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Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility Author(s): John C. Harsanyi Source: Journal of , Vol. 63, No. 4 (Aug., 1955), pp. 309-321 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1827128 Accessed: 18-07-2015 00:34 UTC

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This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions CARDINAL W ELFARE, INDIVIDUALISTIC ETHICS, AND INTERPERSONAL COMPARISONS OF UTILITY'

JOHN C. HARSANY1 Universityof Queensland I uals prefersY to X, thenX should be re- T HE naive conceptof social welfare garded as sociallypreferable to Y. But no as a sum of intuitivelymeasurable other restrictionis to be imposed on the and comparable individual cardi- mathematical form of a social welfare nal utilities has been found unable to function. withstand the methodological criticism Recently,however, Professor Fleming3 of the Pareto school. ProfessorBergson2 has shownthat if one accepts one further has thereforerecommended its replace- fairlyweak and plausible ethical postu- ment by the more general concept of a late, one findsone's social welfarefunc- social welfarefunction, defined as an ar- tion to be at once restrictedto a rather bitrary mathematical function of eco- narrow class of mathematical functions nomic (and other social) variables, of a so as to be expressible(after appropriate formfreely chosen according to one's per- monotone transformationof the social sonal ethical (or political) judg- welfareand individual utilityindexes if ments. Of course, in this terminology necessary)as the weightedsum of the in- everybody will have a social welfare dividuals' utilities.This does not mean, functionof his own, differentfrom that of course, a returnto the doctrine that of everybodyelse, except to the extentto the existenceof an additive cardinalutili- which differentindividuals' value judg- ty function is intuitivelyself-evident. ments happen to coincide with one an- The existence of such a function be- other. Actually, owing to the prevalence comes, rather, the consequence of the of individualisticvalue judgmentsin our ethical postulates adopted and is wholly ,it has been generallyagreed that dependent on these postulates. Still, a social welfarefunction should be an in- Fleming's resultsdo in a sense involve an creasingfunction of the utilitiesof indi- unexpected revival of some views of the viduals: if a certain situation,X, is pre- pre-Paretoperiod. ferredby an individual to anothersitua- In this paper I propose, firstof all, to tion, Y, and if none of the otherindivid- examine the precise ethical meaning of Fleming's crucial postulate and to show I I am in(lebtedto rmycolleagues at the Univer- that it expressesan individualisticvalue sity of Queensland, Messrs. R. W. Lane and G. judgment going definitelybeyond the , forhelpful comments. Of course,the responsi- b)ilityfor shortcomingsof this paper and for the generallyadopted individualisticpostu- opinions expressedin it is entirelymine. I M. Fleming,"A Cardinal Concept of Welfare," 2 A. B3ergson (Burk), "A Reformulation of QuarterlyJournal of Economics, LXVI (August, Certain Aspects of WelfareEconomics," Quarterly 1952), 366-84. For a differentapproach to the same Journalof Economics, LII (Fehruary,1938), 310-34, problemsee L. Goodman and H. Markovitz,"Social and "," in A Survey of Con- WelfareFunctions Based on Individual Rankings," temporaryEconomics, ed. H. S. Ellis (Philadelphia, AmericanJournal of Sociology, Vol. LVIII (Novenm- 1949), esp. lplp412-20. ber, 1952). 309

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late mentionedearlier, though it repre- PostulateC transitivityyof social indif- sents,as I shall argue, a value judgment ference).- -If from a social standpoint perfectlyacceptable according to com- neither of X and 1 is preferredto the mon ethical standards (Sec. II). I shall other, and again neitherof Y and Z is also attempt to show that, if both social preferredto the other,then likewisenei- and individual preferencesare assumed therof X and Z is preferredto the other. to satisfy the von Neumann-Morgen- These three postulates are meant to stern-Marschakaxioms about choicesbe- insure that "social " estab- tween uncertainprospects, even a much lishes a completeordering among the pos- weaker ethical postulate than Fleming's sible social situations, from which the sufficesto establish an additive cardinal existenceof a social welfarefunction (at social welfarefunction (Sec. III). In ef- least of an ordinal type) at once follows. fect, it will be submitted that a mere (Actually, two postulates would have logical analysis of what we mean by sufficedif, in the postulates, "weak" value judgments concerningsocial wel- preference,which does not exclude the fare and by social welfare functions possibilityof indifference,had been used , without any additional ethical instead of "strong" preference.) postulates,to a social welfarefunction of Postulate D (positiverelation of social this mathematicalform (Sec. IV). Final- preferencesto individualpreferences).-If ly, I shall turn to the problem of inter- a givenindividual i preferssituation X to personal comparisons of utility, which situation Y, and none of the other indi- gains new interestby the revival of an viduals prefersY to X, then X is pre- additive cardinal welfare concept, and ferredto Y froma social standpoint. shall examine what logical basis, if any, As already mentionedPostulate 1) ex- thereis forsuch comparisons(Sec. V). pressesa generallyaccepted individualis- tic value judgment. II Finally, Fleming's Postulate E states Fleming expresses his ethical postu- essentially that on issues on which two lates in termsof two alternativeconcep- individuals' ()con- tual frameworks:one in terms of an flict,all otherindividuals' interestsbeing "ideal "of G. E. Moore's unaffected,social preferencesshould de- type, the other in terms of a preference pend exclusivelyon comparingthe rela- terminologymore familiar to . tive social importanceof the interestsat Though he evidentlysets greaterstore by stake of each of the two individuals con- the firstapproach, I shall adopt the sec- cerned. In other words, it requires that ond, which seems to be freerof unneces- 4 Of course, when I speak of preferences"from sary metaphysicalcommitments. I have a social standpoint,"often abbreviated to "social" also taken the libertyof rephrasinghis preferencesand the like, I always mean preferences postulates to some extent. based on a given individual's value judgmentscon- cerning "social welfare." The foregoingpostulates PostulateA (asymmetryof social pref- are meant to impose restrictionson any in(lividual's erence).-If "from a social standpoint"4 value judgemnentsof this kind, and thus represent, situation X is preferredto situation Y, as it were, value judgments of the second order, X. that is, value judgments concerningvalue juldg- then Y is not preferredto ments.Later I shall discuss the concept of "l)refer- PostulateB (transitivityof social pref- ences from a social standpoint" at some length erence). If froma social standpointX is and introducethe distinctiveterm "ethical prefer- Y then X is ences" to describe them (in Sec. IV). But at this preferredto Y, and to Z, stage I do not want to prejudge the issue by using preferredto Z. this terminology.

