A Formal Interpretation of the Theory of Relative Deprivation

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A Formal Interpretation of the Theoryof Relative Deprivation

JAMES A. DAVIS, University f Chicago

NationalOpinionResearchCenter s currently onducting study f finan-cial and other actors ffecting hecareer ecisions f graduate tudents n thetraditional rts nd sciences. n casting bout for heoretical ools, t occurredto us that the ot of the American raduate tudent might e characterized,not as one of actual economic estitution ut as one of relative eprivation fthe famous ort xperienced yAmerican oldiers n World War I. It occurredto us that f this were the case, the "theory f relative deprivation"mightexplain good dealofourdata.

We quickly urned o the major writings n that theory. he original on-ceptualization, f course, ccurs n The American oldier 3) volumes nd afamous ritique f the concept ppears n an essay by Merton nd Kitt 2).Rereading hese two works eft us short of our goal. While The AmericanSoldier extwas highly nformal nd the theory was uncodified Merton ndKitt note that nowhere n The American oldier s relative deprivation e-fined), heMerton nd Kitt theory s devoid f substantive ropositions boutrelative eprivation. n order o bridge his gap we proceeded o spell out, na relatively ormal ashion theoretical ystem, hichwillencompassmost ofthe Research Branch uthors' nterpretations f relative eprivation. We donot claimthat this s the theory he Research Branch uthors ctually used,but we do believe hat the theory oes some distance n making xplicit hearguments hich ppear n The American oldier.

Furthermore, e do not claim that the theory s "true" n the sense that

everything owknown bout human ehavior ends osubstantiate t. Rather,it is our belief hat the system f propositions s logically onsistent, as anempirical eference, nd can generate ypotheses or esting. mpirical tudiesof the hypotheses ay result n their ejection r, more robably, heir imita-tion to specific ircumstances nd situations. However,we believethat oneof the advantages f such codification s that the assumptions an be con-firmed r rejected nly when they have been spelledout. The remainder fthis ssay hen s devoted o an exposition f the heory.

THEORY

Let us consider omepopulationwhich an be partitioned n one or moreways nto dichotomous lasses e.g., married . not married r drafted . notdrafted). ur first ssumption sas follows:

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RELATIVE DEPRIVATION 281

1. At least one of these partitionings s considered hroughout he popula-tion to reflect ifferences n desirability. uch a partitioning ivides thepopulation nto wo lasses, hedeprived nd the non-deprived, he atter tate

being niversally referred o the former.Assumption amounts o saying hat one or more of the partitions re interms f a "value" on which here s consensus n the population. t does notassume that everyone utside the universe would agree on this evaluation.Thus, membershipn the Communist arty wouldnot have the ame depriva-tion tatus n an analysis f the U. S. as it would n an analysis f the U.S.S.R.In addition,we should note that we are only ssuming ranking" ere nd donot require hat the deprived xperience ain, only that deprivation e ac-

knowledged s less desirable hannon-deprivation. he theory oes not claimthat n all social groups ne will find onsensus n values. Rather, he theoryconsiders ome of the consequences f situations where there s consensus.Where eopledo not agreeon values, relative eprivation an also occur, utthe amount f relative eprivation n a given groupwill not then be a simplefunction f the variableswe are outlining.

In order o developthe specific mplications f the theory, e will use asour tool "comparisonmatrix." his may be defined s a symmetrical atrixin which ows nd columns onsist f the cross-partitioning f the populationclasses, herowsbeing ssociatedwith go and the columns eing ssociatedwith lter, lthough he entire matrix s from he "viewpoint" f ego. Whilethis will serve as a formal efinition, ts interpretation s not obvious. Thepurpose f the matrix s to list all possible omparisons n the system nderconsideration. inceeach comparison onsists f a certain ypeof ego (e.g., adeprived go) comparing imselfwith a certain ype of alter (e.g., a non-deprived lter), whenwe specify ll the possible ypes f egos paired with llthe possibletypes of alters, we have listed all of the possiblecomparisons.Sincethe possible ypes f egosare identicalwith hepossible ypes f alters,and each is givenby the cross-partition f the classes n the population, urdefinition pparently ill erve oproduce list of possible omparisons.

Let us consider wo pecific xamples. f no population haracteristics therthan deprivation re included n the analysis, he most simple ype of com-parisonmatrix sas follows:

TABLE 1Comparison atrix from heViewpoint f a Given go) for Population artitioned n

Deprivation nlyAlter

Deprived Non-Deprived

Ego Deprived a bNon-Deprived c d



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Four types f comparison re possible, s designated y the etters n thefour ells. To anticipate ur argument omewhat, ell "b" is what producesrelative eprivation ccording o the heory.

Whenweadd a second ocialcategory, hepossibilitiesncrease onsiderably.In general, iven n categories n the analysis, he comparisonmatrix willconsist f (2n)2 cells, ince there re 2ncombinations f dichotomous harac-teristics n any given opulation, nd the matrix onsists f dentical ows ndcolumns.

