusissynonymouswithflourishingand
well‐being)isacomplicatedandcontestednotion,andwearenotendorsingasingular
conception.Inbroadterms,weconceiveofwelfareashowrichlyindividualscanleadthe
lifethattheywant.Thisconceptionofwelfarehasbothsubjectiveandobjectiveelements.
Itissubjectiveinthesensethatindividualshavedifferentpurposesforthemselvesandwill
getsatisfactionfrompursuingdifferentaims.Noteveryone’swelfarewillhingeonwhether
theyhavethecapabilitytodancewellorperformcomplexmathematics.Welfareisalso,at
leastinpart,objectiveinthesensethatthereareaspectsoflifethathaveuniversalappeal:
autonomy,strongpersonalrelationships,opportunitiestorealizeone’sgoals,security,
nourishment,etc.Weusethisgeneralnotionofwelfarethroughoutthepaper,andaimfor
ittobebroadenoughtowarrantsupport.
Havingdefinedwelfare,wecannowsaythatAnnacaresbothabouttheleveland
distributionofit.Thelevelofwelfaresimplymeansthatmorewelfare–orricherlives‐is
betterthanlesswelfare.Thedistributionofwelfaremattersaswell.Annabelievesthat
welfaregainsatthebottomofthedistributionaremoreimportantthanwelfaregainsat
thetopofthedistribution.Thepossibilitythatsomestudentswillhaveverylowwelfareis
especiallytroubling.Shewilltrytoensurethatthechancesofthathappeningarelow.
Certainly,forexample,ifshehasachoicebetweenspendingresourcestoimprovethe
welfareforastudentatthelowendofthedistributionorastudentatthehighend,andif
thesewelfaregainsareequivalent,shewillspendthatmoneyonthestudentwhose
prospectsarelower,allelseequal.Thischoicehastheeffectofreducinginequalitybutis
motivatedoutofaconcernfortheleastadvantaged.
BecauseAnnavaluesgainsatthelowerendofthedistributionmore,shemaybewillingto
spendresourcestoimprovethewelfareforastudentatthelowendofthedistribution
evenifthatstudentwouldgainlessthanastudentatthehighendofthedistribution.This
choicehastheeffectofreducinginequalitywhilealsoreducingaveragewelfare,relativeto
thealternativeofspendingresourcesonthehigher‐endstudent.Thedecisionabouthow
muchtovalueorweightgainsatthebottomofthedistributionrelativetothetopreflects
thekindsoftrade‐offsAnnamustmake.Shebalancesaninterestinimprovingwelfarefor
theworstoffwithaninterestingreaterwelfare,andiswillingtotradeoffgainsatthe
bottomforaveragewelfareandvice‐versa.Wedonotsuggestthatthereisauniversally
appropriateweightthatshouldbegiventoincreasingwelfareonthebottomversus
increasingaveragewelfare,onlythatsheconsidersthesetradeoffsinherdecisions.
Havingcommittedtothetwogoalsofflourishingforallandweightinggainsatthebottom
more,wecannowthinkmorecarefullyaboutgoalsforeducationandforschools,in
particular.Anna’ssphereofinfluenceislimitedtothedistributionofresourcesforschools.
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Becausewelfareisafunctionofvariouscomponents,Annawillfocusmostonthose
componentsthatschoolsaredesignedorabletoproduce.Aprominentideaisthatschools
produceskillsthatareusefulforearningsinthelabormarket,butschooling’ssphereof
influenceextendsbeyondskillsnecessaryforearnings.Schoolsalsoshapechildren’s
attitudesaboutandabilitiesformultiplepurposes,including,amongothers,interpersonal
relationships,artappreciation,civicparticipation,sexualhealth,andphysicalfitness.These
variedqualitiesdonotnecessarilytranslatedirectlytolabormarketsuccessbutare
neverthelessimportantaspectsofwelfare,andschoolscanandshouldaffectthem.
Itisworthemphasizingherethetemporalaspectoftheallocationdecision.WhileAnna
maybeconcernedwithanindividual’swelfarethroughoutthelifespan,herabilityto
influencewelfarebeginsonlywhentheindividualentersschoolandthenpersistsafterthe
individualexitstheschoolsystem.Whatdistinguishesherabilitytoinfluenceindividuals
duringschoolfromherabilitytoinfluencethemaftertheyhavecompletedschoolisthat
herinfluenceduringschoolisdirect,whileherinfluenceafterisprobabilistic.Shedirectly
influencestheexperiencesthatstudentshaveinschool,butsheonlyaffectstheirlikelihood
ofadultoutcomes,suchashealthandlabormarketsuccess.Becauseoftheuncertaintyof
herinfluenceonlateroutcomes,wedescribe“prospectsforwelfare”whenwediscussthe
attributesthechildgainswhileinschoolthatarepredictiveoffuturewelfare.Current
welfare,whichishowwellthechildisdoingasachild,isalsoarelevantaspectofwelfare.
Certainly,thereareinstancesinwhichsacrificesmustbemadeforimprovingone’s
prospectsforfuturewelfare,butthesebenefitsandsacrificesshouldnotalwaystake
precedentovercurrentwelfare.Howmuchweightshouldbegiventocurrentversusfuture
welfarerepresentsanadditionaltrade‐offthatAnnamustconsider,andonceagain,wedo
notspecifywhattheseweightsshouldbe.
Annawishestoimprovetheprospectsofflourishingforallstudentsthroughschooling,
withoutsacrificingchildhoodhappinessandsatisfaction.Inordertobetterunderstand
students’prospectsforwelfare,Annahasschoolscollectinformationonstudents’skills,
knowledgeandmotivations.Hergoalisforthesemeasurestobegoodpredictorsof
students’likelihoodofflourishinginthefuture.They,forexample,couldincludemath
skills,artisticability,andthecapacitytomotivateothers,amongotherfeatures.Wereferto
thesemeasuresas“achievement,”thoughtheyareclearlymuchbroaderthanachievement
measurestypicallycollectedbyschoolstoday.However,likecurrentmeasurestypically
collected,Anna’smeasuresarealsoinherentlyincomplete,capturingsomebutnotallofthe
studentqualitiesthatcancontributetotheirfuturewelfare.