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the distributionof utilitiesbetween each only, without affectingthe interestsof pair ofindividuals should be judged sepa- anybody else, social choice must depend rately on its own merits,independently exclusivelyon i's and j's interests pro- of how utilities(or income) are distribut- vided that i's and j's interestsagree in ed among the other members of the this matter. Postulate E now adds that community. in the assumed case social choice must PostulateE (independentevaluation of depend exclusivelyon i's andj's interests the utilitydistribution5 between each pair (and on weighingthese two interestsone of individuals). (1) There are at least against the otherin termsof a consistent threeindividuals. (2) Suppose that indi- ethical standard), even if i's and j's in- vidual i is indifferentbetween situations terests are in conflict.Thus both postu- X and X' and also between situations Y lates make social choice dependentsolely and Y', but preferssituations X and X' on the individual interests directly af- to situationsY and Y'. Suppose, further, fected.7They leave no room forthe sepa- that individual j is also indifferentbe- rate interestsof a superindividualstate tween X and X' and between Y and Y', or of impersonalcultural values8 (except but (unlike individual i) prefersY and for the ideals of equity incorporatedin Y' to X and X'. Suppose also that all the ethical postulates themselves). otherindividuals are indifferentbetween At firstsight, Postulate E may look in- X and Y, and likewise between X' and consistentwith the widespread habit of yV.6 Then social preferencesshould al- judging the "fairness"or "unfairness"of ways go in the same way betweenX and the distributionof income between two Y as theydo betweenX' and Y' (that is, individuals,not only on the basis of these if froma social standpointX is preferred two people's personal conditions and to Y. then X' should also be preferredto needs, but also on the basis of comparing 1'; if froma social standpointX and Y I In view of consumers'notorious "irrationality," are regarded as indifferent,the same some people may feel that these postulates go too should be true of X' and Y'; and if from far in accepting the consumers' sovereigntydoc- a social standpoint Y is preferredto X, trine.These people may reinterpretthe termsin the postulates referringto individual preferencesas then Y' should also be preferredto X'). denoting,not certainindividuals' actual preferences, Postulate E is a natural extension of but rather their "true" preferences,that is, the the individualistic value judgment ex- preferencesthey would manifestunder "ideal con- ditions," in possession of perfectinformation, and pressed by Postulate D. Postulate D al- actingwith perfectlogic and care. With some inge- ready implies that if the choice between nuityit shouldnot be too difficultto give even some two situationsX and Y happens to affect sort of "operational" meaning to these ideal con- ditions,or to some approximationof them,accepta- the interestsof the individuals i and j ble forpractical purposes. (Or, alternatively,these termsmay be reinterpretedas referringeven to the 5The more general term "utility " preferencesthat these individuals oughtto exhibit is used instead of the term"income distribution," in termsof a givenethical standard. The latterinter- since the utilityenjoyed by each individual will, in pretationwould, of course,deprive the postulatesof general, depend not only on his own income but mostof theirindividualistic meaning.) also, owing to externaleconomies and diseconomies 8 These postulates do not of ,on otherpeople's incomes. exclude, however,the possibility that such considerationmay influence 6 It is not assumed,however, that the otherindi- the relative weightsgiven to differentindividuals' viduals are (like i and j) indifferentbetween X and utilitieswithin the additive social welfarefunction. X' and between Y and Y'. In effect,were this re- Even by means of additional postulates,this could strictiveassumption inserted into Postulate E, this be excludedonly to the extentto whichthe compari- latterwould completelylose the status of an inde- son of individualutilities can be put on an objective pendentpostulate and would become a mere corol- basis independent of individual value judgments lary of Postulate D. (see Sec. V).

