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American Economic Association

The Possibility of Social ChoiceAuthor(s): Amartya SenSource: The American Economic Review, Vol. 89, No. 3 (Jun., 1999), pp. 349-378Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/117024 .

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The Possibilityof Social Choicet

By AMARTYASEN*

A camel, it has been said, is a horse de-

signed by a committee. This might soundlike

a telling example of the terribledeficiencies of

committee decisions, but it is really much toomild an indictment.A camel may not have the

speed of a horse, but it is a very useful andharmoniousanimal-well coordinated o travellong distances withoutfood and water.A com-

mittee that tries to reflect the diverse wishes ofits differentmembers n designing a horsecould

very easily end up with something far less

congruous: perhapsa centaur of Greek myth-ology, half a horse and half something else-amercurial creation combining savagery with

confusion.The difficultythat a small committeeexperi-

ences may be only greater when it comes todecisions of a sizable society, reflecting thechoices of the people, by the people, for thepeople. That, broadlyspeaking, is the subjectof social choice, and it includes within its

capacious frame various problems with thecommon feature of relating social judgments

andgroupdecisions to theviews andinterestsofthe individualswho make up the society or the

group.If thereis a central questionthatcan beseen as the motivating ssue thatinspiressocialchoice theory, it is this: how can it be possibleto arriveat cogent aggregative udgmentsabout

the society (for example,about social welfare,or thepublic interest, r aggregatepoverty ),given thediversityof preferences, oncerns,and

predicamentsof the different ndividualswithinthe society? How can we findany rationalbasisfor making such aggregative udgementsas thesociety prefers this to that, or the societyshould choose this over that, or this s sociallyright ?Is reasonable social choice at all possi-ble, especially since, as Horace noted a longtime ago, theremaybe asmany preferencesasthere are people ?

I. Social ChoiceTheory

In this lecture, I shall try to discuss somechallenges and foundationalproblems faced bysocial choice theoryas a discipline.1The imme-diate occasion for this lecture is, of course, anaward, and I am aware thatI am expected todiscuss, in one form or another,my own workassociated with this event (however immodestthatattemptmightotherwise have been). This Iwill tryto do, but it is, I believe, also a plausibleoccasion to address some general questionsabout social choice as a discipline-its content,

relevance,andreach-and I intend to seize thisopportunity.The Royal Swedish Academy ofSciences referred o welfareeconomics as thegeneral field of my work for which the awardwas given, and separatedout three particularareas: social choice, distribution,and poverty.While I have indeed been occupied, in variousways, with these different subjects, it is socialchoice theory, pioneeringly formulated in itsmodem formby Arrow(1951),2 thatprovidesageneral approach to the evaluation of, andchoice over, alternativesocial possibilities (in-cluding inter alia the assessment of social wel-fare, inequality,and poverty).This I take to be

t This article is the lecture Amartya Sen delivered inStockholm,Sweden, December 8, 1998, when he receivedthe Alfred Nobel MemorialPrize in Economic Sciences.The article s copyrightC The Nobel Foundation1998 and

is published here with the permission of the Nobel Foun-

dation.* The Master's Lodge, TrinityCollege, Cambridge,CB2

1TQ, England.For helpful comments and suggestions,I am

most grateful to SudhirAnand, Kenneth Arrow, Tony At-

kinson, Emma Rothschild, and Kotaro Suzumura. I havealso benefited rom discussionswithAmiyaBagchi, PranabBardhan, Kaushik Basu, Angus Deaton, Rajat Deb, Jean

Dreze, Bhaskar Dutta, Jean-Paul Fitoussi, James Foster,

Siddiq Osmani,PrasantaPattanaik,and Tony Shorrocks.

' This is, obviously, not a surveyof social choice theoryand there is no attempthere to scan the relevant iterature.

Overviewscan be found in Alan M. Feldman(1980), Pra-santaK. Pattanaikand MauriceSalles (1983), Kotaro Su-

zumura (1983), Peter J. Hammond (1985), Jon Elster andAanundHylland(1986), Sen (1986a), David Starrett 1988),DennisC. Mueller (1989), and more extensively in KennethJ. Arrow et al. (1997).

2 See also Arrow (1950, 1951, 1963).

349



350 THEAMERICANECONOMICREVIEW JUNE 1999

reason enough for primarilyconcentratingonsocial choice theory in this Nobel lecture.

Social choice theory is a very broad disci-pline, covering a variety of distinct questions,

and it may be useful to mention a few of theproblems as illustrations of its subject matter(on many of which I have been privileged towork). When would majority rule yield unam-biguous and consistentdecisions? How can wejudge how well a society as a whole is doing inthe lightof thedisparatenterestsof its differentmembers?How do we measureaggregate pov-erty in view of the varying predicamentsandmiseries of the diversepeople that make up thesociety? How can we accommodaterights andliberties of persons while giving adequaterec-

ognition to their preferences?How do we ap-praise social valuationsof public goods such asthe naturalenvironment, r epidemiologicalse-curity? Also, some investigations, while notdirectlyapartof social choice theory,havebeenhelped by the understandinggenerated by thestudyof group decisions (such as the causationand preventionof famines and hunger, or theforms and consequences of gender inequality,or the demandsof individual reedom seen as a

socialcommitment ).The reachandrelevanceof social choice theory can be very extensive

indeed.

II. Originsof SocialChoiceTheoryandConstructive essimism

How did the subject of social choice theoryoriginate? The challenges of social decisionsinvolving divergent nterests and concernshavebeen explored for a long time. For example,Aristotlein ancient Greece and Kautilya n an-cient India, both of whom lived in the fourthcenturyB.c., exploredvarious constructivepos-sibilities in social choice in theirbooks respec-tively entitled Politics and EconomiCs.3

However,social choice theoryas a systematic

discipline irstcame into its own around he timeof the FrenchRevolution.The subject was pio-neeredby Frenchmathematiciansn the late eigh-teenthcentury,such as J. C. Borda (1781) and

Marquis de Condorcet(1785), who addressedthese problems n rathermathematicalerms andwho initiated he formaldisciplineof socialchoice

in terms of voting and related procedures.Theintellectual limateof the periodwas much influ-enced by EuropeanEnlightenment, ith its inter-est in reasoned construction of social order.Indeed,some of the early social choice theorists,most notably Condorcet,were also among theintellectual eadersof the FrenchRevolution.

The French Revolution, however, did notusher in a peaceful social order in France. De-

spite its momentous achievements in changingthe political agendaacross the whole world, inFrance itself it not only producedmuch strifeand bloodshed, it also led to what is often

called, not inaccurately,a reignof terror. n

deed, many of the theorists of social coordina-tion, who had contributed o the ideas behindthe Revolution, perished in the flames of thediscord that the Revolution itself unleashed(this included Condorcetwho took his own lifewhen it became quite likely that others woulddo it forhim). Problemsof social choice, which

were being addressedat the level of theory andanalysis,did not wait, in this case, for a peace-fully intellectualresolution.

The motivation that moved the early socialchoice theorists ncluded the avoidance of bothinstabilityand arbitrarinessn arrangementsorsocial choice. The ambitions of their work fo-cused on the developmentof a frameworkforrational and democraticdecisions for a group,paying adequateattention o thepreferencesandinterestsof all its members.However, even thetheoretical investigations typically yieldedrather pessimistic results. They noted, for ex-ample, that majority rule can be thoroughlyinconsistent,with A defeatingB by a majority,B defeatingC also by a majority,and C in turndefeatingA, by a majorityas well.4

3 Arthashastra, the Sanskrit word (the title of Kauti-lya's book), is best translatediterally as Economics, venthoughhe devoted much space to investigating he demandsof statecraft n a conflictualsociety. English translations fAristotle's Politics and Kautilya's Arthashastra can befound respectively n E. Barker 1958) and L. N. Rangarajan(1987). On the interestingmedieval Europeanwritings onthese issues see, for example, Ian McLean(1990).

4See Condorcet (1785). There are many commentarieson these analyses, including Arrow (1951), Duncan Black(1958), William V. Gehrlein (1983), H. Peyton Young(1988), and McLean (1990). On the potential ubiquityofinconsistency n majorityvoting, see RichardD. McKelvey(1979) andNorman J. Schofield (1983).



VOL.89 NO. 3 SEN: THEPOSSIBILITYOF SOCIALCHOICE 351

A good deal of exploratory work (often,again, with pessimistic results) continued n Eu-rope through the nineteenth century. Indeed,some very creativepeople worked in this area

and wrestled with the difficulties of socialchoice, including Lewis Carroll, the author ofAlice in Wonderland underhis realname,C. L.Dodgson, 1874, 1884).

When the subjectof social choice was revivedin the twentieth enturyby Arrow (1951), he toowas very concernedwith the difficultiesof groupdecisions and the inconsistencies o which theymay lead.While Arrowputthe disciplineof socialchoice in a structured-and axiomatic-frame-work (thereby eading o the birthof social choicetheory n its modem form),he deepened he pre-

existing gloom by establishingan astonishing-and apparently essimistic-result of ubiquitousreach.

Arrow's (1950, 1951, 1963) impossibilitytheorem (formally, the General PossibilityTheorem ) s a result of breathtaking leganceandpower, which showed that even some verymild conditions of reasonablenesscould not besimultaneously satisfied by any social choiceprocedure,within a very wide family. Only adictatorshipwould avoid inconsistencies, butthatof course would involve: (1) in politics, an

extremesacrificeof participatory ecisions, and(2) in welfare economics, a gross inabilityto besensitive to the heterogeneous interests of adiverse population. Two centuries after thefloweringof the ambitions of social rationality,in Enlightenment hinkingand in the writingsofthe theoristsof the FrenchRevolution,the sub-ject seemed to be inescapablydoomed. Socialappraisals,welfare economic calculations,andevaluative statistics would have to be, itseemed, inevitably arbitraryor unremediablydespotic.

Arrow's impossibility heorem aroused m-mediate and intense interest (and generatedamassive literature n response, including manyother impossibility results).SIt also led to the

diagnosis of a deep vulnerability n the subjectthat overshadowed Arrow's immensely impor-tant constructiveprogramof developing a sys-tematic social choice theory that could actually

work.

III. WelfareEconomicsand ObituaryNotices

Social choice difficulties apply to welfareeconomics with a vengeance. By the middle1960's, William Baumol (1965) judiciously re-markedthat statementsabout the significanceof welfare economics had startedhaving anill-concealed resemblance to obituarynotices(p. 2). This was certainly herightreadingof theprevailingviews. But, as Baumolhimself noted,

we have to assess how sound these views were.We have, especially, to ask whether the pessi-mism associated with Arrovian structures insocial choice theorymust be seen to be devas-tatingfor welfare economics as a discipline.

As it happens,traditionalwelfareeconomics,which had been developed by utilitarianecon-omists (such as Francis T. Edgeworth, 1881;AlfredMarshall,1890; ArthurC. Pigou, 1920),had takena very differenttrackfrom the vote-orientedsocial choice theory.It took inspirationnot fromBorda(1781) orCondorcet 1785), but

from their contemporary, Jeremy Bentham(1789). Benthamhad pioneered the use of util-itarian calculus to obtainjudgments about thesocial interestby aggregatingthe personal in-terestsof the different ndividuals n the form oftheirrespectiveutilities.

Bentham's concern-and that of utilitarian-ism in general-was with the total utilityof acommunity.This was irrespectiveof the distri-bution of that total, and in this there is an

5 By varying the axiomatic structure, elated mpossibil-ity results can also be obtained. Examples can be found inArrow (1950, 1951, 1952, 1963), Julian H. Blau (1957,1972, 1979), Bengt Hansson (1969a, b, 1976), Tapas Ma-jumdar (1969, 1973), Sen (1969, 1970a, 1986b, 1993a,1995a), Pattanaik 1971, 1973, 1978), Andreu Mas-Colleland Hugo Sonnenschein (1972), Thomas Schwartz (1972,

1986), Peter C. Fishburn (1973, 1974), Allan F. Gibbard(1973), Donald J.Brown (1974, 1975), KenBinmore (1975,1994), Salles (1975), Mark A. Satterthwaite1975), RobertWilson (1975), Rajat Deb (1976, 1977), Suzumura 1976a,b, 1983),Blau andDeb (1977), JerryS. Kelly (1978, 1987),Douglas H. Blair and Robert A. Pollak (1979, 1982), Jean-Jacques Laffont (1979), Bhaskar Dutta (1980), GracielaChichilnisky(1982a, b), David M. Gretherand Charles R.Plott (1982), Chichilniskyand Geoffrey Heal (1983), HerveMoulin (1983), Pattanaikand Salles (1983), David Kelsey(1984a, b), Bezalel Peleg (1984), Hammond(1985, 1997),MarkA. Aizermanand FuadT. Aleskerov(1986), Schofield(1996), and Aleskerov (1997), among manyothercontribu-tions.




informational imitation of considerableethicaland political importance.For example, a personwho is unlucky enough to have a uniformlylower capability o generateenjoymentand util-

ity out of income (say, because of a handicap)would also be given, in the utilitarian idealworld, a lower share of a given total. This is aconsequence of the single-minded pursuit ofmaximizing the sum-total of utilities (on thepeculiar consequences of this unifocal priority,see Sen, 1970a, 1973a; John Rawls, 1971;Claude d'Aspremontand Louis Gevers, 1977).However, the utilitarian nterest in taking com-parativenoteof the gains andlosses of differentpeople is not in itself a negligible concern. Andthis concern makes utilitarianwelfare econom-

ics deeply interested in using a class of infor-mation-in the form of comparison of utilitygains and losses of different persons-withwhich Condorcet and Borda had not been di-rectly involved.

Utilitarianism has been very influential inshaping welfare economics, which was domi-nated for a long time by an almost unquestion-ing adherence o utilitarian alculus. But by the1930's utilitarianwelfare economics came un-der severe fire. It would have been quitenaturalto question (as Rawls [1971] would masterfully

do in formulatinghis theoryof justice) the util-itarian neglect of distributional ssues and itsconcentration only on utility sum-totals in adistribution-blindway. But that was not thedirection in which the antiutilitarian ritiqueswent in the 1930's and in the decades thatfollowed. Rather,economists came to be per-suadedby argumentspresentedby Lionel Rob-bins and others (deeply influencedby logicalpositivist philosophy) that interpersonal om-

parisonsof utility had no scientific basis: Ev-ery mindis inscrutable o every other mindand

no common denominatorof feelings is pos-sible (Robbins, 1938 p. 636). Thus, theepistemic foundations of utilitarian welfareeconomics were seen as incurablydefective.

There followed attemptsto do welfare eco-nomics on the basis of the different persons'respective orderings of social states, withoutany interpersonalcomparisonsof utility gainsand losses (nor, of course, any comparisonofthe totalutilities of differentpersons,which areneglected by utilitarians s well). While utilitar-ianism and utilitarian welfare economics are

quite indifferent to the distribution of utilitiesbetween different persons (concentrating, asthey do, only on the sum-total of utilities), thenew regime without any interpersonal ompar-

isons in any form, furtherreduced the informa-tional base on which social choice could draw.The already-limited informational base ofBenthamite calculus was made to shrink evenfurther o thatof Borda andCondorcet, ince theuse of differentpersons' utility rankingswith-out any interpersonal omparison s analyticallyquite similar to the use of voting information nmaking social choice.

Facedwiththis informational estriction,util-itarian welfare economics gave way, from the1940's onwards, to a so-called new welfare

economics, which used only one basic crite-rion of social improvement, viz, the Paretocomparison. This criteriononly asserts that analternative ituationwould be definitelybetter fthe change would increase the utility of every-one.6 A good deal of subsequentwelfare eco-nomics restrictsattention o Paretoefficiencyonly (that s, only to makingsurethatno furtherPareto improvementsare possible). This crite-rion takesno interest whatever n distributionalissues, which cannot be addressedwithout con-sidering conflicts of interestand of preferences.

Some further criterion s clearly needed formakingsocial welfare judgmentswith a greaterreach, and this was msightfully explored byAbramBergson (1938) and Paul A. Samuelson(1947). This demand led directly to Arrow's(1950, 1951) pioneering formulationof socialchoice theory,relating ocial preference or decisions)to thesetof individual references, ndthisrelation s called a socialwelfare function. Ar-row(1951, 1963) wenton to considera setof verymild-looking onditions, ncluding: 1) Paretoef-ficiency, (2) nondictatorship, 3) independence

(demanding hat social choice over any set ofalternativesmustdependon preferences nlyoverthose altematives),and (4) unrestricted omain(requiringhat social preferencemust be a com-plete ordering,with full transitivity, nd thatthismust work foreveryconceivable etof individualpreferences).