Howshouldthisbroadtypeofachievementbedistributedacrossstudents?Evenifthe
ultimateaimofschoolingistoprovideallindividualswiththebestchanceforflourishing
lives,notallstudentswillneedthesamebundleofabilitiestogettothesamelevelof
flourishing.Thisdifferencebetweenthedistributionofprospectsforflourishingandthe
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distributionofabilitiescanoccurfortworeasons.First,equivalentamountsofwell‐being
canbehadfromdifferentcombinationsofabilities.Twostudentscanbeequallywelloff
eventhoughonestudentshasdevelopedgreatskillsinmusicbutfewinpainting,whilethe
otherhasgreatskillinpaintingbutfewinmusic.Somebasiclevelofmanyabilitiesislikely
necessaryforallkids—anabilitytorelatetoothers,toappreciateart,numeracyand
literacy—toensurereasonablelifeprospects,butnoteverychildwillrequirethesame
exactbundle.Itmayevenbethatexcellinginaparticularareagivesgreaterwelfarethan
equaldistributionofabilitiesacrossarangeofareas.
Thesecondreasonthatthedistributionofprospectsforwelfareandthedistributionof
abilitiesarenotsynonymousisbecausetherelationshipbetweenabilitiesandwelfarecan
differacrossindividuals.Supposetwoindividualshaveequalbundlesofskillsand
aptitudes,buttheyhavedifferentnativecapacities(orpotentials).Giventhatusingone’s
potential(whichincludestheprocessofdevelopingone’sabilities)isimportantforone’s
welfare,thehigher‐capacityindividualwillbeworseoff,eventhoughtheyhaveequal
bundles.Sheisworseoffbecauseshehasdevelopedlessofhernaturalabilitiesthanthe
otherindividualandbecauseshehashadfeweropportunitiestoenjoythebenefitsof
developingthoseabilities.
Wedonotsayhowmuchofone’swelfareiscomprisedofthedevelopmentofnative
potential,onlythatsuchdevelopmentisoneaspectofwelfare.Takeaslightmodificationto
theexamplejustused:oneindividualhasslightlyhigherachievementthananother,but
thispersonwiththeslightlyhigherachievementhasmuchmorenativepotential.With
respecttothedevelopmentofpotentials,thechildwithslightlyhigherachievementis
worseoffbecauseshehasdevelopedmuchlessofhernativepotentialthantheother.Inthe
aggregate,however,thechildwiththeslightlylowerachievementmaybeworseoffifthe
levelofachievementmattersmoreforoverallwelfare.
Theaccountofpotentialsthatwedescribemightappeartobeflawedbecauseitfavors
childrenbornwithgreaternaturalendowments.However,itshouldbeclearwearenot
arguingthatapersonisentitledtomorewelfareonaccountofhavinggreaterpotential.
Instead,wethinkthatdevelopingone’spotentialcontributestoone’swelfare.Considering
thisaspectofwelfarecanresultinunequaldevelopedbundlesofachievement,butthe
underlyinggoalistosecurehighlevelsofwelfareforallpersons.Ultimately,itiswelfare
thatAnnacaresabout,andshewilluseoverallachievementand,atleasttosomeextent,
thedevelopmentofpotentialasindicatorsofwelfare.
Uptothispoint,wehavepositedtwogoalsaboutwhichourpolicymakerisconcerned:
ensuringahighlevelofwelfareforeveryoneandassigningmoreweighttoimprovements
atthebottom.Becauseachievement,capaciouslyunderstood,matterssomuchforwelfare
andbecauseschoolsareuniquelysituatedtoproduceachievement,Annawilltryto
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influencethelevelanddistributionofachievementwithherdecisionsaboutresource
allocation.Differentchildrenwillendupwithdifferentbundlesofachievementand
resources,andsomechildrenwillevenendupwithdifferentlevelsofmeasured
achievementintheaggregateasaresultofchildrendifferingintheirnaturalcapacities.
Finally,thechild’swelfareduringchildhoodcannotbejettisonedinordertoincreaseher
welfareprospectsasafutureadult;bothmustbeconsidered.Wehavehere,then,thedistal
goalsofincreasingwelfareforeveryonewhileprivilegingwelfaregainsfortheleast
advantagedandtheproximalgoalofcultivatingachievement,broadlydefined,forwelfare.
FeasibilityConstraints:Measurement,Scarcity,StakesandBuy‐In
Wehavethusfarintroducedtheconceptuallandscapeinwhichourpolicymakeroperates.
Inthissection,wedescribereal‐worldconstraintssheislikelytoencounterasshepursues
thesegoals.Specifically,weemphasizefourconstraints:scarcityofresources,buy‐infrom
communitymembers,high‐stakesconsequences,andmeasurement.Thesereal‐world
aspectsoperateasfeasibilityconstraintsthatinfluenceAnna’sabilitytofullyrealizeher
goals.
Scarcity
BecauseAnnacaresaboutboththelevelofwelfareanditsdistribution,shewillhaveto
makedecisionsabouthowmuchachievement‐for‐welfaresheiswillingtotrade‐offinthe
aggregatesothedistributioncanbebetterforthosewhoseprospectsarelowest.Theneed
forthistradeoffoccursbecauseoftheproblemofscarcity.IfAnnawereindifferenttothe
distributionofwelfare(thatis,improvingwelfareforthoseatthebottom),shewould
simplyallocateresourcesasefficientlyaspossible.Thosestudentswhostoodtogainthe
mostforagivenamountofresourceswouldreceivethoseresources.Otherfeasibility
constraintsmightstillaffectherabilitytodistributeresourcesefficiently,butshewould
nothavetoworryabouttrading‐offdistributionalconcerns.Becausedistributiondoes
enterintoherdecision‐making,shewillhavetobalanceconcernsaboutleveland
distribution.
Distributionalconcernsbecomeparticularlysalientwhenachildhasverylow‐levelsof
achievementsuchthathisprospectsforflourishingareseverelyreduced.Ifthischildisalso
verycostlytoteach,thenotherstudentswillhavelowerprospectsforflourishingsothis
onechildcanhavebetterchances.Situationslikethesearenoteasilysorted,butAnnamust
bemindfulofbothfactorswhenshedecideshowtoallocateresourcesforschools.