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions 312 JOHN C. HARSANYI their incomes with the incomes of the come distributionin the restof the socie- other membersof their respectivesocial ty in so far as the income distribution groups. Thus people's judgments on the in the rest of the societyaffects the utili- income distribution between a given ty levels of these two individuals them- workerand his employerwill also depend selves and consequentlythe distribution on the currentearnings of other similar of utilitybetween them. Postulate E de- workersand employers.But the conflict mands only that, once these effectshave with Postulate E is more apparent than been allowed for,the distributionof in- real. In a societywith important external come in the rest of the society must not economiesand diseconomiesof consump- have any furtherinfluence on our value tion,where the utilityof a given income judgment. depends not only on its absolute size but III also on its relation to other people's in- In accordance with prevalentusage in comes, it is not inconsistentwith Postu- welfareeconomics, 1leming's postulates late E that, in judging the income dis- referto social or individual preferences tributionbetween two individuals,other betweensure prospectsonly. However, it people's incomes should also be taken seems desirable to have both sorts of into account. An income distributionbe- preferencesdefined for choices between tween a given worker and a given em- uncertainprospects as well. More often ployer, which in the original situation than not, we have to choose in practice seemed perfectly"fair" in terms of a between social policies that promise given ethical standard, may require ad- given definiteresults only with largeror justment in the worker's favor, once smallerprobabilities. On the otherhand, have generallygone up, since the if we subscribeto some sort of individu- worseningof this worker'sposition rela- alistic ethics,we should like to m-ake so- tive to that of his fellowsmust have re- cial attitude toward uncertaintysome- duced him to a lower level of utility. how dependent on individual attitudes Postulate E requiresthat the distribu- toward it (at least if the latter do not tion of utilitybetween two individuals manifesttoo patent and too great an in- (once the utilitylevels of the two indi- consistencyand irrationality). viduals are given) should always be Since we admit the possibilityof exter- judged independentlyof how utilityand nal economies and diseconomiesof con- income are distributed among other sumption, both social and individual membersof the society. In the absence prospects will, in general, specify the of external economies and diseconomies amounts of differentcommodities con- of consumption,this would necessarily sumed an(l the stocks of differentgoods also mean judging the distributionof in- held by all individualsat differentfuture come between two individuals independ- dates (up to the tim-ehorizon adopte(I) ently of the incomes of others. In the together with their respective proba- presence of such economies and dis- bilities. economies, however, when the utility As the von Neumann-Morgenstern level of any person depends not only on axioms9 or the Marschak postulates1? his own incomebut also on otherpersons' incomes,it is not inconsistentwith Pos- 9 See J. von Neumann and 0. MAorgenstern, Theoryof Games and Economic Behavior (2d e.; tulate E that our value judgmenton the Princeton,1947), pp. 641 ff. distributionof income between two in- 10J. Marschak, "Rational Behavior, Uncertain dividuals should be influencedby the in- Prospects, and Measurable Utility,"'Econome/rica,

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions WELFARE, ETHICS, AND UTILITY 313 equivalent to them (which latter I shall to Fleming's Postulate D ratherthan to adopt) are essential requirementsfor ra- his Postulate E. tional behavior, it is natural enough to I propose to show that Postulate c suf- that both social and individual ficesto establish that the cardinal social preferences"1should satisfy them. This welfarefunction defined by Postulate a gives us: can be obtained as a weightedsum of the Postulatea -Social preferencessatis- cardinal individual utility functionsde- fy NMarschak'sPostulates 1, II, III', and finedby Postulate b (on the understand- IV. ing that the zero point of the social wel- Postulate b. Individual preferences fare functionis appropriatelychosen). satisfythe same fourpostulates. TheoremL.---There exists a social wel- in addition, we need a postulate to farefunction such that its actuarial value secure the dependence of social prefer- is maximized by choices conformableto ences on individual preferences: the social preferencesgiven. This social Postulatec. If two prospectsP and Q welfare functionis unique up to linear are indifferentfrom the standpoint of transformation. everyindividual, they are also indifferent Theorem II.-For each individual froma social standpoint. there exists a utilityfunction such that Postulate c once more represents,of its actuarial value is maximized by course,an individualisticvalue judgment choices conformableto the individual's though a very weak one, comparable preferences. This utility function is unique up to linear transformation. XVIII (1950), 111-41, esp. 116-21. Marschak's Both theoremsfollow from Marschak's postulatescan be summarizedas follows.Postulate I (comnpleheordering): The relationof preferenceestab- argument. lishes a complete ordering among all prospects. Let W denote a social welfarefunction Postulate II (continuity): If prospect P is pre- satisfyingTheorem I and Uj denote a ferredto prospectR, while prospectQ has an inter- mediate position between them (being preferredto utility function of the i'th individual, R but less preferredthan P), then there exists a satisfyingTheorem II. Moreover, let W mixtureof P and R, with appropriateprobabilities, be chosen so that W = 0 if for all the n such as to be exactlyindifferent to Q. PostulateIII' U1 = U2 = ... = = 0. (sotf/icientnumber of nonindifferentprospects): There individuals Un are at least fourmutually nonindifferent prospects. TheoremIII. W is a single-valued Postolote I V (equivalenceof mixtureof equivalent function of U1, U2, . . . , Un. This fol- prospects):If prospects Q and Q' are indifferent, then,for any prospectP, a given mixtureof P and Q lows, in view of Theorems I and II, from is ini(lifferenttoa similarmixture of P and Q', (that is, Postulate c. to a mixtureof P and Q' whichhas the same proba- Theorem IV.-W is a homogeneous bilitiesfor the correspondingconstituent prospects). PostulateI is needed to establishthe existenceof functionof the firstorder of U1, U2, .... even an ordinalutility (or welfare) function,while Un. the otherthree postulates are requiredto establish Proof.-We want to show that, if the the existenceof a (or welfare)func- tion.But, as PostulatesII and III are almosttrivial, individual utilities U1 = u1; U2 = u2; Postulate IV may be regardedas being decisive for ... .; U = ut correspondto the social cardinalityas against mereordinality. welfareW = w, thenthe individualutili- 11There are reasonsto believe that,in actuality, ties U1 = k-ul; U2 = k-u2;. . . ; Un = individual preferencesbetween uncertain prospects - do not always satisfythese postulates of rational k un correspond to the social welfare behavior (for example, owing to a certain "love W = k-w. of (langer"; see Marschak, op. cit., pp. 137-41). In This will be shown firstfor the case this case we fall may back again upon the prefer- ? ences each individual would manifestunder "ideal where0 k < 1. Suppose that prospect = = Z conditions"(see n. 5). 0 representsU1 U2 . * . ( n= 0