Arrow's impossibilitytheoremdemonstrated

6 Or, at least, if it enhanced the utility of at least oneperson and did not harm the interestof anyone.



VOL 89 NO. 3 SEN: THE POSSIBILITYOF SOCIALCHOICE 353

that it is impossible to satisfy these conditionssimultaneously.7 n orderto avoid this impossi-bility result, different ways of modifying Ar-row's requirements were tried out in the

literature that followed, but other difficultiescontinued to emerge.8 The force and wide-spread presence of impossibility results gener-ated a consolidatedsense of pessimism,andthisbecame a dominant hemein welfare economicsand social choice theory n general.Is thisread-ing justified?

IV. Complementarityf FormalMethodsandInformal Reasoning

Before I proceed furtheron substantivemat-

ters, it may be useful to commentbriefly on thenature of the reasoningused in answering thisand related questions. Social choice theoryis asubject n which formal and mathematical ech-niques have been very extensively used. Thosewho are suspicious of formal(andin particular,of mathematical)modes of reasoningare oftenskeptical of the usefulness of discussing real-world problemsin this way. Their suspicion isunderstandable,but it is ultimately misplaced.The exercise of trying to get an integratedpic-ture from diverse preferences or interests ofdifferent people does involve many complexproblemsin which one could be seriously mis-led in the absence of formal scrutiny. Indeed,Arrow's (1950, 1951, 1963) impossibility theo-rem-in many ways the locus classicus n this

field-can hardlybe anticipatedon the basis ofcommon sense or informalreasoning.This ap-plies also to extensions of this result, for exam-ple to the demonstrationhat an exactly similar

impossibility to Arrow's holds even withoutany imposed demandof internalconsistency ofsocial choice (see Sen, 1993a Theorem 3). Inthe process of discussing some substantive is-sues in social choice theory, I shall have theopportunityto consider various results whichtoo are not easily anticipated without formalreasoning.Informal nsights, importantas theyare, cannot replace the formal investigationsthat are needed to examine the congtuity andcogency of combinations of values and of ap-parentlyplausibledemands.

This is not to deny thatthetask of widespreadpublic communication s crucial for the use ofsocial choice theory.It is centrally mportant orsocial choice theoryto relate formalanalysis toinformaland transparentxamination.I have toconfess that in my own case, this combinationhas, in fact, been something of an obsession,and some of the formalideas I have been mostconcernedwith (suchas anadequate rameworkfor informationalbroadening, he use of partialcomparabilityand of partialorderings,and theweakeningof consistency conditionsdemandedof binaryrelationsandof choice functions)callsimultaneously or formalinvestigation and forinformal explication and accessible scrutiny.9Ourdeeply felt, real-worldconcernshave to besubstantively ntegratedwith the analyticaluseof formaland mathematical easoning.

V. Proximityof Possibilityand Impossibility

The generalrelationshipbetween possibilityand impossibility results also deserves some

attention, n order to understand he natureandrole of impossibility theorems. When a set ofaxiomsregarding ocial choice can all be simul-taneouslysatisfied,theremay be several possi-ble procedures hatwork, amongwhichwe haveto choose. In order to choose between the dif-ferentpossibilities throughthe use of discrimi-

7 There is also the structural ssumption hatthereareatleasttwo distinct ndividuals butnotinfinitelymany)and atleast threedistinct social states (not perhaps he most unre-alisticof assumptions hateconomists have ever made).Theaxioms referredto here are those in the later version of

Arrow'stheorem:Arrow(1963). Since thepresentation ereis informal and permits some technical ambiguities, thoseconcerned with exactness are referredto the formal state-ments in Arrow (1963), or in Sen (1970a) or Fishburn(1973) or Kelly (1978). Regardingproof, there are variousversions, including, of course, Arrow (1963). In Sen(1995a) a very short-and elementary-proof is given. Seealso Sen (1970a, 1979b), Blau (1972), Robert Wilson(1975), Kelly (1978), SalvadorBarbera 1980, 1983), Bin-more(1994), and JohnGeanakopolous 1996), amongothervariants.

8 Forcritical accountsof the literature, ee Kelly (1978),Feldman (1980), Pattanaikand Salles (1983), Suzumura(1983), Hammond (1985), Walter P. Heller et al. (1986),

Sen (1986a, b), Mueller (1989), and Arrowet al. (1997).

9In fact, in my main monograph in social choicetheory-Collective Choice and Social Welfare (Sen,1970a), chapterswith formal analysis (the starred hap-ters) alternatewithchaptersconfinedto informaldiscussion

(the unstarred hapters).



354 THE AMERICANECONOMICREVIEW JUNE 1999

nating axioms, we have to introduce furtheraxioms, until only one possible procedurere-mains. This is something of an exercise inbrinkmanship.We have to go on cutting down

alternativepossibilities, moving-implicitly-towardsan impossibility, but then stop just be-fore all possibilitiesare eliminated, o wit, whenone and only one option remains.

Thus, it should be clear thata full axiomaticdetermination f a particularmethodof makingsocial choice must inescapably lie next door toan impossibility-indeed just short of it. If itlies farfrom an impossibility (withvariouspos-itive possibilities), then it cannot give us anaxiomatic derivationof any specific method ofsocial choice. It is, therefore, o be expectedthat

constructivepaths in social choice theory, de-rived from axiomaticreasoning, would tend tobe paved on one side by impossibility results(opposite to the side of multiple possibilities).No conclusion about the fragility of socialchoice theory (or its subject matter) emergesfrom this proximity.

In fact, the literaturethat has followed Ar-row's work has shown classes of impossibilitytheorems and of positive possibility results, allof which lie quiteclose to each other. 0Therealissue is not, therefore, he ubiquity of impossi-

bility (it will always lie close to the axiomaticderivationof any specific social choice rule),but the reach and reasonablenessof the axiomsto be used. We haveto get on withthe basic taskof obtaining workablerules thatsatisfy reason-able requirements.

VI. MajorityDecisionsand Coherence

In the discussion so far, I have made noattempt o confine attention o particular onfig-

urationsof individualpreferences, gnoring oth-ers. Formally, this is required by Arrow9condition of unrestricteddomain, which in-sists that the social choice proceduremust workfor every conceivable cluster of individualpref-erences. It must, however, be obvious that, forany decision procedure, some preference pro-files will yield inconsistencies and incoherenceof social decisions while otherprofileswill notproduce these results.

Arrow (1951) himself had initiated, alongwith Black (1948, 1958), the search for ade-

quate restrictions that would guaranteeconsis-tent majority decisions. The necessary andsufficient conditionsfor consistent majorityde-cisions can indeed be identified (see Sen andPattanaik,1969).11While much less restrictivethanthe earlierconditionsthathad been identi-fied, they are still quite demanding; ndeed it isshown that they would be easily violated in

many actualsituations.The formalresultson necessaryor sufficiency

conditions of majority decisions can only give as

much hope-or generate as much disappoint-

ment-about voting-basedsocial choice as theextentof socialcohesionandconfrontationintheactualpatternsof individualpreferences)wouldallow. Choice problems or the society come in

many shapes and sizes, and there may be lesscomfort n these resultsfor some types of socialchoice problems hanfor others.When distribu-tional issues dominateand when people seek to

1o See Hansson (1968, 1969a, 1969b, 1976), Sen (1969,1970a, 1977a, 1993a), Schwartz(1970, 1972, 1986), Pat-tanaik (1971, 1973), Alan P. Kirmanand Dieter Sonder-

mann (1972), Mas-Colell and Sonnenschein 1972), Wilson(1972, 1975), Fishburn (1973, 1974), Plott (1973, 1976),Brown (1974, 1975), John A. FerejohnandGrether 1974),Binmore (1975, 1994), Salles (1975), Blair et al. (1976),Georges A. Bordes (1976, 1979), Donald E. Campbell(1976), Deb (1976, 1977), Parks (1976a, b), Suzumura(1976a, b, 1983), Blau and Deb (1977), Kelly (1978), Peleg(1978, 1984), Blair and Pollak (1979, 1982), Blau (1979),Bernard Monjardet (1979, 1983), Barbera (1980, 1983),Chichilnisky (1982a, b), Chichilnisky and Heal (1983),Moulin (1983), Kelsey (1984, 1985), Vincenzo Denicolo(1985), Yasumi Matsumoto (1985), Aizennan and Ales-kerov (1986), TaradasBandyopadhyay 1986), Isaac Levi(1986), and Campbelland Kelly (1997), among many othercontributions.

l See also Ken-ichi Inada (1969, 1970), who has been a

major contributorto this literature. See also William S.

Vickrey (1960), BenjaminWard (1965), Sen (1966, 1969),Sen and Pattanaik 1969), and Pattanaik 1971). Other ypesof restrictionshave also been consideredto yield consistentmajoritydecisions; see Michael B. Nicholson (1965), Plott(1967), Gordon Tullock (1967), Inada (1970), Pattanaik

(1971), Otto A. Davis et al. (1972), Fishbum(1973), Kelly(1974a, b, 1978), Pattanaik and Sengupta (1974), Eric S.

Maskin (1976a, b, 1995), Jean-MichelGrandmont 1978),Peleg (1978, 1984), Wulf Gaertner 1979), Dutta (1980),

Chichilnisky and Heal (1983), and Suzumura (1983),among other contributions.Domain restrictions or a wider

class of voting rules have been investigated by Pattanaik(1970), Maskin (1976a, b, 1995), and Ehud Kalai and E.

Muller (1977). The vast literaturehas been definitively

surveyed by Gaertner 1998).




maximize heirown shares withoutconcern or

others as,forexample, n a cakedivision prob-lem, with each preferringany division that in-creasesher own share,no matterwhat happens o

the others), then majorityrule will tend to bethoroughly nconsistent.Butwhen there s a mat-

ter of national utrage forexample, n response o

the inabilityof a democraticgovernment o pre-vent a famine),the electoratemay be reasonablyunivocalandthoroughly onsistent.12Also, whenpeople clusterin parties,with complex agendas

and dialogues, nvolvinggive andtake as well as

some general attitudes o values like equity or

justice, the ubiquitous nconsistenciescan yieldground o more congruousdecisions.13

So far as welfare economics is concerned,

majorityrule and voting proceduresare partic-ularly proneto inconsistency, given the central-ity of distributionalssues in welfare-economic

problems.However, one of the basic questionsto ask is whethervoting rules (to which socialchoice proceduresare effectively restrictedin

the Arrovian framework)provide a reasonable

approach o social choice in the field of welfare

economics. Are we in the rightterritory n try-ing to make social welfare judgments through

variantsof voting systems?

VII. InformationalBroadening ndWelfareEconomics

Voting-basedproceduresare entirely natural

forsome kindsof socialchoiceproblems, uch as

elections,referendums,r committeedecisions.'4They are,however,altogether nsuitableor manyotherproblemsof social choice.'5 When, for ex-ample, we want to get some kind of an aggrega-

tive index of social welfare,we cannot rely onsuch proceduresor at leasttwo distinctreasons.

First,votingrequires ctiveparticipation,nd fsomeone decides not to exercise her voting right,her preferencewould find no directrepresentationin social decisions. Indeed,becauseof lower par-ticipation,he interestsof substantial roups-forexample of African Americans in the UnitedStates-find inadequateepresentationn nationalpolitics.)In contrast,n makingreasonable ocialwelfare udgments, he interestsof the less asser-tive cannotbe simply ignored.

Second, even with the active involvementofevery one in voting exercises, we cannotbut beshort of important nformationneeded for wel-fare-economic evaluation (on this see Sen,

1970a, 1973a). Throughvoting, each person canrankdifferentalternatives.But there s no directway of getting interpersonalcomparisons ofdifferentpersons' well-being from voting data.We must go beyond the class of voting rules

(explored by Borda and Condorcetas well asArrow) to be able to address distributionalissues.

Arrowhad ruledout the use of interpersonalcomparisonssince he had followed the generalconsensus that had emerged in the 1940's that(as Arrowput it) interpersonal omparisonof

12 This is one reason why no faminehaseveroccurredn

an independentand democraticcountry (not runby alien-

ated rulers,orby a dictator,or by a one-party tate).See Sen

(1984), Dreze and Sen (1989), Frances D'Souza (1990),HumanRightsWatch (1992), andRed Cross andRed Cres-

cent Societies (1994).13 On differentaspectsof this general political issue, see

Arrow (1951), James M. Buchanan (1954a, b), Buchanan

and Tullock (1962), Sen (1970a, 1973c, 1974, 1977d,

1984), Suzumura 1983), Hammond (1985), Pattanaikand

Salles (1985), Andrew Caplin and Barry Nalebuff (1988,1991), Young (1988), and Guinier (1991), among other

writings, and also the Symposium n votingproceduresn

the Journal of EconomicPerspectives (Winter1995), with

contributionsby Jonathan Levin and Nalebuff (1995),

Douglas W. Rae (1995), Nicolaus Tideman (1995), Robert

J. Weber (1995), Michel Le Breton and John Weymark

(1996), and Suzumura 1999), amongothers.

14 There are, however, some serious problems arisingfrom a possible lack of correspondencebetween votes and

actual preferences,which could differ because of strategicvoting aimed at manipulationof voting results. On this seethe remarkablempossibility heoremof Gibbard 1973) andSatterthwaite 1975). There is an extensive literatureon

manipulationand on the challenges of implementation,on

which see also Pattanaik (1973, 1978), Steven J. Brams(1975), Ted Groves and John Ledyard 1977), BarberaandSonnenschein (1978), Dutta and Pattanaik (1978), Peleg(1978, 1984), Schmeidler and Sonnenschein (1978), Das-

gupta et al. (1979), Green and Laffont (1979), Laffont(1979), Dutta (1980, 1997), Pattanaikand Sengupta(1980),Sengupta (1980a, b), Laffont and Maskin (1982), Moulin(1983, 1995), and Leo Hurwicz et al. (1985), among othercontributions.Thereis also a nonstrategic mpossibility in

establishingan exact one-to-one correspondencebetween:(1) preferring, 2) dispreferring,and (3) being indifferent,on the one hand, and (1*) voting for, (2*) voting against,and (3*) abstaining,on the otherhand,no matter whethervoting is costly, or enjoyable, or neither (see Sen, 1964).

15 On this, see Sen (1970a, 1977a).




utilities has no meaning (Arrow, 1951 p. 9).The totality of the axiom combinationused byArrow had the effect of confining social choiceprocedures o rules that are, broadly speaking,of the voting type.16 His impossibility resultrelates, therefore, o this class of rules.

To lay the foundations of a constructive so-cial choice theory, if we want to reject thehistoricalconsensus against the use of interper-sonal comparisons n social choice, we have toaddress two important-and difficult-ques-tions. First, can we systematically incorporateand use somethingas complex as interpersonalcomparisons nvolving many persons?Will thisbe a territory f disciplined analysis,rather hana riot of confusing (and possibly confused)

ideas? Second,how can the analyticalresultsbeintegratedwith practicaluse? On what kind ofinformationcan we sensibly base interpersonalcomparisons?Will the relevant informationbeactually available,to be used?

The first is primarilya question of analyticalsystem building, and the second that of episte-mology as well as practical reason. The latterissue requiresa reexaminationof the informa-tional basis of interpersonal omparisons,andI

would presently arguethat it calls for an ines-capably qualified response. But the first ques-

tion can be addressedmoredefinitively through

constructive analysis. Without going into tech-nicalities of the literaturethat has emerged, Iwould like to reportthat interpersonal ompar-isons of various types can be fully axiomatizedand exactly incorporated n social choice pro-cedures (throughthe use of invariancecondi-tions in a generalized framework, formallyconstructedas social welfare functionals, onwhich see Sen, 1970a, 1977c).17 Indeed,inter-personal comparisons need not even be con-fined to all-or-none dichotomies. We may beable to makeinterpersonal omparisons o someextent, but not in every comparison, nor ofevery type, nor with tremendousexactness (seeSen, 1970a, c).

We may, for example, have no great diffi-

culty in accepting that EmperorNero's utilitygainfrom theburningof Rome was smaller hanthe sum-total of the utility loss of all the otherRomans who suffered from the fire. But thisdoes not requireus to feel confident hat we canput everyone's utilities in an exact one-to-onecorrespondence with each other. There may,thus,be room for demanding partial ompara-bility -denying both the extremes: full com-parability and no comparability at all. Thedifferentextentsof partialcomparability an begiven mathematically xact forms (precisely ar-

ticulatingthe exact extent of inexactness).18 Itcan also be shown that theremay be no generalneed for terriblyrefined nterpersonal omparisons for arriving at definite social decisions.Quite often,rather imitedlevels of partialcom-parabilitywill be adequatefor making socialdecisions.19Thus the empirical exercise neednot be as ambitiousas it is sometimes feared.