CommunityBuy‐In(orthedemocraticprocess)
Anna’spreferencesforcompensatingthosewhoseachievementislower(andtherefore
havelowerprospectsforwelfare)willbeaffectedbytheneedforcommunitybuy‐in.
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Revenuesforeducationcomefromtaxes.Ifrevenuesaredistributedentirelytoonegroup
(ortooneindividual),non‐receivinggroups(orpersons)maychoosetotaxthemselvesata
lowerrateorvotetoreplaceAnnawithanalternativedecisionmaker.Herbudget
constraintthereforewillbesensitivetothedistributivedecisionsshemakes,asthese
distributivedecisionswillinfluencefamilies’willingnesstopay,keeptheirchildreninthe
publicschoolsystem,andkeepAnnainherposition.Whileshemustmakedistributive
decisionsundergeneralconditionsofscarcity,communitybuy‐inplacesanadditional
resourceconstraintonhowmuchshecanallocatetoparticularpersonsorgroups.
Annamustestimatetheamountofresourcesthatshewillhavetodistributewith
uncertainty,asshedoesnothavefullinformationabouthowmuchfamilieswilltolerate
redistribution.Thistolerationconstraintalsowillvaryovertimeaspopulationsandvalues
change.InsofarasAnnacaresaboutprovidingcompensationtostudentsacrosstime,this
budgetconstraintwillbeeveronhermind.
TheHigh‐StakesofAchievement
Scarcitybecomesespeciallysalientwhenweconsiderhowimportantachievementisfor
welfare.Aswehavestructuredtheproblem,Annahasquiteabitofdiscretionabouthowto
distributeresourcesbetweenschools,butshehasverylittleinfluenceoutsideofschools.
Weassumethatbackgroundconditionsare,atleastinthenearterm,moreorlessfixed.A
child’seducationislikelytoalterherlifeprospectssubstantially,becauseeducationaffects
earningsandtheavailabilityofopportunitiesfordiverseandmeaningfulwork,aswellas
mentalandphysicalhealth.
Thehigh‐stakesnatureofthewelfarereturnstoachievementwillinfluencehowmuch
Annaregardstrade‐offsbetweenlevelsanddistributionalconcerns.Whenanindividual’s
welfareprospectsareespeciallybleak,shemaypursuelessefficient(morecostly)
educationalinterventionsifthoseinterventionscanimprovetheprospectsoftheleast
advantagedperson.Differentbackgroundconditions–supposing,say,thatagenerous
welfarestateguaranteedaminimumincomeforallpersonsirrespectiveoftheirskillsand
aptitudes–couldchangetherelationshipbetweenachievementandwelfare,whichinturn
couldchangeAnna’sdecisions.Shemightfavorthedevelopmentofdifferentbundlesof
achievement,orshemightchangeherdistributivepreferences.Shemightshiftherconcern
awayfromimprovingtheachievementofthelowestpersontosomethingcloserto
increasingaverageachievementasmuchaspossible,ifbackgroundconditionswere
different.
Measurement
Thelastfeasibilityconstraintwecallattentiontoistheproblemofmeasurement.Anna’s
broadmeasureofachievementisherbestguessastoachild’sprospectsforfuturewelfare.
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Whiledifferencesinchildren’sachievementmaybeduetocognitiveimpairmentsorsocial
backgroundconditions,takenalone,neitherofthesesourcesofdifferenceareworthy
obstaclesforcompensation.Theyareallequallymorallyarbitrary,aschildrenareneither
responsiblefortheirfamily’ssocialclassnortheirowncognitiveability.Whatmattersis
thatachievementisimportantforflourishing,andachievementhastwodimensions:how
muchachievementonehaspredictshowmuchflourishingoneislikelytoexperience,and
developingone’spotentialisimportantforone’sflourishing.
Themeasurementofachievementpresentssomeconceptualchallenges.Thefirstchallenge
isthatwedonotknowthepreciselinkconnectingaparticularbundleofskills(academic,
physical,artistic,civic,andinterpersonal)toanindividual’swelfare.Thislinkisunknown,
first,becauseindividualsmaygaindifferentbenefitsfromaparticularsetofachievements.
However,evenleavingthesesubjective(orindividual)differencesaside,wedonotknow
whatwelfareindividuals,onaverage,gainfromaparticularsetofachievements.
Asanapproximationofthewelfarebenefitsderivedfromskills,wecanlinkmeasuresof
priorachievementtocurrentincome,whichisonecontributortolong‐runwelfare.Income
maybeamoreconcretemeasurethanwelfare,butlinkingachievementtoincomeisnota
panacea.Theobservedrelationshipbetweenmeasuredachievementandincomeisstillan
averagerelationship,meaningthatindividualswillhavedifferentincomeexperiencesfrom
thesamelevelofmeasuredachievement.Moreover,incomefailstocapturethenon‐
pecuniarybenefitsofachievementthatarealsoimportantforwelfare,suchasjobchoice,
artappreciationandliteracy.Broaderanalysesthatlinkachievementmeasurestoafuller
setofoutcomes,suchashealthandfamilystability,provideadditionalrelevantinformation
andaremoresatisfyingapproximationsoftheaveragelinkbetweenachievementand
welfare.Theseadditionaloutcomesarestilldescriptionsofaverages,butwitharich
enoughsetofoutcomeswewouldhaveafulleraccountoftheobjectivewelfarebenefitsof
achievement.