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for the differentindividuals and conse- 11p we obtain the desired resultfor the quently represents W = 0 for society, case where k > 1 (by an appropriate while prospect P represents U1 = ul; choice of p we can make k equal to any U2 = H12; . * . ; Un = un for the former number >1). and W = w forthe latter. Moreover,let TheoremV. W is a weightedsum of Q be the mixed prospect of obtaining the individual utilities,of the form prospect (with the probability either 0 W'=la. U, 1 - p) or prospect P (with the proba- bility p). Then, obviously,Q will repre- where ai stands for the value that W sentU1 = P ul; U2 = . ... ; Un = takes when Ui = 1 and Uj = 0 for all p u, for the individuals and W= p -w j 5 i. for society. Now, if we write k= p, a Proof.--Let Si be a prospect repre- comparison between the values of the sentingthe utilityUi to the ith individu- variables belonging to prospect P and al and the utilityzero to all other indi- those belonging to prospect Q will, in viduals. Then, accordingto Theorem IV, view of Theorem III, establish the de- forSi we have W = ai- Us. sired resultfor the case where0 < k ? 1 Let T be the mixedprospect of obtain- (p, being a probability,cannot be <0 ing eitherS or S2 or . . . Sn, each with or > 1). probability 11n. Then T will represent Next let us consider the case where the individual utilitiesU11n, U2/n, . k < 0. Let us choose prospect R so that U/is and the social welfare prospect 0 becomes equivalent to the 1 mixed prospect of obtainingeither pros- W=-*wNa -Us 1'1 pect R (with the probabilityp) or pros- pect P (with the probability 1 - p). A In view of Theorem IV, this directlyim- little calculation will show that in this plies that if the individual utility func- case prospect R will represent U1 = tions take the values U,, U2, . . ,Un (1- 1Pp)-u1; U2 = (1 - 1P)-112; ... ; respectively,the social welfarefunction Un = (1 - I/p) -un for the differentin- has the value dividuals and W = (1 - 1 p) -w for so- W= la* U., ciety. If we now write k = 1 - 11p, a comparison between the variables be- as desired.'2 longing to R and those belonging to P IV will establish the desired result for the case k < 0 (by an appropriate choice of In the pre-Pareto conceptual frame- the probabilityp, we can make k equal to work,the distinctionbetween social wel- any negative number). fare and individual utilities was free of Finally, the case where k > 1 can be ambiguity. Individual utilities were as- taken care of by findinga prospect S sumed to be directlygiven by introspec- such that prospectP becomes equivalent tion, and social welfarewas simplytheir to the mixed prospectof obtainingeither sum. In the modern approach, however, S (with a probability p) or 0 (with a the distinctionis far less clear. On the probability1 - p). Then this prospectS one hand, our social welfareconcept has will be connectedwith the values U1 = 12 If we want a formalguaranty that no indi- vidual's utility can be given a negative weight in = ... U,. = l/p*Ul; U2 lp8U2; ; l/p. the social welfarefunction, we must add one more it. and W- 1p-w. If we now writek = postulate (for instance,Postulate D of Sec. II).