Before proceedingto the informationalbasisof interpersonal omparisons, et me ask a big

16 It should be explained that restrictingsocial choiceprocedures to voting rules is not an assumption that isinvoked by Arrow (1951, 1963); it is a part of the impos-

sibility theoremestablished by him. It is an analyticalcon-sequence of the set of apparently reasonable axiomspostulated or reasonedsocial choice. Interpersonal ompar-ison of utilities is, of course, explicitly excluded, but the

proofof Arrow's theoremshows that a set of otherassump-tions with considerable plausibility, taken together, logi-cally entail other features of voting rules as well (aremarkableanalytical result on its own). The derived fea-

turesinclude,in particular,he demandingrequirementhatno effective note be takenof the nature of the social states:only of the votes that are respectively cast in favorof-andagainst-them (a property that is often called neutrali-ty -a somewhat flatteringname for what is afterall onlyan informational estriction).While the eschewal of inter-personal comparisons of utilities eliminates the possibilityof takingnoteof inequalityof utilities (andof differences ngains and losses of utilities), the entailed component of

neutrality revents attentionbeing indirectly paid to dis-tributional ssues through aking explicit note of the natureof the respective social states (for example, of the incomeinequalities in the different states). The role of inducedinformational onstraints n generating mpossibilityresultsis discussed in Sen (1977c, 1979b).

17 See also Patrick Suppes (1966), Hammond (1976,1977, 1985), Stephen Strasnick (1976), Arrow (1977),d'Aspremont and Gevers (1977), Maskin (1978, 1979),Gevers (1979), Kevin W. S. Roberts(1980a, b), Suzumura(1983, 1997), CharlesBlackorbyet al. (1984), d'Aspremont(1985), and d'Aspremont and Philippe Mongin (1998),among other contributions.

18 See Sen (1970a, c), Blackorby (1975), Ben J. Fine(1975a), KaushikBasu (1980), T. Bezembinderand P. vanAcker (1980), and Levi (1986). The study of inexactnesscan also be extended to fuzzy characterizations.

19See also AnthonyB. Atkinson(1970), Sen (1970a, c,1973a), Dasguptaet al. (1973), and MichaelRothschildandJosephE. Stiglitz (1973).



VOL.89 NO. 3 SEN: THE POSSIBILITYOF SOCIALCHOICE 357

analytical question:how much of a change in

the possibilityof social choice is broughtabout

by systematic use of interpersonalcompari-sons? Does Arrow's impossibility, and related

results, go away with the use of interpersonalcomparisons n social welfare judgments?The

answerbriefly is, yes. The additional nforma-

tional availabilityallows sufficient discrimina-

tion to escape impossibilitiesof this type.There s an interestingcontrasthere. It can be

shown that admitting cardinality of utilities

without interpersonal comparisons does not

change Arrow's impossibility theorem at all,

which can be readilyextendedto cardinalmea-

surabilityof utilities (see Theorem 8*2 in Sen,

1970a). In contrasteven ordinal interpersonalcomparisons s adequate o break the exact im-

possibility. We knew of course that with some

types of interpersonalcomparisonsdemandedin a full form (includingcardinal nterpersonal

comparability),we can use the classicalutilitar-

ianapproach.20 ut it turnsout thateven weaker

forms of comparabilitywould still permitmak-

ing consistent social welfare judgments, satis-

fying all of Arrow's requirements,n addition o

being sensitive to distributional oncerns(even

thoughthe possible rules will be confined to a

relatively small class).21The distributionalssue is, in fact, intimately

connected with the need to go beyond voting

rules as the basis of social welfarejudgments.As was discussedearlier,utilitarianism oo is in

an importantsense distribution ndifferent: ts

program s to maximize the sum-totalof utili-

ties, no matterhow unequallythat total may bedistributed(the extensive implications of this

distributionalndifferencearediscussedin Sen,

1973a). But the use of interpersonalcompari-

sons can take other forms as well, allowing

public decisions to be sensitive to inequalitiesin well-being and opportunities.

The broad approachof social welfare func-

tionals opens up the possibility of using manydifferent types of social welfare rules, whichdiffer in the treatment of equity as well as

efficiency, and also in their informationalre-quirements.22 urther,with the removal of the

artificial barrier that had prohibited interper-sonal comparisons,many otherfields of norma-

tive measurementhave also been investigatedwith the axiomatic approachof social welfareanalysis. My own efforts in such fields as theevaluationand measurementof inequality Sen,1973a, 1992a, 1997b), poverty (Sen, 1976b,

1983b, 1985a, 1992a), distribution-adjustednational income (Sen, 1973b, 1976a, 1979a),and environmental evaluation (Sen, 1995a),have drawn solidly on the broadened infor-

mational framework of recent social choice

theory.23

VIII. InformationalBasis of Interpersonal

Comparisons

While the analytical issues in incorporatinginterpersonalcomparisons have been, on the

whole, well sorted out, there still remains theimportantpractical matter of finding an ade-

quate approachto the empirical discipline of

making interpersonal omparisonsand then us-ing them in practice.The foremost question tobe addressedis this: interpersonalcomparisonof what?

The formal structuresof social welfarefunc-tions are not, in any sense, specific to utilitycomparisons only, and they can incorporateother types of interpersonal comparisons aswell. The principal ssue is the choice of some

20On this, see particularlyJohn C. Harsanyi's (1955)

classic paper,which stood againstthe pessimistic literature

that followed Arrow's (1951) impossibility theorem. See

also JamesA. Mirrlees (1982).21 See Sen (1970a, 1977c), Rawls (1971), Edmund S.

Phelps (1973), Hammond(1976), Strasnick 1976), Arrow

(1977), d'Aspremont and Gevers (1977), Gevers (1979),

Roberts (1980a,b), Suzumura (1983, 1997), Blackorby

et al. (1984), and d'Aspremont 1985), among othercontri-

butions.

22 On this and relatedissues, see Sen (1970a, 1977c),

Hammond 1976), d'AspremontandGevers (1977), Robert

Deschamps and Gevers (1978), Maskin (1978, 1979),

Gevers (1979), Roberts (1980a), Siddiqur R. Osmani

(1982), Blackorby et al. (1984), d'Aspremont (1985), T.

Coulhon and Mongin (1989), Nick Baigent (1994), and

d'Aspremontand Mongin (1998), among many other con-

tributions.See also Harsanyi 1955) andSuppes (1966) forpioneeringanalyses of the uses of interpersonalcompari-

sons. Elster and John Roemer (1991) have provided fine

criticalaccountsof the vast literatureon this subject.23 My work on inequality(beginning with Sen, 1973a)

has been particularlynfluencedby the pioneeringcontribu-

tions of Atkinson(1970, 1983, 1989). The literatureon this

subjecthas grown very fast in recent years; for a critical

scrutinyas well as references o the contemporaryiterature,

see JamesFoster and Sen (1997).




accountingof individualadvantage,which neednot take the form of comparisons of mentalstatesof happiness, and could instead focus onsome other way of looking at individual well-

being or freedom or substantiveopportunities(seenin theperspectiveof a corresponding val-uative discipline).

Therejectionof interpersonal omparisonsofutilities in welfare economic and in socialchoice theory that followed positivist criticism(such as that of Robbins, 1938) was firmlybased on interpreting hem entirely as compar-isons of mental states. As it happens,even withsuch mental statecomparisons, he case for un-qualifiedrejectionis hardto sustain.24 ndeed,as has beenforcefully arguedby thephilosopher

Donald Davidson (1986), it is difficult to seehow people can understand anything muchabout otherpeople's minds and feelings, with-out making some comparisonswith their ownminds andfeelings. Such comparisonsmay notbe extremely precise, but then again, we knowfrom analytical nvestigationsthatvery preciseinterpersonal omparisonsmaynot be neededtomake systematic use of interpersonal ompari-sons in social choice (on this and related ssues,see Sen, 1970a, c, 1997b;Blackorby, 1975).

So thepicture s not so pessimisticeven in the

old home groundof mental state comparisons.But, more importantly, nterpersonalcompari-sons of personal welfare, or of individual ad-vantage,need notbe basedonly on comparisonsof mental states. In fact, there may be goodethical groundsfor not concentrating oo much

on mental-statecomparisons-whether of plea-sures or of desires.Utilities may sometimes bevery malleable in response to persistent depri-vation. A hopeless destitutewith much poverty,

or a downtrodden aborer iving under exploit-ative economic arrangements,or a subjugatedhousewife in a society with entrenchedgenderinequality,or a tyrannizedcitizen under brutalauthoritarianism,may come to terms with herdeprivation. She may take whatever pleasureshe can from smallachievements,and adjustherdesires to take note of feasibility (therebyhelp-ing the fulfilment of her adjusteddesires). Buther success in such adjustmentwould not makeherdeprivationgo away.The metricof pleasureor desiremay sometimes be quiteinadequate n

reflecting the extent of a person's substantivedeprivation.25

There may indeed be a case for taking in-comes, or commodity bundles, or resourcesmore generally,to be of direct interest n judg-ing a person's advantage,and thismay be so forvarious reasons-not merely for the mentalstates they may help to generate.26 n fact, theDifference Principle in Rawls's (1971) theoryof justice as fairness is based on judgingindividual advantage in terins of a person'scommand over what Rawls calls primary

goods, which are general-purposeresourcesthat are useful for anyone to have no matterwhather exact objectives are.

This procedure can be improved upon bytaking note not only of the ownership of pri-mary goods andresources,but also of interper-sonal differences in converting them into thecapability to live well. Indeed, I have tried toarguein favor of judging individualadvantagein termsof therespectivecapabilities,whichthe

24 If interpersonal omparisonsare takento be entirely amatterof opinions or of valuejudgments,then the questioncan also be raised as to how the divergent opinions orvaluations of differentpersons may be combined together

(thislooks like a social choice exercise on its own). Roberts(1995) has extensively investigatedthis particular ormula-tion, taking interpersonal omparison to be an exercise ofaggregationof opinions.If, however, interpersonal ompar-isons are taken to have a firmer factual basis (e.g., somepeople being objectivelymore miserablethan others),thenthe use of interpersonalomparisonswill call for a differentset of axiomatic demands-more appropriate or epistemol-ogy than for ethics. For contrastingperspectives on inter-personalcomparisonsof well-being, see Ian Little (1957),Sen (1970a, 1985b), Tibor Scitovsky (1976), Donald Da-vidson(1986), and Gibbard 1986); see also empiricalstud-ies of observed misery (for example, Dreze and Sen, 1989,1990, 1995, 1997; ErikSchokkaertand Luc Van Ootegem,1990; Robert M. Solow, 1995).

25 This issue and its far-reachingethical and economicimplicationsare discussed in Sen (1980, 1985a, b). See alsoBasu et al. (1995).

26 Thewelfare relevanceof realincomecomparisonscanbe dissociated from their mental-statecorrelates; see Sen(1979a). See also the related iterature n fairness, een interms of nonenvy; for example, Duncan Foley (1967),Serge-ChristopheKolm (1969), ElishaA. Paznerand DavidSchmeidler (1974), Hal R. Varian(1974, 1975), Lars-Gun-nar Svensson (1977, 1980), Ronald Dworkin(1981), Suzu-mura(1983), Young (1985), Campbell (1992), and Moulinand William Thomson (1997). Direct social judgments oninterpersonaldistributions ver commodities have been an-alyzed by FranklinM. Fisher(1956).




person has, to live the way he or she has reasonto value.27This approach ocuses on the sub-stantive freedoms thatpeople have, rather hanonly on the particular utconmes ith whichtheyend up. For responsible adults, the concentra-tion on freedom ratherthan only achievementhas some merit, and it can provide a generalframeworkfor analyzing individual advantageand deprivation n a contemporary ociety. Theextent of interpersonalcomparisons may onlybe partial-often based on the intersection ofdifferentpoints of view.28 But the use of suchpartial comparabilitycan make a majordiffer-ence to the informationalbasis of reasoned so-cial judgments.

However, given the natureof the subjectand

the practicaldifficulties of informationalavail-ability and evaluation, it would be overambi-tious to be severely exclusive in sticking only toone informational pproach, ejectingall others.In the recent literature n applied welfare eco-nomics, various ways of making sensible inter-personal comparisons of well-being haveemerged. Some have been based on studyingexpenditurepatterns,and using this to surmiseabout comparativewell-being of differentper-sons (see Pollak and Terence J. Wales, 1979;Dale W. Jorgenson et al., 1980; Jorgenson,

1990; Daniel T. Slesnick, 1998), while othershave combined this with other informationalinputs (see Angus S. Deaton and John Muell-bauer, 1980; Atkinson and Francois Bour-guignon, 1982, 1987; Fisher, 1987, 1990;

Pollak, 1991; Deaton, 1995).29 Others havetried to use questionnairesand have looked forregularities in people's answers to questionsabout relative well-being (see, for example,Arie Kapteyn and Bernard M. S. van Praag,1976).

There have also been illuminating works inobserving important features of living condi-tions and in drawingconclusions on quality oflife and comparativeliving standardson thatbasis; indeed there is a well-established tradi-tion of Scandinavianstudies in this area (see,for example, Allardt et al. [1981] and RobertErikson andRune Aberg [1987]). The literatureon basic needs and their fulfilmenthas alsoprovided an empiricalapproach o understand-

ing comparativedeprivations.30Further,underthe intellectual leadership of Mahbub ul Haq(1995), the United Nations Development Pro-gramme(UNDP) has made systematicuse of aparticular ype of informationalbroadeningtomake comparisonsbased on observed featuresof living conditions(reportedn UNDP, HumanDevelopmentReports).3

It is easy enough to pick holes in each ofthese methodologiesand to criticize the relatedmetrics of interpersonal omparisons.But therecan be little doubt about the welfare-economic

interest in the far-reaching uses of empiricalinformation that have emerged from theseworks. They have substantiallybroadened ourunderstanding of individual advantages andtheir empirical correlates. Each of these meth-odologies clearly has some limitations as wellas virtues, and our evaluation of their relativemeritsmay well diverge, dependingon ourre-spective priorities.I have had the occasion toargue elsewhere(and briefly also in this lecture,

27 See Sen (1980, 1985a, b, 1992a), Dr6ze and Sen(1989, 1995), and MarthaNussbaum and Sen (1993). See

also Roemer (1982, 1996),Basu (1987), Nussbaum(1988),RichardJ. Arneson (1989), Atkinson(1989, 1995), G. A.Cohen (1989, 1990), F. Bourguignonand G. Fields (1990),

Keith Griffin and John Knight (1990), David Crocker(1992), SudhirAnand andMartinRavallion (1993), Arrow(1995), Meghnad Desai (1995), and Pattanaik (1997),

among other contributions.There have also been severalimportant ymposia on the capability perspective, such asGiornaledegliEconomistie Annali di Economia (1994) andNotizie di Politeia (1996, Special Volume), including con-tributionsby AlessandroBalestrino(1994, 1996), GiovanniAndrea Cornia (1994), Elena Granaglia 1994, 1996), En-rica ChiapperoMartinetti 1994, 1996), SebastianoBavetta(1996), Ian Carter (1996), Leonardo Casini and lacopoBernetti (1996), and ShahrashoubRazavi (1996); see alsoSen (1994, 1996b) with my responses o these contributions.

28 On this, see Sen (1970a, c, 1985b, 1992a, 1999a, b).

29 See also Slesnick (1998).30 A good introduction o the basic needs approachcan

be found in Paul Streeten et al. (1981). See also IrmaAdelman(1975), DharamGhaiet al. (1977), JamesP. Grant(1978), Morris D. Morris (1979), Chichilnisky (1980),NanakKakwani 1981, 1984),Paul Streeten 1984), FrancesStewart(1985), Robert Goodin (1988), and Alan Hamlinand Phillip Pettit(1989), among othercontributions.Focus-ing on the fulfillmentof minimumneeds can be tracedtoPigou (1920).

31 See for example United Nations Development Pro-gramme 1990) and thesubsequentyearlyHumanDevelop-ment Reports. See also Sen (1973b, 1985a), Adelman(1975), Grant 1978), Morris (1979), Streetenet al. (1981),Desai (1995), andAnandand Sen (1997) on related ssues.




earlier on) in favor of partial comparabilitiesbased on evaluation of capabilities,32but be-yond that specific issue (on which others maywell take a differentview), I want to emphasize

here themore generalpointthatthepossibilitiesof practical welfare economics and socialchoice have been immensely widened throughthese innovative, empiricalworks.