Arelated,butdistinct,problemformeasuringachievementisthatevenabroadconception
ofachievementthatalignswellwiththequalitiesthatcontributetowelfareisprobabilistic
anddoesnotguaranteewell‐being.Achievementaffectsstudents’prospects(or
probabilities)forwelfare.Thislackofsuretyimpliesthatstudentsmayhaveahigh
expectedwelfaregiventheirabilities,buttheycanalsohavesomeprobabilityofverylow
welfare.Suppose,forexample,thatastudenthasunusuallygoodabilityinthearts,butfew
skillsinliteracyornumeracy.Perhapsthisstudent’sexpectedwelfareisequivalenttomost
otherstudents,assheisveryskilledasanartistand,ifshedoeshavesuccess,herwelfare
willbeveryhigh;yet,becauseherbundleofskillsisnotwelldistributed,shealsohas
considerableriskofverylowwelfare.Shecouldreducethisriskbyimprovingherliteracy
andnumeracyskills,eventhoughdevelopmentoftheseattributestakestimeawayfrom
herartandareunrelatedtothewelfaregainsshegetsfrompursuingherart.Inthisway,
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someelementsofachievementcanactasinsuranceforfuturewelfare,astheyaremore
likelytoproducewelfare,albeitatalowerrate.AnaversiontolowwelfarewillleadAnna
tofocusonachievementelementsthatprotectagainstverylowwelfare.
Inorderforthesemeasurestocapturethesubjective(orindividual)elementsofwelfare,
weneedtoassumethathealth,familyandincomeareequallyimportantforallpersons.If
wearewillingtomakethatassumption,theobjectiveandsubjectiveelementsofwelfare
converge.Ifwearenotwillingtomakethatassumption,linkingachievementtoindividual
welfareismoredifficult.Givingstudentstheopportunitytochoosetheirownclasses,and
givingthemmultipleopportunitiestoenterandexitschoolcanhelpmatchachievementto
individualneeds,butdeterminingwhoisworseoffintermsofprospectsforsubjective
welfareisadifficulttask.Ideally,Annawouldbeabletoprovideindividuatedpackagesof
achievement‐statesforallstudents,tieddirectlytofuturewelfare,butsuchinformationis
largelyunavailable.
Annaalsofaceschallengesinmeasuringachild’spotential,theseconddimensionof
achievementtakentoberelevantforwelfare.Thismeasurementwouldbeusefultoheras
sheattemptstoassesswhetherachildhashadtheopportunitiestodevelopthatpotential.
Wehaveclaimedthatpotentialmattersobjectivelyforwelfare,butbecausechildren’s
naturalpotentialsarefundamentallyunobserved,themeasurementproblemiscloserto
thatofsubjectivewelfare.Sheobservesachievementlevelsbutnot,forexample,the
opportunitiestodevelopthemathome.Ifsheseestwochildrenwithdifferentachievement
levelsbutdoesn’tobservetheiropportunitiesoutsideofschool,shewillnotknowwhether
thedifferencescomefromdifferencesinopportunitiesorinnaturalpotential.Asaresult,
Annamayseektoobserveopportunities,butsuchobservationisexpensiveatalargescale,
orshemayseekproxiesforsuchopportunitysuchasparents’financialresources,whichis
farlessaccuratebutfarlowercost.
Whenindividuatedpackagesofachievementareunavailableandwhenachild’spotentialis
unknown,ausefulproxyforAnnawillbetomakebetween‐groupcomparisons(suchas
thoseindicatedbyrace,genderand/orsocialclass).Abetween‐groupcomparisonsimply
comparesthedistributionsofachievement(again,broadlyunderstood)betweentwo
groups.IfthecomparisonisbetweengroupsthatAnnabelieveshaveapproximatelythe
samedistributionofpotential,high‐(orlow‐)achievingmembersofonegroupshouldhave
thesamelevelandcombinationofskillsasthehigh‐(orlow‐)achievingmembersof
anothergroup.WhenAnnabelievesthattherespectivedistributionsofpotentialarethe
same,differencesbetweengroups,onaverage,provideevidencethatachievement‐based
opportunitiesforwelfarefromthedevelopmentofpotentialarenotequallydistributed.
Usingcomparisonsacrossgroupsasindicatorsofunequalprospectsforwelfaredepends
uponbroadandaccuratemeasuresofachievement.Ifgroupshavedifferentlifegoalsand
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thereforedifferintheirpreferencesforbundlesofachievement,andifthemeasureof
achievementfavorsonetypeofachievementmorethananother,thendifferencesinmean
measuredachievementmaynotreflecttruedifferencesinprospectsforflourishing.
Imaginethatonegroupcaresonlyaboutsingingandisverygoodatit,whileanothergroup
caresonlyaboutdancingandisalsoverygoodatthat.Ifourmeasureofachievement
favorsdancing,thenitwillappearasifthedancinggroupisdoingbetterthanthesinging
group,wheninfacttheirprospectsforflourishingareequal(assumingdancingandsinging
enableindividualstohaveequalprospectsforflourishing).Withthisprobleminmind,
Annawillwanttobecarefulwiththemeasurementofachievementandconsiderthe
possibilitythatgroupdifferencesaredrivenbymeasurementissuesandbyparticular
grouppreferencesforabilities‐bundles,ratherthantruedifferencesinprospectsfor
flourishing.Clearly,groupdifferencesinachievement,suchasdifferencesinmath
achievementbetweenboysandgirls,canreflecttrueinequalitiesinprospectsforwelfare.
Annawillhavetobemindfulofthecomparisongroupssheselectsandthecorresponding
assumptionthatthetwogroups,onaverage,havethesamepotential.
Evenifgroupshavethesameaverageachievement,theremaybedifferenceinprospects
forwelfareacrossindividualswithinthesamegroup.Thisdifferencecorrespondstothe
firstproblemofmeasurementdescribedabove,linkingachievementlevelstoflourishing.
Consideragroupofindividualswhohavehadeverypossibleopportunitytodevelop
potential.Forthisgroup,therewillstillbeadistributionofachievement,reflecting
differentlevelsofcognitivecapacity.Theexistenceofthisdistributionsuggeststhatthelife
prospectsmaydifferamongindividualsduetodifferencesinachievement,evenifthey
havehadthesameopportunitiestodeveloptheirpotentials.Thus,addressingaverage
groupdifferencesisnotsufficientforaddressingalldifferencesinprospectsforwelfare
especiallyifthewithingroupdistributionofachievementisverylarge.