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions WELFARE, ETHICS, AND UTILITY 315 come logically nearer to an individual what this individual prefers(or, rather, utilityconcept. Social welfareis no long- would prefer)on the basis of impersonal er regardedas an objective quantity,the social considerationsalone, and the lat- same for all, by necessity.Rather, each termust expresswhat he actually prefers, individual is supposed to have a social whetheron the basis of his personal in- welfarefunction of his own, expressing terestsor on any otherbasis. The former his own individual values in the same may be called his "ethical" preferences, way as each individualhas a utilityfunc- the latter his "subjective" preferences. tion of his own, expressinghis own indi- Only his "subjective" preferences(which vidual taste. On the other hand, our in- define his utility function) will express dividual utility concept has come logi- his preferencesin the full sense of the cally nearer to a social welfareconcept. word as they actually are, showing an Owing to a greaterawareness of the im- egoistic attitude in the case of an egoist portance of externaleconomies and dis- and an altruisticattitude in the case of economiesof consumptionin our society, an altruist. His "ethical" preferences each individual's utilityfunction is now (which definehis social welfarefunction) regardedas dependent not only on this will, on the otherhand, expresswhat can particular individual's economic (and in only a qualified sense be called his noneconomic)conditions but also on the "preferences": they will, by definition, economic (and other) conditions of all expresswhat he prefersonly in thosepos- other individuals in the community-in sibly raremoments when he forcesa spe- the same way as a social welfarefunction cial impartial and impersonal attitude is dependent on the personal conditions upon himself.'4 of all individuals. In effect,the ethical postulates pro- At the same time,we cannot allow the 14 Mr. Little's objection to Arrow'snondictator- distinctionbetween an individual's so- ship postulate (see Little's review article in the cial welfarefunction and his utilityfunc- Journal of Political Economy,LX [October, 1952], esp. 426-31) loses its force, once the distinction tion to be blurredif we want (as most of between "ethical" and "subjective" preferencesis us do, I think) to uphold the principle noted. It does, then,make sense that an individual that a social welfarefunction ought to be should morallydisapprove (in termsof his "ethical" preferences)of an unequal incomedistribution which based not on the utilityfunction (subjec- benefitshim financially,and should still preferit tive preferences)of one particular indi- (in termsof his "subjective" preferences)to a more vidual only (namely, the individual egalitarianone or shouldeven fightfor it-behavior morally regrettablebut certainlynot logically in- whose value judgments are expressed in conceivable. this welfarefunction), but ratheron the Arrow's distinction between an individual's utilityfunctions (subjective preferences) "tastes" (which ordersocial situationsonly accord- ing to their effectson his own consumption)and of all individuals,representing a kind of his "values" (which take account also of external "fair compromise"among them.'3 Even economiesand diseconomiesof consumptionand of if both an individual's social welfare ethical considerations,in orderingsocial situations) does not meet the difficulty,since it does not explain function and his utility function in a how an individualcan withoutinconsistency accept sense express his own individual prefer- a social welfarefunction conflicting with his own ences, they must express preferencesof "values." This can be understoodonly if his social welfarefunctions represents preferences of another differentsorts: the formermust express sort than his "values" do. (Of course,in my termi- 13 This principleis essentiallyidentical with Pro- nology Arrow's "values" fall in the class of "sub- fessorArrow's "nondictatorship"postulate in his jective" preferencesand not in the class of "ethical" Social Choice and Individual Values (New York, preferences,as is easily seen fromthe way in which 1951), p. 30 (see also n. 12). he definesthem.)

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions 316 JOHN C. HARSANYI posed in Sections II and 111-namely, axioms and consequently must definea Postulates D, E, and c can be regarded cardinal social welfarefunction equal to as simplyan implicitdefinition of what the arithmeticalmean18 of the utilitiesof sort of "impartial" or "impersonal" atti- all individuals in the society (since the tude is requiredto underlie"ethical" pref- arithmeticalmean of all individual utili- erences:these postulatesessentially serve ties gives the actuarial value of his un- to exclude nonethical subjective prefer- certain prospect, defined by an equal ences fromsocial welfarefunctions. But probabilityof being put in the place of thisaim may also be securedmore direct- any individual in the situation chosen). ly by explicitly definingthe impartial More exactly, if the formerindividual and impersonalattitude demanded. has any objective criterionfor comparing I have argued elsewhere' that an in- his fellows'utilities with one anotherand dividual's preferences satisfy this re- with his own (see Sec. V), his social wel- quirementof impersonalityif they indi- fare function will represent the un- cate what social situation he would weightedmean of these utilities,while in choose if he did not know what his per- the absence of such an objective criterion sonal positionwould be in the new situa- it will, in general,represent their weight- tion choosen (and in any of its alterna- ed mean, with arbitraryweights depend- tives) but ratherhad an equal chance of ing only on his personalvalue judgments. obtaining any of the social positions'6 In the formercase social welfarewill in existingin this situation,from the high- a sense be an objective quantity,whereas est down to the lowest. Of course, it is in the lattercase it will containan impor- immaterialwhether this individual does tant subjective element;but even in this not in fact know how his choice would latter case it will be somethingvery dif- affect his personal interests or merely ferentfrom the utilityfunction of the in- disregardsthis knowledgefor a moment dividual concerned.19 when he is makinghis choice. As I have tried to show17 in either case an imper- V sonal choice (preference)of thiskind can There is no doubt about the fact that in a technical sense be regarded as a people do make, or at least attempt to choice between "uncertain" prospects. make, interpersonalcomparisons of utili- This implies, however, without any ty, both in the sense of comparingdiffer- additional ethical postulates that an in- ent persons' total satisfactionand in the dividual's impersonalpreferences, if they 18 Obviously,the (unweightedor weighted)mean are rational, must satisfy Marschak's of the individual utilities definesthe same social welfarefunction as theirsum (weightedby the same "I See my "Cardinal Utilityin relative weights), except for an irrelevantpropor- and in the Theory of Risk-taking," Journal of tionalityconstant. PoliticalEconomy, LXI (October,1953), 434-35. 19The concept of ethical preferencesused in this 16 Or, rather,if he had an equal chance of being sectionimplies, of course,an ethical theorydifferent "put in the of" any individualmember of the place fromthe now prevalentsubjective attitude theory, society,with regardnot only to his objective social since it makes a person's ethical judgments the (and economic) conditions,but also to his subjec- expression,not of his subjective attitudes in gen- tive attitudesand tastes. In otherwords, he ought eral, but ratherof certain special unbiased imper- to judge the utilityof anotherindividual's position sonal attitudesonly. I shall set out the philosophic not in terms of his own attitudes and tastes but case forthis ethical theoryin a forthcomingpublica- ratherin termsof the attitudes and tastes of the tion. (For a similar view, see J. N. Findlay, "The individual actually holdingthis position. Justificationof Attitudes," Mind, N.S., LXIII 17Op. cit. [April,19541, 145-61.)