In fact, despite their differences, they fit ingeneral into the overall pattern of informa-tional widening to which recent analyticalwork in social choice theory has forcefullypointed. The analytical systems explored inthe recent literatureon welfare economics andsocial choice are broader than those in theArrovian model (and correspondingly less

uptight, and less impossible, on which seeSen, 1970a, 1977c). They are also analyti-cally general enough to allow differentempirical interpretations and to permit alter-native informational bases for social choice.The diverse empirical methodologies, consid-ered here, can all be seen in this broaderanalytical perspective. The movements in

hightheory have been, in this sense, closelylinked to the advances in practicaleconom-ics. It is the sustained exploration of con-structive possibilities-at the analytical as

well as practical levels-that has helped todispel some of the gloom that was associatedearlier with social choice and welfareeconomics.

IX. Povertyand Famine

The variety of information on which socialwelfareanalysiscan drawcan be well illustratedby the study of poverty. Poverty is typicallyseen in termsof the lowness of incomes, andithas been traditionally measured simply by

countingthe number of people below the pov-erty-line income; this is sometimes called thehead-count measure. A scrutiny of this ap-proachyields two differenttypes of questions.First, s povertyadequately een as low income?

Second, even if poverty is seen as low income,is the aggregatepoverty of a society best char-acterized by the index of the head-countmeasure?

I take up these questions in turn. Do we getenough of a diagnosis of individualpoverty bycomparing the individual's income with a so-cially given poverty-line income? What aboutthe person with an income well above the pov-erty line, who suffersfrom an expensive illness(requiring, ay, kidney dialysis)? Is deprivationnot ultimately a lack of opportunity o lead aminimally acceptablelife, which can be influ-enced by a numberof considerations, ncludingof course personal income, but also physicaland environmental characteristics, and other

variables(such as the availability and costs ofmedical and other facilities)? The motivationbehind such anexercise relatesclosely to seeingpovertyas a seriousdeprivationof certainbasiccapabilities.This altemativeapproach eads to aratherdifferent diagnosis of poverty from theones that a purely income-based analysis canyield.34

This is not to deny that lowness of incomecan be very important n many contexts, sincethe opportunitiesa person enjoys in a marketeconomy can be severely constrained by her

level of real income. However, various con-tingencies can lead to variations in the con-version of income into the capability to livea minimally acceptable life, andif thatis whatwe are concerned with, there may be goodreason to look beyond income poverty. Thereare at least four different sources of variation:(1) personal heterogeneities (for example,proneness to illness), (2) environmental di-versities (for example, living in a storm-proneor flood-prone area), (3) variations in socialclimate (for example, the prevalence of crime

or epidemiological vectors), and (4) differ-ences in relative deprivation connected withcustomary patternsof consumption in partic-ular societies (for example, being relativelyimpoverished in a rich society, which can lead

32 See particularlySen (1992a).33 The literatureon implementation as also grown in

the directionof practicalapplication; or analysesof someof the different ssues involved, see Laffont(1979), Maskin(1985), Moulin (1995), Suzumura1995), Dutta(1997), andMaskin and Tomas Sjostrom(1999).

See Sen (1980, 1983b, 1985a, 1992a, 1993b, 1999a),Kakwani (1984), Nussbaum(1988), Dreze and Sen (1989,1995), Griffin and Knight (1990), IftekharHossain (1990),Schokkaertand Van Ootegem (1990), Nussbaumand Sen(1993), Anand and Sen (1997), andFosterand Sen (1997),amongothercontributions.




to deprivation of the absolute capabilitv totake part in the life of the community).3

There is, thus, an importantneed to go be-yond income informationn poverty analysis,in

particular o see poverty as capability depriva-tion. However (as was discussed earlier), thechoice of the informational base for povertyanalysiscannotreally be dissociatedfromprag-matic considerations,particularly nformationalavailability.It is unlikelythat theperspectiveofpoverty as income deprivation an be dispensedwith in the empirical iterature n poverty,evenwhen the limitations of thatperspectiveareen-tirely clear. Indeed, n many contexts the rough-and-ready way of using income informationmay provide the most immediate approachto

the study of severe deprivation.36For example, the causationof famines is of-

ten best seen in terms of a radicaldecline in thereal incomes of a section of the population,leading to starvationand death (on this see Sen,1976d, 198 ).37 The dynamics of income earn-ing and of purchasingpower may indeed be themost important omponent of a famine investi-gation. This approach,in which the study ofcausal influences on the determinationof therespective incomes of different groups plays acentral part, contrasts with an exclusive focus

on agricultural production and food supply,

which is often found in the literatureon thissubject.

The shift n informationalocus fromfood sup-ply to entitlementsinvolving ncomes as well as

supply,andtheresulting elativeprices)can makea radicaldifference, incefaminescan occurevenwithoutanymajordecline-possibly withoutanydecline at all-of food production r supply.38 If,

for example,the incomes of ruralwage laborers,or of serviceproviders,or of craftsmen ollapsethroughunemployment, r througha fall of realwages, or through decline n thedemand or therelevantservices or craft products, he affectedgroupsmayhaveto starve, venif the overall oodsupplyin the economy is undiminished. tarva-tion occurs when some people cannotestablish

entitlementover an adequate amount of food,through urchase r throughood production, ndthe overallsupplyof food is only one influenceamong manyin the deterninationof the entitle-ments of the respectivegroupsof people in theeconomy.Thus, an income-sensitive ntitlementapproach anprovidea betterexplanation f fam-ines than canbe obtained hroughan exclusivelyproduction-orientediew. It can alsoyield a moreeffectiveapproacho theremedyingof starvationand hunger (on this see particularlyDreze andSen, 1989).

The natureof the problem tends to identifytheparticular space on which the analysishasto concentrate. t remainstrue that n explainingthe exact patternsof famine deaths and suffer-ings, we can get additional understandingbysupplementing he income-basedanalysis withinformationon the conversion of incomes intonourishment, which will depend on variousother influences such as nmetabolicates, prone-ness to illness, body size, etc.39These issues are

35 On this see Sen (1992a) and Foster and Sen (1997).The last concern-that a relativedeprivationof income canlead to an absolute deprivationof a basic capability--wasfirst discussedby Adam Smith (1776). Adam Smith's claimthat necessarygoods (and correspondinglyminimum n-comes needed to avoid basic deprivation)must be defineddifferently for different societies also suggests a generalapproachof using a parametrically ariable poverty-lineincome. Such variationscan be used to reflect the disparateconditions of different persons (including, for example,

proneness to illness). On these issues, see Deaton andMuellbauer 1980, 1986), Jorgenson 1990), Pollak (1991),Deaton(1995), and Slesnick (1998), among other contribu-tions. Under certain conditions, the definitionof poverty ashaving an income below the parametricallydeterniined

povertyine will be congruentwith the characterization fpoverty as capability deprivation (if the parametricvaria-tions are firmly linked to the income needed to avoid spec-ified levels of capability deprivation).

36 These issues are insightfully scrutinizedby PhilippeVan Parijs(1995).

37 See also Mohiuddin Alamgir (1980), Ravallion(1987), Dreze and Sen (1989, 1990), Jeffrey L. Coles andHammond 1995), Desai (1995), Osmani (1995), and PeterSvedberg(1999), on relatedmatters.

38 As empiricalstudies of faminesbring out, some actualfamines have occurred with little or no decline in foodproduction such as the Bengal famine of 1943, the Ethio-pian famine of 1973, or the Bangladeshfamine of 1974),whereas others have been influenced substantiallyby de-clines in food production on this see Sen, 1981).

39 An important urther ssue is the distributionof foodwithin the family, which may be influenced by severalfactors other than family income. Issues of gender inequal-ity and the treatmentof childrenand of old people can beimportant n this context. Entitlement analysis can be ex-tended in these directions by going beyond the familyincome into the conventions and rules of intrafamilydivi-sion. On these issues, see Sen (1983b, 1984, 1990),




undoubtedly mportant or investigatingthe in-cidence of nutritional ailures, morbidities,andmortalities. However, in a general analysis of

the occurrenceand causationof famines, affect-

ing large groups, these additionalmatters maybe of secondary importance.While I shall notenter further nto the famine literaturehere, Iwould like to emphasizethat the informationaldemands of famine analysis give an importantplace to income deprivationwhich have moreimmediacy and ready usability than the moresubtle-and ultimately more informed-dis-tinctions based on capability comparisons (onthis see Sen [1981] and Dreze andSen [1989]).

I turn now to the second question. The mostcommon and most traditionalmeasure of pov-

erty had tended to concentrateon head count-ing. But it must also make a difference as tohowfar below the poverty line the poor indi-vidually are,andfurthermore, ow the depriva-tion is shared and distributedamong the poor.The social dataon therespectivedeprivations fthe individuals who constitute the poor in asociety need to be aggregated ogether o arriveat informativeandusable measuresof aggregatepoverty. This is a social choice problem, andaxioms can indeed be proposedthatattemptto

captureour distributional oncerns in this con-

structiveexercise (on this see Sen, 1976b).40Several distribution-sensitivepoverty mea-

sures have been derived axiomatically in therecent social choice literature,and various al-ternativeproposalshave been analyzed.WhileIshall, here, not go into a comparative assess-ment of these measures (nor into axiomaticre-quirements that can be used to discriminatebetween them), elsewhere I have tried to ad-dress this issue, jointly with James Foster(Fos-ter and Sen, 1997).4' However, I would like to

emphasize the fact that we face here an embar-rassment of riches (the opposite of an impasseor an impossibility),once the informationalba-sis of social judgments has been appropriately

broadened. To axiomatize exactly a particularpoverty measure,we shall have to indulgein thebrinkmanship f which I spoke earlier (Sec-

tion V), by adding other axiomatic demandsuntil we are just shortof an impossibility, withonly one surviving poverty measure.

X. ComparativeDeprivation ndGenderInequality

At one level, poverty cannot be dissociatedfrom the misery caused by it, and in this sense,

the classical perspective of utility also can beinvoked in this analysis. However, the mallea-bility of mental attitudes, on which I com-mented earlier,may tendto hide andmuffle theextent of deprivation n many cases. The indi-gent peasantwho managesto build some cheerin his life should not be taken as nonpoor ongroundsof his mental accomplishment.

This adaptabilitycan be particularly mpor-tant in dealing with gender inequalityand de-privation of women in traditionally unequalsocieties. This is partly because perceptions

have a decisive part to play in the cohesion offamily life, and the culture of family livingtends to put a premiumon makingallies out ofthe ill treated.Women may-often enough-work much harderthan men (thanksto the ri-gours of household chores), and also receiveless attentionin health care and nutrition,andyet the perceptionthat there is an incorrigible

Vaughan (1987), Dreze and Sen (1989), BarbaraHarriss(1990), Bina Agarwal (1994), Nancy Folbre(1995), Kanbur(1995), and Nussbaum and JonathanGlover (1995), among

other contributions.

40 The so-called Sen measure of poverty can, in fact,be improved by an importantbut simple variation llunmi-natingly proposed by AnthonyF. Shorrocks 1995). I haveto confess favoring the Sen-Shorrocksmeasure over theoriginal Sen index.

41 James Foster is a major contributor o the povertyliterature; see, for example, Foster (1984), Foster et al.(1984), and Foster and Shorrocks 1988). For discussionsof

some major ssues in the choice of an aggregativemeasure

of poverty, see also Anand (1977, 1983), Blackorby and

Donaldson (1978, 1980), Kanbur(1984), Atkinson (1987,1989), ChristianSeidl (1988), Satya R. Chakravarty1990),

Camilo Dagum and Michele Zenga (1990), Ravallion(1994), Frank A. Cowell (1995), and Shorrocks (1995),

among many others (thereis an extensive biblic -raphy ofthis large literature n Foster and Sen, 1997). One of theimportant ssues to be addressed s the need for-and lim-itations of- 4decomposability (and the weaker require-ment of subgroup consistency, on which see also

Shorrocks,1984). Foster (1984) gives argumentsn favor of

decomposability(as did Anand, 1977, 1983), whereasSen(1973a, 1977c) presents arguments against it. There is aserious attempt n Fosterand Sen (1997) to assess both thepros and the cons of decomposabilityand subgroupconsis-

tency.




inequalityhere may well be missingin a societyin which asymmetricnorms are quietly domi-

nant.42This type of inequalityand deprivationmay not, underthesecircumstances,adequately

surface in the scale of the mental metric ofdissatisfactionand discontent.The socially cultivatedsense of contentment

and serenitymay even affect the perceptionof

morbidityandillness. When,many yearsago, I

was workingon a famine-related tudyof post-famine Bengalin 1944,1 was quitestruckby theremarkable act that the widows surveyedhadhardly reportedany incidence of being in in-

different health, whereas widowers, com-

plained massively about just that (Sen, 1985a

AppendixB). Similarly, t emergesin interstate

comparisons in India that the states that areworst provided n educationand health-care a-

cilities typically reportthe lowest levels of per-

ceived morbidity, whereas states with goodhealthcare and school education ndicatehigherself-perceptionof illness (withthe highestmor-bidity reports coming from the best provided

states, such as Kerala).43Mental reactions, themainstayof classical utility, can be a very de-

fective basis for the analysis of deprivation.Thus, in understandingpovertyand inequal-

ity, there is a strong case for looking at real

deprivationand not merely at mental reactionsto that deprivation.There have been many re-cent investigations of gender inequality andwomen's deprivationn termsof undernutrition,clinically diagnosedmorbidity,observed illiter-

acy, and even unexpectedly high mortality

(comparedwithphysiologicallyjustifiedexpec-

tations).44Such interpersonal omparisonscan

easily be a significantbasis of studies of povertyand of inequality between the sexes. They canbe accommodatedwithin a broadframeworkofwelfare economics and social choice (enhanced

by the removal of informational onstraints hatwould rule out the use of these types of data).

XI. The LiberalParadox

This ecturehas includeddiscussionof why andhow impossibility esults n social choice can beovercome hroughnformational roadening.Theinformational ideningconsidered o farhas been

mainly concemed with the use of interpersonalcomparisons. ut thisneed not be the only formofbroadeninghat s needed n resolvinganimpasse

in social choice. Consider, or example,an impos-sibilitytheoremwhichis sometimesreferredo asthe iberalparadox, r the mpossibilityof the

Paretian iberal Sen, 1970a,b, 1976c). The the-orem shows the impossibility f satisfyingeven avery minimaldemand or libertywhen combinedwithan insistenceon Pareto fficiency (givenun-restricted omain).45

Since there have been some debates on thecontentof liberty n the recent iteraturesee, forexaunple,Nozick, 1974;PeterGardenfors, 981;RobertSugden, 1981, 1985, 1993; Hillel Steiner,

1990; Gaertneret al., 1992; Deb, 1994; MarcFleurbaeyand Gaertner,1996; Pattanaik,1996;Suzumura,1996), perhapsa quick explanatoryremarkmay be useful.Libertyhas manydifferentaspects, ncluding wo ratherdistinct eatures: 1)it can help us to achievewhatwe would choose toachieve in our respective privatedomains, forexaunple,n personal ife (thisis its opportunityaspect ), nd(2) it can leaveus directly n chargeof choices over privatedomains,no matterwhatwe may or may not achieve(this is its processaspect ). n social choice theory, he folrmulation

of libertyhas been primarily oncernedwith theformer, hatis, the opportunity spect.This mayhave been adequate o show thepossibleconflictbetween the Paretoprincipleandthe opportunityaspectof liberty (on which Sen [1970a, b] con-centrated), ut an exclusiveconcentration n the

42 On this see Sen (1984, 1990, 1993c),and the literature

cited there.43 The methodological ssue underlying his problem n-

volves positionalobjectivity -what is observationally b-

jective from a given positionbut may not be sustainable n

interpositional omparisons.This contrastand its far-reach-ing relevance is discussed in Sen (1993c).

The literatureon missing women (in comparison

with the expected number of women in the absence of

unusually high feminine mortalityrates found in some so-

cieties) is one example of such empiricalanalysis;on thissee Sen (1984, 1992c), Vaughan (1987), Dreze and Sen

(1989, 1990), Ansley J. Coale (1991), and StephanKlasen

(1994). See also Jocelyn Kynch and Sen (1983); Harriss

(1990); Ravi Kanburand LawrenceHaddad(1990); Agar-

wal (1994); Folbre (1995); Nussbaumand Glover (1995),

among other works.

45There is also some analytical nterest in the sourceof the impossibility result involved here, particularly ince

both Paretoefficiency and minimal iberty arecharac-terizedin terns of the same set of preferencesof the sameindividuals.On this see Sen (1976c, 1992b).




opportunityaspect cannot provide an adequateunderstanding f the demandsof liberty (in thisrespect,Sugden [1981, 1993] and Gaertner t al.[1992] werecertainly ight oreject he sufficiency

of the opportunity-centeredormulation n stan-dard social choice theory).46However, socialchoice theorycan also be made to accommodatethe process aspect of liberty throughappropriaterecharacterization,nd particularlyhroughvalu-ing dueprocess n addition o substantive ppor-tunities(on this see Sen, 1982b, 1997a, 1999b;Stig Kanger,1985; Deb, 1994; Hammond,1997;Suzumura, 996; Martinvan Hees, 1996).