Annawillneedinformationaboutindividuals’achievement(notonlygroupaverages)and,
ideally,someinformationaboutdifferencesinchildren’sexperiences,atleastatthe
extremes.Withthisinformation,shecancompensatethelowerachievingstudentsrelative
tootherswithsimilarexperiencesandshecancompensatethosewithlesserexperiences
relativetootherswithsimilarachievement.Nopolicymakercanaccomplishaperfect
equatingofoverallwelfare,firstly,becauseofthedifficultyofmakingtrade‐offs,butalso
becauseoftheimperfectandpotentiallycostlymeasuresofachievementandexperiences
available.Asaresult,Annawillseektoidentifysubstantialdifferencesinprospectsfor
welfareandcompensateforthose,butitisunlikelyshewillgathersufficientinformationto
identifyandcompensateforsmallerwithingroupdifferences.
Insummary,measurementconstraintscansubstantiallyhinderAnna’sabilitytoallocate
resourcesacrossstudents.Betweengroupdifferencesinaverageachievementareuseful
indicators,asAnnawillhavestrongreasontobelievethesedifferencesstemfrom
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differencesinopportunities.Shecandirectresourcestoreducingaveragedifferenceswith
confidencethatsheisaddressingsomeaspectofachievementinequalitiesrelatedto
welfare.Withingroupdifferencesaremoredifficulttomeasureand,asaresult,Annamay
focusonlyonclearlyunequalprospectsforwelfareacrossstudentswithingroups.
TheFrameworkinUse:ReturningtotheCases
Letustakeaccount.Weofferedoutcomesaneducationalpolicymakerisconcernedwith:
thelevelanddistributionofcurrentandfuturewelfare.Prospectsforwelfarestemfrom
variousqualitiesthatstudentsdevelop.Werefertothisconglomerationofknowledge,
skillsandattitudesasachievement.Studentscanhaveequalprospectsforflourishingand
yethavedifferentbundlesoftheelementsofachievement.Somemaydevelopstronger
reasoningskills,andothersstrongerrelationalskills.Astudent’swelfarecomesnotonly
fromtheskillsshedevelopsbutalsofromtheopportunitiesthatshehashadtodevelopher
potential.Asaresult,studentsmaydifferevenintheiroveralllevelofachievementandstill
haveequalwelfarebecausestudentswithhighernativeabilitieswillneedtodevelopmore
capabilitiestohavethesamebenefit.Ideally,everychildwouldreceivethecorrectly
specifiedandindividuatedcombinationofskillsandattitudesnecessaryforequalandhigh
prospectsforwelfare(balancedagainstchildhoodwelfare),butsuchaperfectpackageis
notlikelygiventheconstraints.
Non‐idealconditionsstronglyaffectourpolicymaker’sabilitytoreachhergoals.Four
constraintsinparticularwillaffectherdecisions.First,resourcesarescarce,so
policymakerswillhavetomakedifficultdecisionsbetweenequalizingdistributionsand
increasingtheoveralllevelofachievement‐for‐welfare.Second,resourcesarenotjust
scarcebutalsoinflux.Thepolicymaker’sdecisionsabouthowtoallocateresourcescan
affectthelevelorresourcesshehasavailabletodistributeinthenextperiod.Ifshepursues
equalitytooheavily,theamountofresourcesavailablefordistributioninthenexttime
seriescanbelower.Third,thehighstakesnatureofthelabormarketmeansthatthoseon
thelowendoftheachievementdistributionarelikelytohaveadverselifeprospects.Anna
musttakethiscontextintoconsideration.Ifstakeswerelower,shewouldmakedifferent
decisionsabouthowtoallocateresources.Fourth,andfinally,measurementisimperfect,
soAnnadoesnotobservethefullrangeofachievementpossessedbyeachchild.Shealso
doesnotobservechildren’spotentialdirectlyandsodoesnotknowforsurewhetherthey
havehadequalopportunitiestodevelopit.
ThisframeworkcanbeusefulforAnnaasshedecideshowtoallocateresourcesacross
studentsandschools.Itisalsousefulinunderstandingwhysomeoftheresourceallocation
decisionsthatweobserveinpracticehavebeenmade.Inordertobringthisframeworkto
life,wereturntothecasesthatweintroducedearlyonandusethemtoillustratehownon‐
idealconditionsaffectdecision‐making.
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Case1:Differentbackgrounds,differentachievementlevels
Thiscaseincludestwochildrenfromdifferentsocioeconomicbackgroundswhohavevery
differentachievementlevels.WesaidthatAnnacaresaboutthelevelofwelfare(especially
thewelfareoftheleastadvantaged),aswellasthedistributionofit.Thelevelof
achievementmattersforwelfare,asdoeshavingopportunitiestodevelopone’snatural
ability.Whatdoweknowfromtheinformationprovided?Weknowthatthechildwhose
achievementislowerislikelytohaveworseprospectsforwelfaredowntheroad.With
respecttothedevelopmentofpotential,wewouldneedtoseewherethesetwochildren
fallintheachievementdistributionsoftheirrespectiveincomegroups.Iftheyfallinabout
thesameplaceandweassumethatthedistributionofnativeabilityisthesameacrossthe
twogroups,thenwewouldhavereasontobelievethatthetwochildrenhavehaddifferent
chancestodeveloptheirnativepotential.Here,weseethatthechildfromthelow
socioeconomicbackgroundisworseoffbecauseofthedifferenceinachievementlevel(and
theresultantdifferencesinprospectsforflourishing)and,possibly,thedifferenceinthe
developmentofpotential.
Thebudgetconstraintmeansthatshewillhavetousesomeresourcesthatwould
otherwisegotoimprovingachievement,andthereforeprospectsforwelfare,forother
students.Incaseswherethecoststoraiseachievementequalamountsarethesame
betweenthetwochildren,Anna’sprincipledcommitmentistoraisetheachievementofthe
childfromthelowsocioeconomicbackground.Thiscommitmentarisesbecauseequalcost
forequalachievementgainmeansthataverageachievementwillbethesameregardlessof
whoseachievementsheraises.AsAnnacaresaboutaveragesandimprovingtheless
advantaged,iftheaverageisunaffectedbyherdistributivechoice,shewillprioritizethe
childwhoisworseoff.