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions WELFARE, ETHICS, AND UTILITY 317 sense of comparingincrements or decre- differentpeople. At the same time,under ments in differentpersons' satisfaction.20 these conditionsthis logical possibilityof The problem is only what logical basis, differentsusceptibilities to satisfaction if any, thereis for such comparisons. would hardly be more than a meta- In general,we have two indicatorsof physical curiosity.If two objects or hu- the utilitythat otherpeople attach to dif- man beings show similarbehavior in all ferentsituations: theirpreferences as re- their relevant aspects open to observa- vealed by theiractual choices, and their tion, the assumption of some unobserv- (verbal or nonverbal) expressionsof sat- able hidden differencebetween them isfactionor dissatisfactionin each situa- must be regardedas a completelygratui- tion. But while the use of these indica- tous hypothesis and one contrary to tors for comparing the utilities that a sound scientificmethod.22 (This principle given person ascribes to differentsitua- may be called the "principle of unwar- tions is relativelyfree of difficulty,their ranteddifferentiation." In the last analy- use for comparing the utility that dif- sis, it is on the basis of thisprinciple that ferentpersons ascribe to each situation we ascribe mental states to otherhuman entails a special problem.In actual fact, beings at all: the denial of this principle this problemhas two ratherdifferent as- would at once us to solipsism.23Thus pects, one purely metaphysicaland one in the case of personswith similarprefer- psychological,which have not, however, ences and expressive reactions we are always been sufficientlykept apart. fullyentitled to assume that they derive The metaphysicalproblem would be the same utilitiesfrom similar situations. presenteven if we tried to compare the In the real world, of course, different utilitiesenjoyed by differentpersons with people's preferencesand theirexpressive identical preferencesand with identical reactions to similar situations may be expressive reactions to any situation. ratherdifferent, and this does representa E1'venin this case, it would not be incon- veryreal difficultyin comparingthe utili- ceivable that such persons should have ties enjoyed by differentpeople--a diffi- differentsusceptibilities to satisfaction cultyin addition to the metaphysicaldif- and should attach differentutilities to ficultyjust discussed and independentof identical situations, for, in principle, it. I shall referto it as the psychological identical preferences may well corre- difficulty,since it is essentiallya question spond to differentabsolute levels of utili- of how psychologicaldifferences between ty (as long as the ordinalproperties of all people in the widest sense (for example, persons' utilityfunctions are the same21), 21 and identical expressive reactions may Even identical preferencesamong uncertain prospects (satisfying the Marschak axioms) are well indicate differentmental states with compatiblewith differentabsolute levels of utility, since theydo not uniquelydetermine the zero points 2' See I. AM.D. Little, A Critique of Welfare and the scales of the correspondingcardinal utility EIconomics(Oxford, 1950), chap. iv. I have nothing functions. to add to Little's conclusion on the possibilityof 22 By making a somewhat free use of Professor interpersonalcomparisons of utility.I onlywant to Carnap's distinction,we may say that the supplement his argument by an analysis of the assump- tion of differentsusceptibilities of satisfactionin logical basis of such comparisons.I shall deal with this case, even thoughit would not be against the the of comparisionsbetween total utilities problem of deductivelogic, would most definitelybe only,neglecting the problem of comparisons between canons against the canons of inductivelogic. differencesin utility,since the social welfarefunc- tions discussed in the previous sections contain 23See Little, A Critique of WelfareEconomics, only total utilitiesof individuals. pp. 56-57.