Itis also importanto avoid heopposite arrow-nessofconcentratingxclusively nlyon theprocessaspectof liberty,as some recentwritershave pre-

ferredo do. Inportantsprocesses re, hiscannotobliterate he relevanceof the opportunity spectwhich too must count.Indeed, he importance f

effectivenessn the realization f liberty n one'spersonalifehasbeenrecognized s importantor along time-even by commentators eeply con-cernedwithprocesses,romJohnStuartMill(1859)to FrankKnight 1947),Friedrich . Hayek 1960),and Buchanan1986).The difficulties f having oweigh process airness gainst ffectiveness f out-comes cannotbe avoidedsimply by ignorng theopportuity aspectof liberty, hrough n exclusiveconcentrationn theprocessaspect.47

Howmight he conflictof the Paretianiberal,nparticular, e resolved?Differentways of dealingwith thisfrictionhave been explored n the litera-ture.48However, t is importanto see thatunlike

Arrow's impossibility result, theliberalparadoxcan-

not be satisfactorilyresolved througl the use of in-

terpersonalomparisons.ndeed,neitherhe claimsof liberty,nor thatof Paretoefficiency,need be

significantly ontingenton interpersonalompari-sons. The force of one's claims overone's privatedomain lies in thepersonal nature of that choice-

not on the relative intensities of the preferences of

different ersonsover a particularerson'sprivatelife. Also, Pareto fficiencydepends n the congru-ence of different ersons'preferences ver a pair-wise choice-not on the comparativetrength fthosepreferences.

Rather, the resolution of this problem lieselsewhere, in particularn the need to see eachof these claims as being qualifiedby the impor-tance of the other-once it is recognized thatthey can be in possible conflict with each other(indeed, the main point of the liberal paradoxwas precisely to identify thatpossible conflict).The recognitionof the importanceof effectiveliberty in one's private domain (precisely overparticular hoices) can coexist withan acknowl-edgementof the relevance of Paretianunanim-ity over any pair (over all choices-whether inone's private domain or not). A satisfactoryresolution of this impossibility must includetakingan evaluative view of the acceptablepri-orities between personal libertyandoverall de-sire fulfillment, and must be sensitive to theinformation egarding he trade-offson this thatthe persons may themselves endorse. This toocalls for an informationalenrichment (takingnote of people's political values as well as in-dividual desires), but this enrichmentis of arather different kind from that of using inter-personal comparisonsof well-being or overalladvantage.49

XII. A ConcludingRemark

Impossibility esults n social choice theory-led by the pioneeringwork of Arrow(1951)-have often been interpreted s being thoroughlydestructive f thepossibilityof reasoned nddem-ocratic ocialchoice, ncludingwelfareeconomics

46 The impossibility of the Paretian iberal does not,however, get resolved simply by concentratingon the pro-cess aspect of liberty,on which see FriedrichBreyer (1977),Breyer and Gardner (1980), Sen (1983b, 1992b), Basu(1984), Gaertner t al. (1992), Deb (1994), Binmore (1996),

Mueller (1996), Pattanaik 1996), and Suzumura 1996).47 On these issues, see Hammond(1997) and also Seidl

(1975, 1997), Breyer (1977), Kanger (1985), Levi (1986),CharlesK. Rowley (1993), Deb (1994), Suzumura 1996),and Pattanaik 1997).

48 See, for example,Seidl (1975, 1997), Suzumura1976b,1983, 1999), Gaertner nd LorenzKrliger 1981, 1983), Ham-mond(1982, 1997),JohnL. Wriglesworth1985), Levi (1986),andJonathan iley (1987),amongothers.See also the sympo-siumon the 'LiberlParadox nAnalyse& KritikSeptember1996), including:Binmore(1996), Breyer(1996), Buchanan(1996), Fleurbaey nd Gaertner1996), Anthonyde JasayandHartrnut liemt(1996), Kliemt(1996), Mueller 1996), Suzu-mura(1996), and van Hees (1996). My own suggestionsare

presentedn Sen (1983a,1992b,1996a).

4 This may, formally,requirea multistage social choiceexercisein the determination f thesepriorities, ollowed bythe use of those priorities n the choice over comprehensivesocial states (on these issues, see Pattanaik, 1971; Sen,

1982b, 1992b, 1996, 1997a; Suzumura,1996, 1999).




In general, informational broadening, in oneform or another,is an effective way of over-coming social choice pessimism and of avoid-ing impossibilities, and it leads directly

to constructive approaches with viability andreach. Formal reasoning about postulated axi-oms (including their compatibility and coher-ence), as well as informal understandingofvalues and norms (including heirrelevanceandplausibility),bothpoint in thatproductivedirec-tion.Indeed,the deep complementarity etweenformal and informal reasoning-so central tothe social sciences-is well illustratedby devel-opments in modem social choice theory.

REFERENCES

Adelman, Irma. DevelopmentEconomics-A Re-

assessment of Goals. American Economic Re-

view, May 1975 (Papersand Proceedings),65(2),

pp. 302-09.

Agarwal, Bina. A field of one's own: Gender and

land rights in SouthAsia. Cambridge:Cambridge

University Press, 1994.

Aizerman, Mark A. and Aleskerov, Fuad T. Vot-

ing Operatorsn the Space of Choice Functions.

MathematicalSocial Sciences, June 1986, 11(3),

pp. 201-42; Corrigendum,June 1988, 13(3), p.

305.Alamgir, Mohiuddin. Famine in South Asia. Bos-

ton: Oelgeschlager, Gunn& Hain, 1980.

Aleskerov, Fuad T. VotingModels in theArrovian

Framework, n Kenneth J. Arrow, Amartya K.

Sen, and Kotaro Suzumura, eds., Social choice

reexamined,Vol. 1.New York:St. Martin'sPress,

1997, pp. 47-67.

Aliardt, Erik; Andren, Nils; Friis, Erik J.; Gislason,

Gyffi I.; Nilson, Sten Sparre; Valen, Henry;

Wendt, Frantz and Wisti, Folmer, eds. Nordic

democracy: Ideas, issues, and institutions n pol-

itics, economy, education,social and culturalaf-fairs of Denmark,Finland, Iceland, Norway, and

Sweden. Copenhagen:Det Danske Selksab, 1981.

Anand, Sudhir. Aspectsof Poverty in Malaysia.

Review of Income and Wealth,March1977, 23(1),

pp. 1-16.

. Inequalityand poverty in Malaysia: Mea-

surement and decomposition.New York: Oxford


Anand, Sudhir and Ravallion, Martin. Human

Development in Poor Countries:On the Role of

Private Incomes and Public Services. Journalof

Economic Perspectives, Winter 1993, 7(1), pp.

133-50.

Anand, Sudhir and Sen, Amartya K. Concepts

of Human Development and Poverty: A Multi-

dimensional Perspective, n United Nations De-

velopment Programme, Poverty and human

development: Human developmentpapers 1997.

New York: United Nations, 1997, pp. 1-20.

Arneson, Richard J. Equalityand Equal Opportu-

nity for Welfare. Philosophical Studies, May

1989, 56(1), pp. 77-93.

Arrow, Kenneth J. A Difficulty in the Concept of

Social Welfare. Journal of Political Economy,

August 1950, 58(4), pp. 328-46.

_______ Social choice and individual values. New

York: Wiley, 1951.

_Le Principe de Rationalite dans les De-cisions Collectives. Economie Appliquee,

October-December 1952, 5(4), pp. 469-84.

. Social choice and individual values, 2nd

Ed. New York:Wiley, 1963.

'Extended Sympathy and the Possibility of

Social Choice. AmericanEconomicReview,Feb-

ruary 1977 (Papers and Proceedings), 67(1), pp.

219-25.

._ A Note on Freedom and Flexibility, in

Kaushik Basu, Prasanta K. Pattanaik, and Ko-

taro Suzumura, eds., Choice, welfare, and de-

velopment: A festschrift in honour of AmartyaK. Sen. Oxford: Oxford University Press, 1995,

pp. 7-16.

Arrow, Kenneth J.g Sen, Amartya K. and Suzu-

mura, Kotaro. Social choice re-examined,Vols. 1

and 2. New York:St. Martin's Press, 1997.

Atkinson, Anthony B. Onthe Measurementof In-

equality. Journal of Economic Theory, Septem-

ber 1970, 2(3), pp. 244-63.

_ Social justice and public policy. Cam-

bridge,MA: MIT Press, 1983.

.e On the Measurement of Poverty. Econo-

metrica, July 1987, 55(4), pp. 749-64._ Poverty and social security. New York:

Wheatsheaf, 1989.

. Capabilities, xclusion,and the Supplyof

Goods, n KaushikBasu,PrasantaK.Pattanaik,nd

Kotaro Suzumura, eds., Choice, welfare, and devel-

opment:Afestschrift n honourof AmartyaK. Sen.

Oxford:OxfordUniversityPress, 1995, pp. 17-31.

Atkinson, Anthony B. and Bourguignon, Francois.

The Comparisonof MultidimensionalDistribu-

tions of Economic Status. Review of Economic

Studies, April 1982, 49(2), pp. 183--201.




. Income Distribution and Differences in

Needs, in G. R. Feiwel, ed., Arrowand the oun-

dation of economic policy. London: Macmillan,

1987, pp. 350-70.

Baigent,Nick Norns,ChoiceandPreferences. iineo,

Institutef PublicEconomics,Universityf Graz,Aus-

tria,ResearchMemorandumo. 9306, 1994.

Balestrino, Alessandro. Povertyand Functionings:

Issues in Measurementand Public Action. Gior-

nale degli Economistie Annali di Economia,July-

September1994, 53(7-9), pp. 389-406.

. A Note on Functioning-Poverty in Afflu-

ent Societies. Notizie di Politeia, 1996, 12(43-

44), pp. 97-105.

Bandyopadhyay, Taradas. Rationality,PathInde-

pendence, and the Power Structure. ournal of

Economic Theory, December 1986, 40(2), pp.338-48.

Barbera',Salvador. PivotalVoters:A New Proofof

Arrow's Theorem. Economics Letters, 1980, 6,

pp. 13-16.

. Pivotal Voters: A Simple Proof of Ar-

row's Theorem, in PrasantaK. Pattanaikand

Maurice Salles, eds., Social choice and welfare.

Amsterdam:North-Holland,1983, pp. 31-35.

Barbera', Salvador and Sonnenschein, Hugo F.

PreferenceAggregationwith RandomizedSocial

Orderings. ournalof EconomicTheory,August

1978, 18(2), pp. 244-54.Barker, E. Thepolitics of Aristotle.London:Oxford


Basu, Kaushik. Revealedpreferenceof government.

Cambridge:CambridgeUniversity Press, 1980.

. ( The Right to Give Up Rights. Eco-

nomica, November 1984, 51(204), pp. 413-22.

. Achievements,Capabilitiesand the Con-

cept of Well-Being: A Review of Commodities

and Capabilitiesby AmarytaSen. Social Choice

and Welfare,March 1987, 4(1), pp. 69-76.

Basu, Kaushik; Pattanaik, Prasanta K. and Suzu-

mura, Kotaro, eds. Choice, welfare, and devel-opment:Afestschriftin honourofAmartyaK.Sen.

Oxford: OxfordUniversityPress, 1995.

Baumol, William. Welfareeconomics and thetheory

of the state, 2nd Ed. Cambridge,MA: Harvard

University Press, 1952, 1965.

Bavetta, Sebastiano. IndividualLiberty, Control

and the 'Freedomof Choice Literature'. Notizie

di Politeia, 1996, 12(43-44), pp. 23-29.

Bentham, Jeremy. An introduction o theprinciples

of morals and legislation. London: Payne, 1789;

republished,Oxford:ClarendonPress, 1907.

Bergson, Abram. A Reformulationof Certain As-

pects of Welfare Economics. QuarterlyJournal

of Economics, February1938, 52(1), pp. 310-34.

Bezembinder, T. and van Acker, P. Intransitivity

in Individualand GroupChoice, in E. D. Lanter-

mann and H. Feger, eds., Similarityand choice:

Essays in honor of Clyde Coombs. New York:

Wiley, 1980, pp. 208-33.

Binmore, Ken. An Examplein Group Preference.

Journal of Economic Theory, June 1975, 10(3),

pp. 377-85.

. Playing fair: Game theory and the social

contract, Vol. I. Cambridge, MA: MIT Press,

1994.

. Right or Seemly? Analyse & Kritik, Sep-

tember 1996, 18(1), pp. 67-80.

Black, Duncan. TheDecisions of a CommitteeUs-ing a Special Majority. Econometrica,July 1948,

16(3), pp. 245-61.

. The theory of committees and elections.

London:CambridgeUniversity Press, 1958.

Blackorby, Charles. Degrees of Cardinality and

Aggregate PartialOrderings. Econometrica,Sep-

tember-November1975, 43(5-6), pp. 845-52.

Blackorby, Charles and Donaldson, David. Mea-

sures of Relative Equality and Their Meaning in

Terms of Social Welfare. Journal of Economic

Theory,June 1978, 18(1), pp. 59-80.

. Ethical Indices for the Measurement ofPoverty. Econometrica, May 1980, 48(4), pp.

1053--60.

Blackorby, Charles; Donaldson, David and Wey-

mark, John A. Social Choice with Interpersonal

Utility Comparisons:A DiagrammaticIntroduc-

tion. InternationalEconomicReview,June 1984,

25(2), pp. 325-56.

Blair, Douglas H.; Bordes, Georges A.; Kelly,

Jerry S. and Suzumura, Kotaro. Impossibility

Theorems without Collective Rationality. Jour-

nal of Economic Theory,December 1976, 13(3),

pp. 361-79.Blair, Douglas H. and Pollak, Robert A. Collec-

tive RationalityandDictatorship:The Scope of the

Arrow Theorem. Journal of Economic Theory,

August 1979, 21(1), pp. 186-94.

.. Acyclic Collective Choice Rules. Econo-

metrica, July 1982, 50(4), pp. 931-44.

Blau, Julian H. The Existence of Social Welfare

Functions. Econometrica, April 1957, 25(2), pp.

302-13.

.. A Direct Proof of Arrow's Theorem.

Econometrica,January1972, 40(1), pp. 61-67.




_ Semiorders and Collective Choice. Jour-

nal of Economic Theory, August 1979, 21(1), pp.

195-206.

Blau, Julian H. and Deb, Rajat. Social Decision

Functions and Veto. Econometrica, May 1977,45(4), pp. 871-79.

Borda, J. C. Memoire sur les Elections au Scrutin.

Histoire de l'AcademieRoyale des Sciences (Par-

is), 1781. [Translated by Alfred de Grazia, Math-

ematical Derivation of an Election System. Isis,

June 1953, 44(1-2), pp. 42-51.]

Bordes, Georges A. Consistency, Rationality, and

Collective Choice. Review of Economic Studies,

October 1976, 43(3), pp. 447-57.

_ Some More Results on Consistency, Ra-

tionality and Collective Choice, in Jean-Jacques

Laffont, ed., Aggregation and revelation of pref-erences. Amsterdam: North-Holland, 1979, pp.

175-97.

Bourguignon, F. and Fields, G. Poverty Mea-

sures and Anti-poverty Policy. RWcherches

Economiques de Louvain, 1990, 56(3-4), pp.

409-27.

Brams, Steven J. Game theory and politics. New

York: Free Press, 1975.

Breyer, Friedrich. The Liberal Paradox, Decisive-

ness over Issues and Domain Restrictions.

Zeitschrift ur Nationalokonomie, 1977, 37(1-2),

pp. 45-60.

. Comment on the Papers by Buchanan and

by de Jasay and Kliemt. Analyse & Kritik, Sep-

tember 1996, 18(1), pp. 148-57.

Breyer, Friedrich and Gardner, Roy. Liberal Par-

adox, Game Equilibrium, and Gibbard Optimum.

1980, Public Choice, 35(4), pp. 469-81.

Brown, Donald J. An Approximate Solution to

Arrow's Problem. Journal of Economic Theory,

December 1974, 9(4), pp. 375-83.

v Acyclic Aggregation over a Finite Set of

Alternatives. Cowles Foundation Discussion Pa-

per No. 391, Yale University, 1975.

Buchanan, James M. Social Choice, Democracy,

and FreeMarkets. ournalof Political Economy,

April 1954a, 62(2), pp. 114-23.

______ Individual Choice in Voting and Market.

Journal of Political Economy, August 1954b,

62(3), pp. 334-43.