Whatconstrainsherdecisioninthiscaseisthatherdistributivedecisionwillaffecther
abilitytohelplowachievingstudentsinthefuture.Bychoosingtodevoteallresourcesto
onechildoronegroupnow,Annamayleadthosewhoreceivenoneoftheresourcesto
electadifferentperson,orchoosetotaxthemselvesatalowerrate,andthesedecisions
couldlowertheavailableresourcesshehastospendinthefuture.
Incaseswherethecoststoraiseachievementofthestudentfromthelowincome
backgroundaregreaterthanthecoststoraiseachievementofthestudentfromthehigh
incomebackground,Anna’sconstraintistwo‐fold.First,becauseshecaresaboutusing
resourcesbothtoimproveprospectsfortheworstoffandtoimproveaveragelevels,she
willtrytofindanoptimaldistributionthatimprovestheprospectsforwelfareofthelower
achievingstudentagreatdeal,whileusingsomeresourcestoimprovetheprospectsofthe
higherachievingstudentaswell.Howmuchweightsheshouldgivetoimprovingwelfareat
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thebottomandtheaveragewilldependonhowmuchsheweightshertwogoals.Second,
asbefore,shestillmustconsiderhercapacitytohelplowachievingstudentsinthefuture.
If,bychoosingtodevoteallresourcestoonechildoronegroupnow,thosewhoreceive
noneoftheresourceschoosetoelectadifferentperson,orchoosetotaxthemselvesata
lowerrate,thiswilllowertheavailableresourcesshehastospendinthefuture.
Theconclusionfromthiscaseisthatgiventhefourparametersoftheframeworkandthe
outcomesshedesires,Annawillconsidercompensatingthechildfromthelessresourced
family.Herstanceisdrivenbywantingtocompensatefordifferencesinwelfare—welfare
thatisaffectedbothbyrelativeachievementdifferencesanddifferentdevelopmentof
potential.Shewilltrytofindsomeamountofresourcesthatimprovestheprospectsof
welfareforthelowerachievingstudentthatissensitivebothtoaveragelevelsandto
maintainingresourcesforfuturestudents.
Case2:Differentbackgrounds,sameachievementlevels
Thissecondcaseincludestwochildrenfromdifferentsocioeconomicbackgroundswho
havethesameachievementlevels.Inthiscase,wehavesomeevidencethatthetwo
childrenhaddifferentopportunitiestodevelopachievement;butthatdespitethis
inequality,thetwochildrenhavethesamelevelofachievement.Here,Annacanbe
reasonablysurethat,insofarasachievementisconcerned,thetwochildrenwillhave
similarlifeprospects.Whateverflourishingbenefitsareassociatedwithalevelof
achievement,thesetwochildrenshouldreceivethesameamounts.Ifwelfarewas
completelydeterminedbyachievementlevel,therewouldbenocompellingreasonto
compensateonechildovertheother.
WhatanimatesAnnaisthatshehasreasontobelievethechildfromalowsocioeconomic
backgroundhasdevelopedlessofhernativepotentialthantheotherchild.Theevidence
forAnna’sconclusionisthatthechildwiththelowersocioeconomicbackgroundscores
muchhigherintheachievementdistributionforhersocialclass,comparedtowherethe
otherchildfallsintheachievementdistributionforhersocialclass.Nowitcouldbethat
Anna’sconclusionisincorrectandthechildwithseeminglyfewerresourceshappensto
haveparticularlydevotedparents.However,onaverage,Annaislikelytoberightand,asa
policymaker,sheiswillingtobewrongonoccasioninordertobecorrectinmostcases.
Becausedevelopingone’spotentialmattersforone’swelfare,thereisreasonto
compensatethechildfromthelowsocioeconomicbackground.
Manyofthesameprincipledandpracticalconstraintsdescribedabovewillapplyhereas
well.Whatevercompensationisrequiredwillfacetheproblemsofscarcityandfewer
resourcesinthenexttimeperiod.
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AnadditionalproblemAnnafaceshereisthecompositionofwelfarefromachievement
levelanddevelopmentofnativepotential.Annadoesnotknowhowmuchofanindividual’s
welfarecomesfromthelevelofachievementandhowmuchcomesfromdevelopingone’s
potential.Suppose,forexample,thatthetwochildrenhaveequallevelsofachievementand
thoselevelsareverylow;oneofthechildrenhasagreatdealofuntappedpotential.Inthis
case,ifhavingalowlevelofachievementmeansthatone’slifeprospectsareverybleak,
thenincreasingbothchildren’sachievementlevelsmaytakepriorityovercompensating
thechildwhohashadfeweropportunitiestodevelopherpotential.If,however,theirlevels
arehighenoughthattheirprospectsforwelfarearereasonable,thencompensatingthe
childwhohashadfeweropportunitiesbecomesmorerelevant.
TheconclusionfromthiscaseisthatAnnawillconsidercompensatingthechildfromthe
lessresourcedfamilyeventhoughherachievementisashighasthatofthechildfromthe
moreresourcedfamily.Ifbothoftheirachievementlevelsareverylow,shemaychooseto
giveresourcestobothstudents.Herstanceisdrivenbywantingtooptimizewelfare,with
anemphasisonthosewhoseprospectsforwelfarearelowest.Shewillconsider
compensatingfordifferencesinwelfarestemmingfromdifferentopportunitiestodevelop
potential,mindfulofthefactthatmarginalwelfaregainsarelargerforchildrenwhose
achievementisatthelowendofthedistribution.
Case3:Samebackgrounds,differentachievementlevelsandcoststoteach
Inthiscase,weconsiderthreestudentswhoallcomefromsimilarsocioeconomic
backgroundswithseeminglysimilarexperiences.Twoofthechildrenhavelowlevelsof
achievement,scoringatthe5thpercentileofachievement,whilethethirdchildhasaverage
achievement,scoringatthe50thpercentile.Wealsoknowthatimprovingtheachievement
ofthefirstchildisfarlessexpensivethanimprovingtheachievementofthesecondchild.
Becausetheyallcomefromfamiliesthatareeffectivelythesameintermsofthevaluethey
placeoneducationandtheirspendingpreferencesmoregenerally,Annacanassumethat
theyhavehadequalopportunitiestodeveloptheirpotential.Thus,theirwelfaredoesnot
differbecauseofdifferencesindevelopmentofpotential.However,intermsofprospects
forwelfare,thechildscoringatthe50thpercentilehashigherprospectsthanthetwo
childrenscoringatthefifth.ThisdifferencesuggeststoAnnathatthetwolow‐scoring
childrenshouldreceivecompensationsothattheirprospectsforwelfareareimproved.