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions 318 JOHN C. HARSANYI differencesin consumption habits, cul- assimilated to the cultural patterns and tural background,social status, and sex attitudes of the second group. Thus it and otherbiological conditions, as well as may easily happen that, if we want to purely psychological differences,inborn comparethe satisfactionsof two different or acquired) affectthe satisfactionthat classes of human beings,we cannot find people derive from each situation. The any individual whose personal experi- problem in general takes the following ences would cover the satisfactions of form.If one individual preferssituation both these classes. X to situationY, whileanother prefers Y Interpersonal comparisons of utility to X, is this so because the formerindi- made in everydaylife seem, however,to vidual attaches a higherutility to situa- be based on a differentprinciple (which tion X, or because he attaches a lower is, of course,seldom formulatedexplicit- utilityto situation Y, than does the lat- ly). If two individuals have opposite ter-or is this perhaps the resultof both preferencesbetween two situations, we these factors at the same time? And, usually try to findout the psychological again, if in a given situationone individ- differencesresponsible for this disagree- ual gives more forciblesigns of satisfac- ment and, on the basis of our general tion or dissatisfactionthan another, is knowledgeof human psychology,try to this so because the formerfeels more in- judge to what extent these psychologi- tense satisfaction or dissatisfaction,or cal differencesare likely to increase or only because he is inclinedto give strong- decrease their satisfactionderived from er expressionto his feelings? each situation. For example, if one indi- This psychological difficultyis acces- vidual is ready at a given rate to sible to direct empirical solution to the supply morelabor than another,we tend extent to which these psychologicaldif- in general to explain this mainly by his ferencesbetween people are capable of having a lower disutilityfor labor if his change, and it is thereforepossible for physique is much more robust than that some individuals to make direct com- of the other individual and if thereis no parisons between the satisfactionsopen ascertainable differencebetween the two to one human type and those open to individuals' economic needs; we tend to another.24Of course,many psychological explain it mainly by his having a higher variables are not capable of change or are utility for income (consumptiongoods) capable of change onlyin some directions if the two individuals' physiques are but not in others.For instance,a number similar and if the formerevidently has of inbornmental or biological character- much greater economic needs (for ex- istics cannot be changed at all, and, ample, a largerfamily to support). though the cultural patterns and atti- Undoubtedly, both these methods of tudes of an individualborn and educated tackling what we have called the "psy- in one social group can be considerably chologicaldifficulty" are subject to rath- changed by transplanting him to an- er large marginsof error.25In general,the other,usually they cannot be completely greaterthe psychological,biological, cul- two 24 On the reliabilityof comparisonsbetween the tural, and social differencesbetween utility of differentsituations before a change in 25 Though perhaps it would not be too difficult one's "taste" (taken in the broadestsense) and after to reduce these margins quite considerably (for it, see the firsttwo sections of my "Welfare Eco- example, by using appropriate statistical tech- nomics of Variable Tastes," Revjcw of Economic niques), should there be a need for more precise Studies,XXI, (1953-54), 204-8. results.

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions WELFARE, ETHICS, AND UTILITY 319 people, the greater the margin of error material. For example, we must assume attached to comparisons between their that men and women equal in abstrac- utility. tive ability (and the otherrelevant char- Particular is connected acteristics)would tend to find the same with the second method,since it depends satisfactionin workingon mathematical on our general knowledgeof psychologi- problems. cal laws, which is still in a largelyunsat- Of course, the assumption that the isfactorystate.26 What is more, all our "unchangeable" variables in themselves knowledgeabout the psychologicallaws have no influenceis ex hypothesinot open of satisfactionis ultimatelyderived from to direct empiricalcheck. It can be jus- observinghow changes in different(psy- tifiedonly by the a prioriprinciple that, chologicaland other) variables affectthe when one variable is alleged to have a satisfactionsan individual obtains from certaininfluence on another,the burden various situations.We thereforehave no of prooflies on thosewho claim the exist- directempirical evidence on how people's ence of such an influence.27Thus the sec- satisfactionsare affectedby the variables ond method of interpersonalutility com- that, for any particular individual, are parison rests in an important sense on not capable of change. Thus we can, in empirical evidence more indirect28than general,judge the influenceof these "un- that underlyingthe firstmethod. On the changeable" variables only on the basis other hand, the second method has the of the correlationsfound between these advantage of also being applicable in and the "changeable" variables, whose those cases where no one individual can influencewe can observe directly. For possibly have wide enough personal ex- instance,let us take sex as an example of perience to make direct utilitycompari- "unchangeable" variables (disregarding sons in termsof the firstmethod. the fewinstances of sex change) and ab- stractive ability as an example of In any case, it should now be suffi- "changeable" variables. We tend to as- cientlyclear that interpersonalcompari- sume that the average man findsgreater 27 This principlemay be called the "principleof unwarrantedcorrelation" and is again a principle satisfaction than the average woman of inductivelogic, closelyrelated to the principleof does in solvingmathematical puzzles be- unwarranteddifferentiation referred to earlier. cause, allegedly, men in general have 28 There is also another reason for which con- greaterabstractive ability than women. clusions dependenton the principleof unwarranted correlationhave somewhat less cogency than con- But this reasoning depends on the im- clusions dependent only on the principle of un- plicit assumption that differencesin the warranted differentiation.The former principle "unchangeable" variables, if unaccom- refersto the case where two individuals differin a certainvariable X (in our example,in sex) but where p)anliedby differencesin the "change- thereis no special evidence that theydiffer also in a able" variables, are in themselves im- certain other variable Y (in susceptibilityto satis- faction). The latter principle,on the other hand, 26 Going back to our example, for instance, the refersto the case where there is no ascertainable disutilityof labor and the utilityof income are un- differenceat all between the two individuals in likely,to be actually independentvariables (as I any observable variable whatever, not even in X have tacitlyassumed), thoughit may not always be (in sex). Now, though the assumption that these clear in which fwaytheir mutual influenceactually two individuals differin Y (in susceptibilityto goes. In any case, income is enjoyed in a different satisfaction)would be a gratuitoushypothesis in way, dependingon the ease with which it has been either case, obviously it would be a less unnatural earned,and labor is put up with in a differentspirit, hypothesisin the firstcase (where thereis some ob- dependingon the strengthof one's need for addi- served differencebetween the two individuals) tional income. than in the second case (wherethere is none).