. Liberty,marketand state. Brighton,U.K.:

Wheatsheaf, 1986.

_ An Ambiguity in Sen's Alleged Proof of

the Impossibility of a Pareto Libertarian. Analyse

& Kritik, September 1996, 18(1), pp. 118-25.

Buchanan, James M. and Tullock, Gordon. The

calculus of consent.Ann Arbor,MI: University of

Michigan Press, 1962.

Campbell, Donald E. DemocraticPreferenceFunc-

tions. Journal of Economic Theory, April 1976,12(2), pp. 259-72.

D Equity, efficiency,and social choice. Ox-

ford: OxfordUniversity Press, 1992.

Campbell, Donald E. and Kelly, Jerry S. The

Possibility-Impossibility Boundary in Social

Choice, in Kenneth J. Arrow, Amartya K. Sen,

and Kotaro Suzumura,eds., Social choice re-ex--

amined, Vol. 1. New York: St. Martin's Press,

1997, pp. 179-204.

Caplin, Andrew and Nalebuff, Barry. On 64%-

MajorityRule. Econometrica, July 1988, 56(4),

pp. 787-814._ Aggregationand Social Choice: A Mean

Voter Theorem. Econometrica, January 1991,

59(1), pp. 1-24.

Carter, Ian. TheConceptof Freedom n the Work

of AmartyaSen: An AlternativeAnalysis Consis-

tent with Freedom's IndependentValue. Notizie

di Politeia, 1996, 12(43-44), pp. 7-22.

Casini, Leonardo and Bernetti, lacopo. Public

ProjectEvaluation,Environmentand Sen's Theo-

ry. Notizie di Politeia, 1996, 12(43-44), pp. 55-

78.

Chakravarty, Satya R. Ethical social index num-

bers. Berlin:Springer-Verlag,1990.

Chichilnisky, Graciela. Basic Needs and Global

Models. Alternatives, 1980, 6.

Topological Equivalence of the Pareto

Conditionand the Existence of a Dictator. Jour-

nal of MathematicalEconomics, March 1982a,

9(3), pp. 223-34.

- 'Social Aggregation Rules and Continu-

ity. QuarterlyJournalof Economics,May 1982b,

97(2), pp. 337-52.

Chichilnisky, Graciela and Heal, Geoffrey. Nec-

essaryandSufficientConditionsfor Resolution of

the Social Choice Paradox. Journalof Economic

Theory,October1983, 31(1), pp. 68-87.

Coale, Ansley J. Excess Female Mortalityand the

Balance of Sexes: An Estimateof the Number of

'MissingFemales' Populationand Development

Review, September 1991, 17(3), pp. 517-23.

Cohen, G. A. Onthe Currencyof EgalitarianJus-

tice. Ethics, July 1989, 99(4), pp. 906-44.

-_____ . '.Equality of What? On Welfare, Goods

and Capabilities. Recherches Economiques de

Louvain, 1990, 56(3-4), pp. 357-82.




Coles, Jeffrey L. and Hammond, Peter J. Walra-

sian EquilibriumwithoutSurvival:Existence,Ef-

ficiency, and Remedial Policy, in KaushikBasu,

PrasantaK. Pattanaik, nd KotaroSuzumura, ds.,Choice, welfare,and development:Afestschriftin

honour of Amartya K. Sen. Oxford:OxfordUni-

versity Press, 1995, pp. 32-64.

Condorcet, Marquis de. Essai sur l'application de

l'analyse a la probabilitedes decisions rendues a

la pluralite des voix. Paris:L'ImprimerieRoyale,

1785.

Cornia, Giovanni Andrea. Poverty n LatinAmer-

ica in the Eighties: Extent, Causes and Possible

Remedies. Giornaledegli Economistie Annali di

Economia, July-September 1994, 53(7-9), pp.

407-34.Coulhon, T. and Mongin, Philippe. SocialChoice

Theoryin the Case of von Neumann-Morgenstern

Utilities. Social Choice and Welfare,July 1989,

6(3), pp. 175-87.

Cowell, Frank A. Measuring inequality, 2nd Ed.

London:HarvesterWheatsheaf,1995.

Crocker, David. Functioningand Capability:The

Foundationsof Sen's and Nussbaum's Develop-

ment Ethic. Political Theory,November 1992,

20(4), pp. 584-612.

Dagum, Camilo and Zenga, Michele. Income and

wealthdistribution,nequalityand poverty.Berlin:Springer-Verlag,1990.

Dasgupta, Partha; Hammond, Peter J. and

Maskin, Eric S. Implementationof Social

Choice Rules. Reviewof EconomicStudies,April

1979, 46(2), pp. 181-216.

Dasgupta, Partha; Sen, Amartya K. and Starrett,

David. Noteson the Measurement f Inequality.

Journalof EconomicTheory,April 1973, 6(2), pp.

180-87.

d'Aspremont, Claude. Axiomsfor Social Welfare

Ordering, n Leonid Hurwicz,David Schmeidler,

and Hugo Sonnenschein, eds., Social goals and

social organization.Cambridge:CambridgeUni-


d'Aspremont, Claude and Gevers, Louis. Equity

and InformationalBasis of Collective Choice.

Reviewof EconomicStudies,June 1977, 44(2), pp.

199-209.

d'Aspremont, Claude and Mongin, Philippe. A

WelfaristVersionof Harsanyi'sAggregationThe-

orem. Center for Operations Research and

EconometricsDiscussionPaperNo. 9763, Univer-

site Catholiquede Louvain, 1997.

Davidson, Donald. Judging InterpersonalInter-

ests, in Jon Elster and Aanund Hylland, eds.,

Foundations of social choice theory. Cambridge:

CambridgeUniversity Press, 1986, pp. 195-211.

Davis, Otto A.; DeGroot, Morris H. and Hinich,Melvin J. Social PreferenceOrderingsand Ma-

jority Rule. Econometrica, January 1972, 40(1),

pp. 147-57.

Deaton, Angus S. Microeconometric analysis for

developmentpolicy: An approach rom household

surveys. Baltimore,MD: Johns Hopkins Univer-

sity Press (for the WorldBank), 1995.

Deaton, Angus S. and Muellbauer, John. Econom-

ics and consumer behaviour. Cambridge:Cam-

bridgeUniversity Press, 1980.

. On Measuring Child Costs: With Appli-

cations to Poor Countries. Journal of PoliticalEconomy, August 1986, 94(4), pp. 720-44.

Deb, Rajat. On Constructing GeneralizedVoting

Paradoxes. Review of Economic Studies, June

1976, 43(2), pp. 347-5 1.

On Schwartz's Rule. Journal of Eco-

nomic Theory,October1977, 16(1), pp. 103-10.

. Waiver, Effectivity and Rights as Game

Forms. Economica, May 1994, 16(242), pp. 167-

78.

de Jasay, Anthony and Kliemt, Hartmut. The

Paretian Liberal, His Liberties and His Con-

tracts. Analyse & Kritik, September 1996, 18(1),

pp. 126-47.

Denicolo, Vincenzo. Independent Social Choice

Correspondences Are Dictatorial. Economics

Letters, 1985, 19, pp. 9-12.

Desai, Meghnad. Poverty, amine and economic de-

velopment.Aldershot,U.K.: Elgar, 1995.

Deschamps, Robert and Gevers, Louis. Leximin

and UtilitarianRules: A Joint Characterization.

Journal of Economic Theory, April 1978, 17(2),

pp. 143-63.

Dodgson, C. L. (Carroll, Lewis). Facts, figures,and

fancies, relatingto the elections to the Hebdoma-

dal Council, the offer of the ClarendonTrustees,

and theproposal to convert theparks into cricket

grounds.Oxford:Parker,1874.

. The principles of parliamentary represen-

tation. London:Harrisonand Sons, 1884.

Dreze, Jean and Sen, Amartya. Hunger and public

action. Oxford: OxfordUniversity Press, 1989.

. Economic development and social oppor-

tunity.Delhi;New York: OxfordUniversity Press,

1995.

, eds. Political economy of hunger, Vols.

1-3. Oxford:OxfordUniversity Press, 1990.




_ Indian development: Selected regional per-

spectives. Delhi; New York: Oxford University

Press, 1997.

D'Souza, Frances, ed. Starvingin silence: A report

on famine and censorship.London: International

Centreon Censorship,1990.

Dutta, Bhaskar. On the Possibility of Consistent

Voting Procedures. Review of EconomicStudies,

April 1980, 47(3), pp. 603-16.

_ Reasonable Mechanisms and Nash Imple-

mentation, n KennethJ. Afrow, AmartyaK. Sen,

and Kotaro Suzumura, eds., Social choice re-

examined,Vol. 2. New York: St. Martin'sPress,

1997, pp. 3-23.

Dutta, Bhaskar and Pattanaik, Prasanta K. On

Nicely Consistent Voting Systems. Economet-

rica, January 1978, 46(1), pp. 163-70.

Dworkin, Ronald. What s Equality?Part 1: Equal-

ity of Welfare and WhatIs Equality?Part 2:

Equality of Resources. Philosophy and Public

Affairs,Fall 1981, 10(4), pp. 283-345.

Edgeworth, Francis T. Mathematicalpsychics: An

essay on the application of mathematicsto the

moral sciences. London: Kegan Paul, 1881.

Elster, Jon and Hylland, Aanund, eds. Foundations

of social choice theory. Cambridge:Cambridge


Elster, Jonand Roemer,

John,eds. Interpersonal

comparisons of well-being. Cambridge: Cam-

bridgeUniversity Press, 1991.

Erikson, Robert and Aberg, Rune. Welfare n tran-

sition: A survey of living conditions in Sweden,

1968-1981. Oxford: Oxford University Press,

1987.

Feldman, Alan M. Welfareeconomics and social

choice theory.Boston: MartinusNijhoff, 1980.

Ferejohn, John A. and Grether, David M. On a

Class of Rational Social Decision Procedures.

Journal of Economic Theory,August 1974, 8(4),

pp. 471-82.Fine, Ben J. A Note on 'InterpersonalAggregation

and PartialComparability'. Econometrica,Janu-

ary 1975a, 43(1), pp. 173-74.

. Individual Liberalism in a Paretian Soci-

ety. Journal of Political Economy, December

1975b, 83(6), pp. 1277-81.

Fishburn, Peter C. The theory of social choice.

Princeton, NJ: Princeton University Press,

1973.

' OnCollective Rationality and a General-

ized ImpossibilityTheorem. Reviewof Economic

Studies, October1974, 41(4), pp. 445-57.

Fisher, Franklin M. Income Distribution,Value

Judgments and Welfare. QuarterlyJournal of

Economics,August 1956, 70, pp. 380-424.

X Household Equivalence Scales and Inter-

personal Comparisons. Review of EconomicStudies,July 1987, 54(3), pp. 519-24.

_____ Household Equivalence Scales: Reply.

Review of Economic Studies, April 1990, 57(2),

pp. 329-30.

Fleurbaey, Marc and Gaertner, Wulf. Admissi-

bility and Feasibilityin Game Form. Analyse &

Kritik, September1996, 18(1), pp. 54-66.

Folbre, Nancy. Whopays for the kids: Gender and

the structureof constraint.New York, Routledge,

1995.

Foley, Duncan. ResourceAllocationand the Public

Sector. YaleEconomicEssays, Spring1967, 7(1),

pp. 73-76.

Foster, James. OnEconomic Poverty:A Survey of

AggregateMeasures. Advances in Econometrics,

1984, 3, pp. 215-51.

Foster, James; Greer, Joel and Thorbecke, Erik.

A Class of Decomposable Poverty Measures.

Econometrica,May 1984, 52(3), pp. 761-66.

Foster, James and Sen, Amartya K. OnEconomic

Inequality After a Quarter Century ;annexe in

Sen (1997c).

Foster, Jamnes nd Shorrocks,Anthony F. Poverty

Orderings. Econometrica,January1988, 56(1),

pp. 173-77.

Gaertner, Wulfo An Analysis and Comparisonof

Several Necessary and Sufficient Conditions for

Transitivity Under the Majority Decision Rule, in

Jean-JacquesLaffont, ed., Aggregation and reve-

lation of preferences.Amsterdam:North-Holland,

1979, pp. 91-112.

Equity- andInequity-typeBorda Rules.

MathematicalSocial Sciences, April 1983, 4(2),

pp. 137-54.

Domain Conditions in Social Choice The-ory. Mimeo, Universityof Osnabruck,Germany,

1998.

Gaertner, Wulf and Kruger, Lorenz. Self-Sup-

porting Preferences and Individual Rights: The

Possibility of a Paretian Libertarianism. Eco-

nomica, February1981, 48(189), pp. 17-28.

_ Alternative Libertarian Claims and Sen's

Paradox. Theory and Decision, 1983, 15, pp.

211-30.

Gaertner, Wulf; Pattanaik, Prasanta K. and Sum

zumura, Kotaro. IndividualRights Revisited.

Economica, May 1992, 59(234), pp. 161-78.




Gardenfors, Peter. Rights, Games and Social

Choice. Nous, September1981, 15(3), pp. 341-56.

Geanakopolous,John. 'Three BriefProofsof Arrow's

Impossibility heorem. Cowles FoundationDiscus-

sion PaperNo. 1128, Yale University,1996.Gehrlein, William V. Condorcet'sParadox. The-

ory and Decision, June 1983, 15(2), pp. 161-97.

Gevers, Louis. OnInterpersonalComparability nd

Social Welfare Orderings. Econometrica,Janu-

ary 1979, 47(1), pp. 75-89.

Ghai, Dharam; Khan, Azizur R.; Lee, E. and

Alfthan, T. A. The basic needs approach to de-

velopment.Geneva: InternationalLabour Organi-

zation, 1977.

Gibbard, Allan F. Manipulation of Voting

Schemes:A General Result. Econometrica,July

1973, 41(4), pp. 587-601.

. InterpersonalComparisons:Preference,

Good, andthe IntrinsicRewardof a Life, in Jon

Elster and Aanund Hylland, eds., Foundations of

social choice theory. Cambridge:CambridgeUni-


Goodin, Robert. Reasons for welfare. Princeton:

PrincetonUniversity Press, 1988.

Granaglia, Elena. Piu o Meno Equaglianzadi Ri-

sorse? Un Falso Problema per le Politiche So-

ciali. Giornale degli Economisti e Annali di


349-66.

. Two Questions to Amartya Sen. Notizie

di Politeia, 1996, 12(43-44), pp. 31-35.

Grandmont, Jean-Michel. Intermediate references

andtheMajorityRule. Econometrica,March1978,

46(2), pp. 317-30.

Grant, James P. Disparity reductionrates in social

indicators. Washington,DC: Overseas Develop-

ment Council, 1978.

Green, Jerry and Laffont, Jean-Jacques. Incen-

tives in public decision-making. Amersterdam,

North-Holland,1979.

Grether, David M. and Plott, Charles R. Nonbi-

nary Social Choice: An ImpossibilityTheorem.

Review of EconomicStudies,January1982, 49(1),

pp. 143-50.

Griffin, Keith and Knight, John, eds. Human de-

velopmentand internationaldevelopment trategy

for the 1990s. London:Macmillan,1990.

Groves, Ted and Ledyard, John. OptimalAlloca-

tion of Public Goods: A Solution to the 'Free

Rider' Problem. Econometrica,July 1977, 45(4),

pp. 783-809.

Guinier, Lani. Thetyrannyof the majority:Funda-

mentalfairness in representativedemocracy.New

York: Free Press, 1991.

Hamlin, Alan and Pettit, Phillip, eds. The good

polity: Normative analysis of the state. Oxford:

Blackwell, 1989.Hammond, Peter J. Equity,Arrow's Conditions,

and Rawls' Difference Principle. Econometrica,

July 1976, 44(4), pp. 793-804.

. Dual Interpersonal Comparisons of Utility

and the Welfare Economics of Income Distribu-

tion. Journal of Public Economics, February

1977, 7(1), pp. 51-71.

. Liberalism, ndependentRights, and the

Pareto Principle, in L. J. Cohen, J. Los, H.

Pfeiffer,and K.-P. Podewski, eds., Logic, method-

ology, and thephilosophy of science, Vol. 6. Am-

sterdam:North-Holland,1982, pp. 217-43.

. Welfare Economics, in George R. Fei-

wel, ed., Issues in contemporarymicroeconomics

and welfare. Albany: State University of New

York Press, 1985, pp. 405-34.

. Game Forms versus Social Choice Rules

as Models of Rights, in Kenneth J. Arrow,Am-

artyaK. Sen, and KotaroSuzumura,eds., Social

choice re-examined,Vol. 2. New York: St Mar-

tin's Press, 1997, pp. 82-95.