DoesthefactthatoneofthesechildrencanlearnmuchmorequicklymatterforAnna’s
distributivequestion?Itwouldbequiteeasytopreserveequality,sothatneitherofthese
twochildrenendupworsethantheother,giventhesedifferencesinspeed.Supposethe
firstchildlearnsfortwicethepriceoftheotherchild.Maintainingequalitysimplymeans
thatthischildshouldreceivetwiceasmanyresources.Thisresourceallocationwould
persistuntilbothchildrencaughtuptothechildscoringinthe50thpercentile.Atthat
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point,becausethe50thpercentilechildlearnsataratesomewherebetweenthefirsttwo,
shewillreceive1.5timesasmanyresources.Thisapproachpreservesequalityand
improvesthewelfareprospectsforbothdisadvantagedstudents.
Theprincipledconstraintthatcompeteswiththisanalysisisacommitmenttoincreasing
averagelevelofachievement(whichisassumedtoimprovewelfareprospects).Thechild
wholearnsveryquicklyisjustasbadlyoffastheother.Forfewerresourcesthatchild’s
prospectscouldbeimprovedconsiderably.Bypreservingequality,thischild’sprospects
areworse.Imagineifinsteadofbeingtwiceasexpensive,thefirstchildwas20timesor50
timesasexpensivetoteach.Preservingequalityinthiscasewoulddeprivetheotherchild
scoringatthefifthpercentileagreatdealofresources,achievementandwelfare.
ThisdynamicmeansthatAnnawillonceagainhavetoconsidertherelationshipbetween
achievementandwelfareandhowmuchachievementisneededtoimproveone’slife
prospectsareasonableamount.Supposeweknowthatchildrenwhoscoreatorabovethe
30thpercentilehavemuchbetterlifeprospectsthanthosewhoscorebelowit—this
representsadiscontinuityor“bigjump”inwelfare.Inthiscase,Annamightbewillingto
favorthefasterlearningstudent,therebyleavingtheotherstudentbehind,becausegetting
thefasterlearningstudenttothe30thpercentilewillgreatlyimproveherprospectsfor
welfare.Here,acommitmenttoahighlevelofwelfarehastheeffectofdisfavoringtheleast
advantagedstudent.IfAnnaonlycaredabouttheworstoff,theconsequencewouldbethat
noneofthechildrenmakeittothe30thpercentile(thehypotheticaldiscontinuity)before
sherunsoutofresources.
TheconclusionfromthiscaseisthatAnnawillconsidercompensatingthechildrenwith
lowerachievement.Shewillavoidleavinganystudentbehind,butshewillweighthe
benefitsofmaintainingequalityagainstthelossinoverallwelfareforthechildwhoisless
costlytoeducate.Herstanceisdrivenbywantingtocompensatefordifferencesinwelfare
stemmingfromdifferentachievementlevels,whileatthesametimeaimingforgreater
averagewelfare.
Case4:Samebackgrounds,differentachievementlevelsandparentingpractices
Inthefinalcase,twostudentshavethesamesocioeconomicconditionsbutdifferent
parentalstrategies.Theseparentalstrategiesresultinonestudentwithalower
achievementlevelandlessofherpotentialdevelopedthantheother.Giventheheuristic
weprovided,itisnotpossibletosaythatonechildhasdevelopedmoreofherpotential
thantheother,becausethechildrencomefromthesamesocioeconomicbackground,
makingbetween‐groupcomparisonsimpossible.However,inthiscasewemadeitexplicit
thattheparentingpracticeshadtheeffectofloweringachievementanddevelopingless
potential.Thatis,weexpectthepotentialofchildrenwhoreceiveonetypeofparentingto
bethesameasthepotentialofchildrenwhoreceivetheothertypeofparentingbutthat
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themeasuredachievementofthetwogroupsisdifferent.Onthesurface,thestudentwith
theparentingpracticesthatleadtolowerachievementshouldthereforereceivesome
compensationonaccountofthesedifferences.However,Annarecognizesthatthe
informationshehasaboutachild’sachievementisincomplete.Achildmayhaveother,
unmeasuredattributesthatwillbeusefulforwelfare,currentlyandlaterinlife.Moreover,
shedoesnotknowthelinkbetweenchildhoodexperiencesandcurrentandfuturewelfare.
Itmaybethatahappychildhoodandaslightlylessprosperousadulthoodare,allthings
considered,betterfortotalwelfarethanareanunhappychildhoodandamoreprosperous
adulthood.TheseuncertaintiesinfluenceAnna’sdecisions.
Annaisconcernedthathermeasurementofachievementdoesnotcorrespondtocurrent
andfuturewelfare.Shecanusechildhoodexperiencestohelpestablishwhetherobserved
achievementwillindeedbecommensurate.Supposethat,inthecaseabove,thelower
scoringchildhadparentsorguardiansthatwereuninterestedinherdevelopmentand
wellbeing.Inthiscase,shemightconcludethatthedifferencesinmeasuredachievement
willnegativelyaffectthechild’sprospectsforflourishing,andsoshouldbecompensated.
Consideranalternativepossibility,oneinwhichtheparentsofthechildwithlowered
measuredachievementdonotbelievethatthemeasureofachievementaccuratelycaptures
theknowledge,skillsandattitudesthattheirchildneedsforflourishinglaterinlife.The
parentsaregivingthechildpotentiallyusefulqualities–suchastheabilitytohavepositive
personalrelationsandtogainhappinessfromexperiences–thatwillserveherwellinlife
butthatAnnadoesnotobserveonherachievementmeasure.Learningthesequalities
requiresthatthechildspendslesstimedevelopingotherelementsofachievement—
elementsthatAnnadoesmeasure.Inthiscase,Annamayconcludethatthedifferencesin
measuredachievementarenotpredictiveofthechildren’sprospectsforflourishingand
willnotcompensate.