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions 320 JOHN C. HARSANYI

sons of utility are not value judgments the basis of personal guesses more or less based on some ethical or political postu- dependent on our own value judgments. lates but ratherare factual propositions On the other hand, if the information bTasedon certain principlesof inductive needed is available, individualisticethics logic. consistentlyrequires the use, in the so- At the same time,Professor Robbins29 cial welfarefunction, of individual utili- is clearly rightwhen he maintains that ties not subjected to restrictivepostu- propositionswhich purport to be inter- lates. The impositionof restrictiveethi- personalcomparisons of utility often con- cal or political conventionson the indi- tain a purelyconventional element based vidual utilityfunctions would necessari- on ethical or political value judgments. ly qualify our individualism, since it For instance,the assumptionthat differ- would decrease the dependence of our ent individuals have the same suscepti- on the actual bilityto satisfactionoften expresses only preferencesand actual susceptibilitiesto the egalitarian value judgment that all satisfaction,of the individual members individuals should be treated equally of the society,putting in its place a de- ratherthan a in a factual psycho- pendence on our own ethical or political logical equality betweenthem. Or, again, value judgments (see nn. 5 and 6). differentpeople's total satisfaction is To sum up, the morecomplete our fac- oftencompared on the tacit understand- tual informationand the more complete- ing that the gratificationof wants re- ly individualisticour ethics,the more the garded as "immoral" in terms of a cer- differentindividuals' social welfarefunc- tain ethicalstandard shall not count. But tions will convergetoward the same ob- in order to avoid confusion,such propo- jective quantity,namely, the unweighted sitions based on ethical or political re- sum (or ratherthe unweightedarithme- strictivepostulates must be clearly dis- tic mean) of all individual utilities.This tinguished from interpersonalcompari- followsboth from(either of two alterna- sons of utility without a conventional tive sets of) ethical postulates based on elementof this kind. commonlyaccepted individualisticethi- It must also be admitted that the use cal value judgments and fromthe mere of conventionalpostulates based on per- logical analysis of the concept of a social sonal value judgmentsmay sometimesbe welfare function.The latter interpreta- due not to our freechoice but ratherto tion also removescertain dil-'culties con- our lack of the factual informationneed- nected with the concept of a social wel- ed to give our interpersonalutility com- fare function,which have been brought parisonsa moreobjective basis. In effect, out by Little's criticism of certain of if we do not know anything about the Arrow's conclusions. relative urgency of differentpersons' Of course,the practicalneed forreach- economicneeds and still have to make a ing decisionson public policy will require decision,we can hardly avoid acting on us to formulatesocial welfarefunctions- explicitlyor implicitly even if we lack 29 See L. Robbins, "Robertson on Utility and the factual informationneeded forplac- Scope,"Economica,,N.S.,XX(1953),99-ill,esp. 109; see also his AnwEssay onlthe Nature and Signific(ance ing interpersonalcomparisons of utility of Economic Science (2d ed.; London, 1948), chap. on an objective basis. But even in this vi; and his "InterpersonalComparisons of Utility," the Economic Journal, XlIII (December, 1938) case, granting proposed ethical pos- 635-41. tulates (or the proposedinterpretation of

This content downloaded from 128.135.12.127 on Sat, 18 Jul 2015 00:34:52 UTC All use subject to JSTOR Terms and Conditions WELFARE, ETHICS, AND UTILITY 321 the concept of a social welfarefunction), alternativehypotheses, even if his factu- our social welfarefunction must take the al informationis insufficientto do this on formof a weightedsum (weightedmean) an objective basis---so in welfare eco- of all individual utility functions,with nomicswe have also foundthat a rational more or less arbitraryweights chosen ac- man (whose choices satisfy certain cordingto our own value judgments. simple postulates of rationalityand im- There is here an interestinganalogy partiality) must likewise act as if he with the theory of statistical decisions made quantitative interpersonal com- (and, in general, the theoryof choosing parisons of utility,even if his factual in- among alternative hypotheses). In the formationis insufficientto do this on an same way as in the latter, it has been objective basis. shown30 that a rational man (whose Thus if we accept individualistic choices satisfycertain simple postulates ethics and set public policy the task of of )must act as if he ascribed satisfyingthe preferencesof the individ- numericalsubjective probabilitiesto all ual membersof the society (decidingbe- tween conflictingpreferences of different 30See Marschak's discussion of what he calls individuals according to certain stand- "Ramsey's norm," in his paper on "Probability in ards of impartialequity), our social wel- the Social Sciences," in AlathematicalThinking in tlheSocial Sciences, ed. P. F. Lazarsfeld (Glencoe, farefunction will always tend to take the Ill., 1954), Sec. I, esp. pp. 179-87; also reprintedas form of a sum (or mean) of individual No. 82 of "Cowles CommissionPapers" (N.S.). utilities; but whetherthe weights given For a surveyof earlierliterature see K. J. Arrow, to these individual utilitieshave an ob- AlternativeApproaches to the Theory of Choice in jective basis or not will depend whollyon Risk-takingSituations," ,XIX (Octo- ber, 1951), 404-37, esp. 431-32, and the references the extentof our factual (psychological) therequoted. information.

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