Hansson, Bengt. ChoiceStructuresand Preference

Relations. Synthese, October 1968, 18(4), pp.

443-58.

'Group references. Econometrica,Janu-

ary 1969a, 37(1), pp. 50-54.

. Voting and Group Decision Functions.

Synthese,December 1969b,20(4), pp. 526-37.

. 'The Existence of Group Preferences.

Public Choice, Winter1976, 28(28), pp. 89-98.

Haq, Mahbub uL Reflections on human develop-

ment. New York: Oxford University Press,

1995.

Harriss, Barbara. The IntrafaniilyDistributionof

Hunger n SouthAsia, n Jean Dreze andAmartyaSen, eds., Thepoliticaleconomyof hunger.Oxford:

OxfordUniversityPress,1990, pp. 351-424.

Harsanyi, John C. CardinalWelfare, Individualist

Ethics,andInterpersonalComparisonsof Utility.

Journal of PoliticalEconomty,August 1955, 63(3),

pp. 309-21.

Hayek, Friedrich A. The constitution of liberty.

London:Routledge, 1960.

Helier, Walter P.; Str, Ross M. and Starrett,

David A., eds. Social choice and public decision

making:Essays in honorof Kenneth . Arrow,Vol.

1. Cambridge:CambridgeUniversityPress, 1986.




Hossain, Iftekhar. Poverty as capability failure.

Helsinki: Swedish School of Economics, 1990.

Human Rights Watch. Indivisible human rights:

The relationshipbetweenpolitical and civil rights

to survival, subsistence, and poverty. New York:

Human Rights Watch, 1992.

Hurwicz, Leo; Schmeidler, David and Sonnens-

chein, Hugo, eds. Social goals and social organi-

zation. Cambridge:Cambridge University Press,

1985.

nada, Ken-ichi. The SimpleMajorityDecisionRule.

Economwtrica,uly 1969,37(3), pp. 490-506.

. MajorityRule and Rationality. Journal

of Economic Theory, March 1970, 2(1), pp. 27-

40.

Jorgenson, Dale W. AggregateConsumerBehaviorand the Measurementof Social Welfare. Econo-

metrica, September 1990, 58(5), pp. 1007-40.

Jorgenson, Dale W.; Lau, Lawrence and Stoker,

Thomas. Welfare Comparisonunder Exact Ag-

gregation. American Economic Review, May

1980 (Papers and Proceedings), 70(2), pp. 268-

72.

Kakwani, Nanak. Welfare Measures:An Interna-

tionalComparison. ournalof DevelopmentEco-

nomics, February1981, 8(1), pp. 21-45.

. Issues in Measuring Poverty. Advances

in Econometrics, 1984, 3, pp. 253-82.Kalai, Ehud and Muller, E. Characterization f

DomainsAdmittingNondictatorialSocial Welfare

Functions and Nonmanipulable Voting Rules.

Journal of Economic Theory, December 1977,

16(2), pp. 457-69.

Kanbur, Ravi. The Measurementand Decomposi-

tion of Inequalityand Poverty, n Frederickvan

der Ploeg, ed., Mathematicalmethods n econom-

ics. New York:Wiley, 1984, pp. 403-32.

. Children and Intra-Household Inequality:

A TheoreticalAnalysis, in KaushikBasu, Pras-

anta K. Pattanaik,and Kotaro Suzumura, eds.,Choice, welfare,and development:Afestschriftin

honour of AmartyaK Sen. Oxford: Oxford Uni-


Kanbur, Ravi and Haddad, Lawrence. How Se-

riousIs theNeglect of Intrahouseholdnequality?

EconomicJournal, September1990, 100(402), pp.

866-81.

Kanger, Stig. On Realizationof Human Rights.

Acta Philosophica Fennica, May 1985, 38, pp.

71-78.

Kapteyn, Arie and van Praag, Bernard M. S. A

New Approach to the Constructionof Family

Equivalent Scales. European EconomicReview,

May 1976, 7(4), pp. 313-35.

Kelly, Jerry S. Voting Anomalies, the Number of

Voters, and the Number of Alternatives. Econo-

metrica,March 1974a, 42(2), pp. 239-51.

. Necessity Conditionsin Voting Theory.

Journal of Economic Theory, June 1974b, 8(2),

pp. 149-60.

. Arrow impossibility theorems. New York:

Academic Press, 1978.

. Social choice theory: An introduction. Ber-

lin: Springer-Verlag,1987.

Kelsey, David. Acyclic Choice without the Pareto

Principle. Review of Economic Studies, October

1984a, 51(4), pp. 693-99.4

'The Structureof Social Decision Func-tions. Mathematical Social Sciences, December

1984b, 8(3), pp. 241-52.

Kirman, Alan P. and Sondermann, Dieter. Ar-

row's Theorem, Many Agents, and Invisible Dic-

tators. Journal of Economic Theory, October

1972, 5(2), pp. 267-77.

Klasen, Stephan. Missing Women Reconsidered.

WorldDevelopment, uly 1994, 22(7), pp. 1061-71.

Kliemt, Hartmut. Das Paradox des Liberalis-

mus-eine Einfiuhrung. Analyse & Kritik,Sep-

tember1996, 18(1), pp. 1-19.

Knight, Frank. Freedomand reform:Essays in eco-nomic and social philosophy. New York:Harper,

1947; republished, ndianapolis,N: Liberty,1982.

Kolm, Serge-Christophe. The Optimum Produc-

tion of Social Justice, in J. Margolis and H.

Guitton,eds., Public economics. New York: Mac-

millan, 1969, pp. 145-200.

Kynch, Jocelyn and Sen, Amartya K. Indian

Women: Well-Being and Survival. Cambridge

Journal of Economics, September-December

1983, 7(3-4), pp. 363-80.

Laffont, Jean-Jacques, ed. Aggregationand revela-

tion of preference. Amsterdam:North-Holland,1979.

Laffont, Jean-Jacques and Maskin, Eric. Tfhe

Theory of Incentives: An Overview, in Wermer

Hildenbrand,ed., Advances in economic theory.

Cambridge: Cambridge University Press, 1982,

pp. 31-94.

Le Breton, Michel and Weymark, John. AnIntro-

duction o ArrovianSocial WelfareFunctionsn the

Economic and Political Domains, in Norman

Schofield, ed., Collectivedecision-making:Social

choice and political economy. Boston: Kluwer,

1996.




Levi, Isaac. Hard choices. Cambridge:Cambridge

UniversityPress, 1986.

Levin, Jonathan and Nalebuff, Barry. An Intro-

duction to Vote-CountingSchemes. Journal of


3-26.

Little, Ian. A critique of welfareeconomics,2nd Ed.

Oxford: OxfordUniversity Press, 1957.

Majumdar, Tapas. A Note on Arrow's Postulates

for Social Welfare Function-A Comment. our-

nal of Political Economy,July/August1969, Pt. I,

77(4), pp. 528-31.

. Amartya Sen's Algebra of Collective

Choice. Sankhya, December 1973, Series B,

35(4), pp. 533-42.

Marshall, Alfred. Principles of economics.London:

Macmillan,1890; 9th Ed., 1961.

Martinetti, Enrica Chiappero. A New Approach

to Evaluationof Well-BeingandPovertyby Fuzzy

Set Theory. Giornaledegli Economistie Annali

di Economia, July-September1994, 53(7-9), pp.

367-88.

. Standard of Living Evaluation Based on

Sen's Approach: Some Methodological Sugges-

tions. Notizie di Politeia, 1996, 12(43-44), pp.

37-53.

Mas-Colell, Andreu and Sonnenschein, Hugo.

GeneralPossibility Theorems for Group Deci-sions. Review of Economic Studies, April 1972,

39(2), pp. 185-92.

Maskin, Eric S. Social Welfare Functions on Re-

stricted Domain. Mimeo, Harvard University,

1976a.

. On Strategyproofness and Social Welfare

Functions When Preferences Are Restricted.

Mimeo, DarwinCollege, and HarvardUniversity,

1976b.

. A Theorem on Utilitarianism. Review of

EconomicStudies, February1978, 45(1), pp. 93-

96.. Decision-Making Under Ignorance with

Implicationsfor Social Choice. Theory and De-

cision, September 1979, 11(3), pp. 319-37.

. The Theory of Implementation in Nash

Equilibrium: A Survey, in Leonid Hurwicz,

David Schmeidler, and Hugo Sonnenschein,eds.,

Social goals and social organization:Essays in

memoryof Elisha Pazner.Cambridge:Cambridge

UniversityPress, 1985, pp. 173-204.

. Majority Rule, Social Welfare Functions,

and Game Forms, n KaushikBasu, PrasantaK.

Pattanaik, and Kotaro Suzumura, eds., Choice,

welfare,and development:Afestschrift in honour

of Amartya K. Sen. Oxford: Oxford University

Press, 1995, pp. 100-09.

Maskin, Eric and Sjostrom, Tomas. Implementa-

tion Theory. Mimeo, HarvardUniversity, 1999.

Matsumoto, Yasumi. Non-binarySocial Choice:

Revealed PreferenceInterpretation. conomica,

May 1985, 52(26), pp. 185-94.

McKelvey, Richard D. General Conditions for

Global Intransitivities n FormalVoting Models.

Econometrica,September1979, 47(5), pp. 1085-

112.

McLeain,Ian. TheBorda andCondorcetPrinciples:

ThreeMedievalApplications. Social Choice and

Welfare,1990, 7(2), pp. 99-108.

Mill, JohnStuart. On

liberty.London:

Parker,1859;republished,London:Harmondsworth, 974.

Mirrlees,James A. 'The EconomicUses of Utilitari-

anism, n AmartyaK. Sen and BernardWilliams,

eds., Utilitarianism nd beyond. Cambridge:Cam-

bridgeUniversityPress,1982, pp. 63-84.

Monjardet, Bernard. Duality n the Theory of So-

cial Choice, in Jean-JacquesLaffont, ed., Aggre-

gation and revelation of preferences. Amsterdam:

North-Holland,1979, pp. 131-43.

On the Use of Ultrafilters in Social Choice

Theory, in Prasanta K. Pattanaik and Maurice

Salles, eds., Social choice and welfare. Amster-dam:North-Holland,1983.

Morris, Morris D. Measuring the conditions of the

world'spoor. Oxford:PergamonPress, 1979.

Moulin, Herve. The strategy of social choice. Am-

sterdam:North-Holland,1983.

. Cooperative microeconomics. Princeton,

NJ: PrincetonUniversityPress, 1995.

Moulin, Herve'and Thomson, William. Axiomatic

Analysesof ResourceAllocationProblems, n Ken-

nethJ. Arrow, AmartyaK. Sen, and KotaroSuzu-

mura,eds., Social choice re-examined,Vol. 1. New

York:St. Martin'sPress,1997, pp. 101-20.Mueller, Dennis C. Public Choice II. Cambridge:

CambridgeUniversityPress, 1989.

. Constitutional and Liberal Rights. Ana-

lyse &Kritik,September1996, 18(1), pp. 96-117.

Nehring, Klaus and Puppe, Clemens. Onthe Mul-

tipreferenceApproach to Evaluating Opportuni-

ties. Social Choice and Welfare,1999, 16(1), pp.

41-64.

Nicholson, Michael B. Conditions or the 'Voting

Paradox' in Committee Decisions. Metroeco-

nomica, January-August1965, 17(1-2), pp. 29-

44.




Nozick, Robert. Anarchy, state and utopia. New

York: Basic Books, 1974.

Nussbaum, Martha. Nature,Function, and Capa-

bility: Aristotle on Political Distribution. Oxford

Studies in Ancient Philosophy, 1988, Supp., pp.

145-84.

Nussbaum, Martha and Glover, Jonathan, eds.

Women, ulture,anddevelopment: studyof human

capabilities.Oxford:ClarendonPress, 1995.

Nussbaum, Martha and Sen, Amartya K., eds. The

quality of life. Oxford: Oxford University Press,

1993.

Osmani, Siddiqur R. Economic inequality and

group welfare. Oxford: Oxford UniversityPress,

1982.

. Tlhe Entitlement Approach to Famine: An

Assessment, in Kaushik Basu, PrasantaK. Pat-

tanaik,and KotaroSuzumura,eds., Choice, wel-

fare, and development:A festschrift in honourof

AmartyaK.Sen. Oxford:OxfordUniversityPress,

1995, pp. 253-94.

Parks, Robert P. FurtherResults on Path Indepen-

dence,Quasitransitivity, ndSocial Choice. Pub-

lic Choice, Summer1976a, 26(26), pp. 75-87.

_ An Impossibility Theorem for Fixed Pref-

erences: A DictatorialBergson-SamuelsonWel-

fare Function. Review of Economic Studies,

October 1976b,43(3), pp. 447-50.Pattanaik, Prasanta K. Voting and collective

choice. London: Cambridge University Press,

1971.

_ . On the Stability of Sincere Voting Situa-

tions. Journal of Economic Theory, December

1973, 6(6), pp. 558-74.

. Strategy and group choice. Amsterdam:

North-Holland,1978.

. ' The Liberal Paradox: Some Interpreta-

tions When Rights Are Represented as Game

Forms. Analyse& Kritik,September1996, 18(1),

pp. 38-53.. On Modelling Individual Rights: Some

Conceptual ssues, n KennethJ.Arrow,Amartya

K. Sen, and KotaroSuzumura, ds., Social choice

re-examined, Vol. 2. New York: St. Martin's

Press, 1997, pp. 100-28.

Pattanaik, Prasanta K. and Salles, Maurice, eds.

Social choice and welfare. Amsterdam: North-

Holland, 1983.

Pattanaik, Prasanta K. and Sengupta, Manimay.

Conditionsfor Transitive and Quasi-Transitive

Majority Decisions. Economica, November

1974, 41(164), pp. 414-23.

e Restricted Preferences and Strategy-

Proofness of a Class of Group Decision Func-

tions. Review of Economic Studies, October

1980, 47(5), pp. 965-73.

Pazner, Elisha A. and Schmeidler, David. A Dif-

ficulty in the Concept of Fairness. Review of

Economic Studies, July 1974, 41(3), pp. 441-43.

Peleg, Bezalel. ConsistentVoting Systems. Econo-

metrica, January1978, 46(1), pp. 153-62.

. Game theoretic analysis of voting in com-

mittees. Cambridge:CambridgeUniversity Press,

1984.

Phelps, Edmund S., ed. Economic justice. Har-

mondsworth,U.K.: Penguin, 1973.

Pigou, Arthur C. The economics of welfare. Lon-

don: Macmillan,1920.

Plott, CharlesR. A Notionof EquilibriumndIts Pos-

sibilityunderMajorityRule. Amenican conomicRe-

view,September 967,57(4), pp. 787-806.

. Path Independence, Rationality, and So-

cial Choice. Econometrica, November 1973,

4](6), pp. 1075-91.

l Axiomatic Social Choice Theory: An

Overview and Interpretation. mericanJournal

of Political Science, August 1976, 20(3), pp. 51 1-

96.

Pollak, Robert A. WelfareComparisonsand Situ-

ationComparison. ournalof Econometrics,Oc-tober-November1991, 50(1-2), pp. 31-48.

Pollak, Robert and Wales, Terence J. Welfare

Comparisonsand EquivalenceScales. American

Economic Review, May 1979 (Papers and Pro-

ceedings), 69(2), pp. 216-21.

Rae, Douglas W. Using District Magnitude to

Regulate Political Party Competition. Journal

of Economic Perspectives, Winter 1995, 9(1),

pp. 65-75.

Rangarajan, L. N., ed. TheArthasastra.New Delhi,

India:Penguin Books, 1987.

Ravallion, Martin. Markets and famines. Oxford:OxfordUniversity Press, 1987.

______*. Poverty comparisons. Chur, Switzerland:

Harwood, 1994._ Household Vulnerability to Aggregate

Shocks: Differing Fortunes of the Poor in Bang-

ladesh and Indonesia, n KaushikBasu, Prasanta

K. Pattanaik,and KotaroSuzumura,eds., Choice,

welfare,and development:Afestschrift in honour

of Amartya K. Sen. Oxford: Oxford University

Press, 1995, pp. 295-312.

Rawls, John. A theory of justice. Cambridge,MA:

HarvardUniversity Press, 1971.




Razavi, Shahrashoub. Excess Female Mortality:

An Indicator of Female Subordination?A Note

Drawing on Village-Level Evidence from South-

eastern Iran. Notizie di Politeia, 1996, 12(43-44), pp. 79-95.

Red Cross and Red Crescent Societies, Interna-

tional Federation of. World disasters report

1994. Dordrecht:MartinusNijhoff, 1994.

Riley, Jonathan. Liberal utilitarianism: Social

choice theory and J. S. Mill's philosophy. Cam-

bridge:CambridgeUniversity Press, 1987.