Finally,itmaybethatthesesameparentsbelievehappinessinchildhoodtobeamore
importantpartofoverallwelfarethandotheparentsofthehigherachievingchild.Inthis
case,Annawillhavetodecidewhetherthislowerachievingchild,despitehavingahappier
childhood,willbepreparedforaflourishinglifeasanadult,andwhetherthehappier
childhoodcompensatesforalessthanoptimaladulthood.Thesearenoteasydecisions,but
learningaboutwhythetwochildrenhavedifferentachievementlevelscaninformAnna
abouthowthesedifferencesinmeasuredachievementwillinfluencetotalwelfare.Ifthe
twochildren,infact,haveequalprospectsforwellbeingthenAnnawouldnotwantto
compensatethechildwithlowermeasuredachievement.
TheconclusionfromthiscaseisthatAnnawillconsidercompensatingthechildwithlower
achievementonlyifshethinksthedifferencesinachievementwillresultinlowerprospects
forwellbeing.Thisdifficultyindecidingwhethertocompensatecomefromherinabilities
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toseethefullrangeofachievementandthefullrelationshipsamongchildhood
experiences,achievementandtotalwellbeing.Somestudentswithlowerobserved
achievementmayhavehigherunobservedachievementandthusequalprospectsfor
flourishing.Onlywhenobservedachievementislowenoughthattheprospectsfor
flourishingarefarlowerthanwhatsheconsidersacceptable(aswediscussedinCase3),
willshecompensate.
Here,wehaveseenthatthestructureweprovided—distalandproximaleducationalgoals
andfeasibilityconstraintsthataffecthowpolicymakerspursuethosegoals—usefully
allowsustodeconstructthecasesintotheirconstituentparts.Wedonotprovidesolutions
tothecases,assolutionsinvolvedecisionsabouthowtoweightaveragewelfareagainst
welfaregainsfortheleastadvantagedandhowtoweightcurrentagainstfuturewelfare,as
wellasknowledgeoftheparticularempiricalconstraintsfacedbyindividualcommunities.
Despitethislackofpreciseprescription,theframeworkproducesgeneralguidelineswith
onlyminimalstructure.
Conclusion
Aspolicymakersorvoters,wemustdecidehowtoallocateresourcesforschoolsacross
studentsandcommunities.Wehaveintroducedaframeworkfordecidinghowtoallocate
resourcesgivenasetoffeasibilityconstraintsandgoalsforstudents.Webeganwiththe
straightforwardassumptionthatthepolicymakerhopesthatschoolingwillincrease
students’averageprospectsforwellbeingandemphasizeimprovementsforstudentswho
areworseoff.Theattributesthatstudentsdevelopinschool(andelsewhere)–whatwe
callachievement–contributetothiswellbeingsothepolicymakercaresabouttheoverall
levelofachievementanditsdistribution.Weintroducedtheideathatindividualwelfare
alsoincreaseswhenindividualshavetheopportunitytodevelopandutilizetheirnatural
capacities.Thus,thepolicymakeralsocaresaboutthelevelanddistributionofthis
opportunitytodevelopcapacity.
Theinnovationofthispaperisdescribingreal‐worldconstraintsfacedbypolicymakers
andshowinghowtheseconstraintsaffectthedecisionsthattheymake.Fourproblemsare
noteworthy.First,theproblemofscarcityrevealswhypolicymakersmustmaketrade‐offs
betweenthecompetingvaluesofaverageandequalwelfare.Second,theproblemof
communitybuy‐inrevealswhy—evenwhencoststoimprovingtheprospectsoftheleast‐
advantagedarethesameasimprovingtheprospectsofthebetteroff—policymakersmay
stilltargetsomeresourcestothosewhoarehighachieving.Third,theproblemofthehigh
stakesnatureofachievementforwelfarerevealswhyimprovingachievementatthe
bottomofthedistributionissoimportant.
Thefinalproblem—thatofmeasurement—hasparticularsalienceinouranalysis.The
policymakerseekstomeasureachievementbecauseitisherbestguessatchildren’s
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prospectsforwell‐beinglaterinlife.Shealsoseekstomeasureopportunitiestodevelop
capacitiessincethoseopportunitiesareimportanttowellbeingforchildren.Yet,she
cannotmeasureeitherconstructaccurately.Ourdiscussionaboveshedslightonhow
policymakersdevelopanduseimperfectachievementindicators,liketestscores,toinform
decisions;italsopointstowhatpolicymakersmightusetocompensatefortheimprecision
ofmeasurement.Thepolicymakermayaimtocollectthefullestpossiblemeasureof
achievementgivenavailableresources.Thisapproachhasthebenefitofproducingabroad
measurebutthemeasureclearlystillwillhaveholesandbecostly.Alternatively,shemay
trytomeasureonlytheminimallevelofeachfeaturethatisdeterminedtobeessentialfor
theaverageflourishingofallstudents—pointsatwhichwelfarefromachievement
increasessubstantially.Thismeasureisincomplete,andshecouldthensupplementitwith
somemeasuresofstudentexperiences,whichcanshedlightonchildhoodwelfareand
opportunitiestodevelopone’scapacities.Thissecondapproachhasthebenefitsofbreadth,
sensitivitytoexperiences,andpracticality,buttheremaybereasonsfordeepermeasures
ofsomefactors.
Itiscommonpracticetomakebetween‐groupcomparisonsineducationalreportcardsand
research,thoughitisnotalwaysclearwhatthesemetricsareusefulfor.Here,wehave
arguedthatthesecomparisonsserveapurposewhenmeasuresofpotentialandindividual
bundlesofachievementmostusefulforachievingwelfareareunavailable.Whenthis
informationisunknown,between‐groupcomparisonsareusefulheuristics,astheyreveal
relevantdifferencesinprospectsforwelfareresultingfromundevelopedpotentialthat
meritcompensationatthegroup,ifnottheindividual,level.
Bykeepingfocusedontheeventualgoalsofeducationandthepracticalproblemsthat
makerealizingthosegoalsdifficult,wehavebothsomeunderstandingofthedistributive
decisionsthataremadeandsomestructureforthinkingabout–givenourgoalsand
constraints–whatdistributionswewouldliketosee.
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