Robbins, Lionel. InterpersonalComparisons of

Utility:A Comment. EconomicJournal,Decem-

ber 1938, 48(192), pp. 635-41.

Roberts, Kevin W. S. PossibilityTheorems with

InterpersonallyComparableWelfareLevels. Re-view of EconomicStudies, January1980a, 47(2),

pp. 409-20.

. Interpersonal Comparability and Social

ChoiceTheory. Reviewof EconomicStudies,Jan-

uary 1980b, 47(2), pp. 421-39.

. Valued Opinions or Opiniated Values:

The Double Aggregation Problem, in Kaushik

Basu, PrasantaK. Pattanaik,and Kotaro Suzu-

mura, eds., Choice, welfare, and development:A

festschrift in honour of AmartyaK. Sen. Oxford:

OxfordUniversity Press, 1995, pp. 141-67.

Roemer, John. A general theory of exploitationandclass. Cambridge,MA: HarvardUniversity Press,

1982.

. Theories of distributive justice. Cambridge,

MA: HarvardUniversity Press, 1996.

Rothschild, Michael and Stiglitz, Joseph E. Some

FurtherResultson theMeasurementf Inequality.

Journalof EconomicTheory,April 1973, 6(2), pp.

188-204.

Rowley, Charles K. Libertyand thestate.Aldershot,

U.K.: Elgar, 1993.

Salles, Maurice. A GeneralPossibilityTheorem or

Group Decision Rules with Pareto-Transitivity.Journalof EconomicTheory,August 1975, 11(1),

pp. 110-18.

Samuelson, Paul A. Foundationsof economicanal-

ysis. Cambridge,MA: HarvardUniversity Press,

1947.

Satterthwaite, Mark A. Strategy-Proofnessand

Arrow's Conditions: Existence and Correspon-

dence Theorems or Voting ProceduresandSocial

WelfareFunctions. Journalof Economic Theory,

April 1975, 10(2), pp. 187-217.

Schmeidler, David and Sonnenschein, Hugo F.

Two Proofs of the Gibbard-Satterthwaite heo-

rem on the Possibility of a Strategy-ProofSocial

Choice Function, in H. W. Gottinger and W.

Leinfeller,eds., Decision theoryand social ethics:

Issues in social choice. Dordrecht:Reidel, 1978,pp. 227-34.

Schofield, Norman J. General nstabilityof Major-

ity Rule. Review of Economic Studies, October

1983, 50(4), pp. 695-705.

, ed. Collective decision-making: Social

choice and political economy. Boston: Kluwer,

1996.

Schokkaert, Erik and Van Ootegem, Luc. Sen's

Concept of the Living StandardApplied to the

Belgian Unemployed. Re'cherchesEconomiques

de Louvain, 1990, 56(3-4), pp. 429-50.

Schwartz, Thomas. Onthe Possibility of RationalPolicy Evaluation. Theoryand Decision, October

1970, 1(1), pp. 89-106.

. Rationalityand the Myth of the Maxi-

mum. Nous, May 1972, 6(2), pp. 97-117.

. The logic of collective choice. New York:

ColumbiaUniversityPress, 1986.

Scitovsky, Tibor. The oyless economy.Oxford:Ox-

ford UniversityPress, 1976.

Seidl, Christian. OnLiberalValues. Zeitschriftfpura-

tionalWkonomie,ay 1975,35(3--4),pp. 257-92.

. PovertyMeasurement:A Survey, n Di-

eterBos, ManfredRose, andChristianSeidl, eds.,Welfareand efficiencyin public economics. Ber-

lin: Springer-Verlag,1988, pp. 71-147.

. Foundations nd Implicationsof Rights,

in KennethJ. Arrow,AmartyaK. Sen, and Kotaro

Suzumura,eds., Social choice re-examined,Vol.

2. New York:St. Martin'sPress, 1997, pp. 53-77.

Sen, Amartya K. Preferences,Votes and the Tran-

sitivity of Majority Decisions. Review of Eco-

nomic Studies,April 1964, 31(2), pp. 163-65.

. A Possibility Theorem on MajorityDeci-

sions. Econometrica,April 1966, 34(2), pp. 491-

09.

. Quasi-Transitivity,Rational Choice and

Collective Decisions. Reviewof Economic Stud-

ies, July 1969, 36(3), pp. 381-93.

. Collective choice and social welfare. San

Francisco,CA: Holden-Day, 1970a.

. The Impossibility of a Paretian Liber-

al. Journal of Political Economy,January-Feb-

ruary1970b, 78(1), pp. 152-57; reprinted n Sen

(1982a).

. InterpersonalAggregation and Partial

Comparability. conometrica,May 1970c,38(3),

pp. 393-409; reprinted n Sen (1982a).




. On economic inequality. Oxford: Oxford

UniversityPress, 1973a; ExpandedEd., 1997c.

. On the Development of Basic Income

Indicators to Supplement the GNP Measure.

UnitedNations EconomicBulletin or Asia and the

Far East, September-December1973b, 24(2-3),

pp. 1-11.

. Behaviour and the Concept of Prefer-

ence. Economica, 1973c, 40(159), pp. 241-59;

reprinted n Sen (1982a).

. Choice, Orderings, and Morality, in S.

Korner,ed., Practical reason. Oxford:Blackwell,

1974; reprinted n Sen (1982a).

. Real National Income. Review of Eco-

nomic Studies,February1976a, 43(1), pp. 19-39;

reprinted n Sen (1982a).

. Poverty: An Ordinal Approach to Mea-

surement. Econometrica, March 1976b, 44(2),

pp. 219-23; reprinted n Sen (1982a).

. Liberty, Unanimity and Rights. Eco-

nomica, August 1976c, 43(171), pp. 217-45; re-

printed n Sen (1982a).

__ Social Choice Theory: A Re-examina-

tion. Econometrica, January 1977a, 45(1), pp.

53-89; reprinted n Sen (1982a).

. Starvation and Exchange Entitlements: A

GeneralApproachandIts Application o the Great

Bengal Famine. CambridgeJournal of Econom-ics, March 1977b, 1(1), pp. 33-59.

. On Weights and Measures: Informational

Constraints n Social Welfare Analysis. Econo-

metrica, October 1977c, 45(7), pp. 1539-72; re-

printed n Sen (1982a).

. Rational Fools: A Critique of the Behav-

ioralFoundationsof EconomicTheory. Philoso-

phy and Public Affairs,Summer1977d, 6(4), pp.


. The Welfare Basis of Real Income Com-

parisons:A Survey. Journal of Economic Liter-

ature,March1979a, 17(1), pp. 1-45; reprintednSen (1984).

. Personal Utilities and Public Judgements:

Or What's WrongwithWelfareEconomics. Eco-

nomic Journal, September 1979b, 89(355), pp.


. Equality of What? in S. McMurrin, ed.,

Tanner lectures on human values, Vol. 1. Salt

Lake City, UT: University of Utah, 1980, pp.


. Poverty and famines: An essay on entitle-

ment and deprivation.Oxford: OxfordUniversity

Press, 1981.

nhoice, welfare and measurement. Oxford:

Blackwell, 1982a;Cambridge,MA: HarvardUni-

versity Press, 1997.

______ * Rights and Agency. Philosophy and

Public Affairs,Spring 1982b, 11(2), pp. 113-32.

. Liberty and Social Choice. Journal of

Philosophy,January1983a, 80(1), pp. 5-28.

. Poor, Relatively Speaking. Oxford Eco-

nomic Papers, July 1983b, 35(2), pp. 153-69.

. Resources, values and development. Cam-

bridge,MA: HarvardUniversityPress, 1984.

_ Commodities and capabilities. Amster-

dam:North-Holland,1985a.

Well-being,Agency and Freedom:The

Dewey Lectures 1984. Journal of Philosophy,

April 1985b, 82(4), pp. 169-221.

. Social Choice Theory, in Kenneth J.

Arrow andMichaelIntriligator, ds., Handbookof

mathematical economics, Vol. III. Amsterdam:

North-Holland,1986a, pp. 1073-181.

. Information and Invariance in Normative

Choice, in WalterP. Heller, Ross M. Starr,and

DavidA. Starrett, ds.,Essays in honorof Kenneth

J. Arrow,Vol. 1. Cambridge:CambridgeUniver-

sity Press, 1986b, pp. 29-55.

e Gender and Cooperative Conflict, in

Irene Tinker, ed., Persistent inequalities. New

York: Oxford UniversityPress, 1990, pp. 123-49.e Inequality reexamined. Cambridge,MA:

HarvardUniversityPress, 1992a.

e* Minimal Liberty. Economica, May

1992b, 59(234), pp. 139-60.

. Missing Women. British Medical Jour-

nal, March1992c, 304(6827), pp. 587-88.

. IntemalConsistency of Choice. Economet-

rica,May 1993a,61(3),pp.495-521.

. Capability and Well-being, in Martha

Nussbaumand AmartyaSen, eds., The quality of

life. Oxford:Oxford UniversityPress, 1993b, pp.

30-53.. Positional Objectivity. Philosophy and

Public Affairs,Spring 1993c, 22(2), pp. 83-135.

e Well-Being, Capability and Public

Policy, Giornale degli Economisti e Annali di


333-47.

. Rationality and Social Choice. American

Economic Review,March1995a, 85(1), pp. 1-24.

_____.6 Environmental Evaluation and Social

Choice: Contingent Valuation and the Market

Analogy. Japanese Economic Review, March

1995b, 46(1), pp. 23-37.




. Rights: Formulation and Consequences.

Analyse & Kritik, September1996a, 18, pp. 53-

70.

. Freedom, Capabilities and Public Action:

A Response. Notizie di Politeia, 1996b, 12(43-

44), pp. 105-25.

.6 Maximizationand the Act of Choice.

Econometrica,July 1997a, 65(4), pp. 745-80.

_______*. Individual Preference as the Basis of So-

cial Choice, in Kenneth J. Arrow, Amartya K.



Press, 1997b.

. On economic inequality [Expanded Ed.,

with a substantialannexejointly with James Fos-

ter]. Oxford: OxfordUniversity Press, 1997c.

. Development as freedom [mimeo]; 1999a

(forthcoming).

. Freedom, rationality and social choice:

Arrow lectures and other essays [mimeo]; 1999b

(forthcoming).

Sen, Amartya K. and Pattanaik, Prasanta K.

Necessaryand Sufficient Conditionsfor Rational

Choice underMajorityDecision. Journal of Eco-

nomic Theory,August 1969, 1(2), pp. 178-202.

Sengupta, Manimay. Monotonicity,ndependencef

Irrelevant lternatives ndStrategy-Proofnessf So-

cialDecision Functions. Reviewof EconomicStud-ies, January1980a, 47(2), pp. 393-407.

. The Knowledge Assumption in the The-

ory of Strategic Voting. Econometrica, July

1980b, 48(5), pp. 1301-04.

Shorrocks, Anthony F. InequalityDecomposition

by Population Subgroups. Econometrica, No-

vember 1984, 52(6), pp. 1369-85.

. Revisiting the Sen Poverty Index. Econo-

metrica,September1995, 63(5), pp. 1225-30.

Slesnick, Daniel T. EmpiricalApproachesto the

Measurementof Welfare. Journal of Economic

Literature,December 1998, 36(4), pp. 2108-65.Smith, Adam. An inquiry nto the wealth of nations.

London: W. Strahanand T. Cadell, 1776; repub-

lished, London: Home University, 1910.

Solow, Robert M. MassUnemploymentas a Social

Problem, n KaushikBasu,PrasantaK. Pattanaik,

and KotaroSuzumura,eds., Choice, welfare, and

development:A festschrift in honour of Amartya

K. Sen. Oxford: Oxford University Press, 1995,

pp. 313-21.

Starrett, David. Foundations of public economics.


Steiner, Hillel. PuttingRights in Their Place: An

Appraisalof A. Sen's Work on Rights. Re'cher-

ches Economiquesde Louvain,1990, 56(3-4), pp.

391-408.

Stewart, Frances. Planning to meet basic needs.

London: Macmillan, 1985.

Strasnick, Stephen. Social Choice and the Deriva-

tion of Rawls's Difference Principle. Journal of

Philosophy, February1976, 73(4), pp. 85-99.

Streeten, Paul. Basic Needs: Some UnsettledQues-

tions. World Development, September 1984,

12(9), pp. 973-78.

Streeten, Paul (with Burki, S. J.; Haq, Mahbub

ul; Hicks, Norman and Stewart, Frances).

First things first: Meeting basic needs in devel-

oping countries. London: Oxford University

Press, 1981.

Sugden, Robert. The political economy of public

choice. New York:Wiley, 1981.

_. Liberty, Preference, and Choice. Econom-

ics andPhilosophy,October1985,1(2), pp. 213-29.

. Welfare, Resources, and Capabilities: A

Review of Inequality Reexamined by Amartya

Sen. Journal of EconomicLiterature,L)ecember

1993, 31(4), pp. 1947-62.

Suppes, Patrick. SomeFormalModels of Grading

Principles. Synthese, December 1966, 16(3/4),

pp. 284-306.

Suzumura, Kotaro. RationalChoice and RevealedPreference. Review of Economic Studies, Febru-

ary 1976a, 43(1), pp. 149-58.

. Remarks on the Theory of Collective

Choice. Economica, November 1976b, 43(172),

pp. 381-90.

_. Rational choice, collective decisions, and

social welfare. Cambridge:CambridgeUniversity

Press, 1983.

. Competition, commitment, and welfare.

Oxford: Oxford University Press, 1995.

_. Welfare, Rights, and Social Choice Pro-

cedure:A Perspective. Analyse &Kritik,Septem-ber 1996, 18(1), pp. 20-37.

. InterpersonalComparisons of the Ex-

tendedSympathyType and the Possibility of So-

cial Choice, in Kenneth J. Arrow, AmartyaK.



Press, 1997, pp. 202-29.

_. Consequences, Opportunities, and Proce-

dures. Social Choice and Welfare, 1999, 16(1),

pp. 17-40.

Svedberg, Peter. Poverty and undernutrition:The-

oryand measurement.Mimeo (studyforWIDER);




1999 (forthcoming).

Svensson, Lars-Gunnar. Social Justice and Fair

Distributions. Lund Economic Studies, 1977, 15.

'Equity Among Generations. Economet-

rica, July 1980, 48(5), pp. 1251-56.

Tideman, Nicolaus. The Single Transferable

Vote. Journal of Economic Perspectives, Winter

1995, 9(1), pp. 27-38.

Tullock, Gordon. The GeneralIhrelevanceof the

GeneralPossibility Theorem. QuarterlyJournal

of Economics, May 1967, 81(2), pp. 256-70.

United Nations Development Programme. (UNDP).

Human development eport 1990. New York: Ox-

fordUniversityPress, 1990.

van Hees, Martin. Individual Rights and Legal

Validity. Analyse & Kritik, September 1996,

18(1), pp. 81-95.

Van Parijs, Philippe. Realfreedom for all: What if

anything)can justify capitalism? Oxford: Oxford


Varian, Hal. Equity,Envy, and Efficiency, Jour-

nal of Economic Theory,September 1974, 9(1),

pp. 63-91.

_ Distributive Justice, Welfare Economics

and a Theory of Justice. Philosophy and Public

Affairs, Spring 1975, 4(3), pp. 223-47.

Vaughan, Megan. The story of an Africanfamine:

Genderandfamine in twentiethcentury Malawi.


Vickrey, William S. Utility, Strategy, and Social

Decision Rules. QuarterlyJournalof Economics,

November 1960, 74, pp. 507-35.

Ward, Benjamin. MajorityVoting andAltemative

Forms of Public Enterprise, n Julius Margolis,

ed., The public economy of urban communities.

Baltimore, MD: Johns Hopkins University Press,

1965, pp. 112-26.

Weber, Robert J. Approval Voting. Journal of


39-49.

Wilson, Robert. Social Choice Without the Pareto

Principle. Journal of Economic Theory,Decem-

ber 1972, 5(3), pp. 478-86.

______ On the Theory of Aggregation. Journal

of Economic Theory, February 1975, 10(1), pp.

89-99.

Wriglesworth, John L. Libertarianconflicts in so-

cial choice. Cambridge: Cambridge University

Press, 1985.

Young, H. Peyton. Condorcet'sTheoryof Voting.

American Political Science Review, December

1988, 82(4), pp. 1231-44.

_ OptimalVoting Rules. Journalof Eco-nomicPerspectives,Winter1995, 9(1), pp. 51-64.

_ ed. Fair allocation. Providence,RI: Amer-

ican MathematicalSociety, 1985.

he possibility of social choice

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