Let us now urn oassumptions and 3.2. Within he population, omparisonsre random.Assumption is rather mportant, oth technically nd substantively.

From technical oint f view, t enablesus to use the alculus f probabilitiesas a language or eriving ypotheses rom hetheory. hus, f the probabilityof comparison is the ameas the proportion , and the probability f com-parison is the ame s proportion , and all comparisons re random, hen tfollows hat the probability f a person omparing ith X and also with Yis the product f the wo probabilities.

From a substantive oint of view, the assumptionmay appear dubious.However,we have ittle r no empirical ata on how peopleactually do com-

pare, and until nough vidence s gathered o refute he assumption, e seeno reason ointroduce more omplicated ne. Taken together, ssumptions1 and 2 suggest n implicit realism" n the theory. While we certainly ohave evidence hat ocial perceptions re often istorted y needs and socialstructural ocation, the theory f relative deprivation implicitly n TheAmerican oldier nd explicitly n this essay) tends to assumefairly implesituations n which ndividual ariation n perception nd evaluation s small.This may be a good place to comment n the relations etween he theory frelative eprivation nd Festinger's heory f socialcomparisons1). Whilewehave not worked ut the formal elations etween he wo, t appears hatboththeories reat he ameempirical henomenon, ith his difference: hetheoryof relative eprivation reats heconsequences or hegroupwhere erceptionsand evaluations re unambiguous; hetheory f socialcomparisons reats heconsequencesfor the individual of comparisonswhere perceptions ndevaluations re ambiguous. t thus appears that both theories re specialcases of some more general uncodified heory, which can specify he cir-cumstances here he Festingermodel applies and the circumstances herethe relative eprivation odel pplies.

Now that we have defined he possible ypes f comparisons nd their re-quency, et us turn o the heart f the theory, set of assumptions bout thepsychological onsequences f various ypesof comparisons. o do so, how-ever, we must ntroduce further istinction. f we consider ny social cate-





284 SOCIOMETRY

willalso experience feeling hat his deprivation tatus s different rom hatof the out-group.We will call this social distance."

Assumptions and 6 are analogues f 3 and 4 at the nter-group evelrather

than he ntra-group evel.These six assumptions omplete he theory. Whether hey re "true" or notis, of course, nknown ithout onsiderable mpirical esearch. urthermore,weshould mphasize hat lthough he analysis f false theories s not alwaysthe best nvestment f time nd effort, ur interest s not n truth r falsityper se, but rather n whether ur theory will uccessfully odify he reasoningused by the Research Branch uthors. Our claim s that n ten out of elevenexamplest does.

Beforeproceeding o specific ases, et us draw a few nferences rom urtheory oruse in the analyses.From assumption and from he appropriateassumptions n 3 through we can, by elementary robability heory,1 efinethe expected robabilities or our various phenomena. onsidering A as theprobability f deprivation mong he A's and QA as the probability f non-deprivation mong the A's, we get the following: All inferences rom hetheory will be given Arabicnumerals.)

1. The proportion f persons n A experiencing elative deprivation

PA X QA2.The proportion f deprived n A experiencing elativegratificationPA X QA

3.The proportion f deprived n A experiencing elative eprivation QA4. The proportion f non-deprivedn A experiencing elative ratification

PA5.The proportion f A's experiencing feeling f unfairness 2 PA X QA)6.The proportion f A's experiencing elative ubordination PA X QNA7. The proportion f A's experiencing elative superiority QA X PNA8. The proportion f A's experiencing ocial distance (PA X QNA) +

(QA X PNA)

We can illustrate hefashion n whichwedeveloped heeight nferences yconsidering wo of them n detail. Inference considers he proportion fpeopleamong those possessing ttribute who experience elativedepriva-tion. Now, according o the theory, n A will experience elative eprivationin the following ombination f circumstances: hen he is deprived imself,

and when he compares ith non-deprived . Now, the proportion f A's whoare deprived s PA by definition; heprobability hat an A, regardless f hisdeprivation tatus, willcomparewith non-deprived equals the proportion

1To keep the argument imple we shall assume throughout hat the number of personsin the n-group s so large that the subtraction f ego himself rom he population of altershas only a negligible ffect n the probabilities.




of non-deprived 's (from ssumption ); hence, he probability f the ointoccurrence mong the A's consists f the product f the two probabilities,i.e. PA X QA. Inference will serve s another xample. ocial distance, ydefinition, riseswhen person n a given ategory ompares ith n out-groupmemberwho differs n deprivation. his can happen two ways: a deprivedego comparing with a non-deprived ut-group lter, or a non-deprived gocomparedwith deprived ut-group lter. Using the same arguments s inexample , the expectation or hefirst ype s (PA X QNA)or the probability(among heA's) that go s deprived imes heprobability hat the out-groupalter withwhomhe compares s non-deprived. he expectation or hesecondis similarly QA X PNA) and the amount f socialdistance s the sum of the

two.Obviously, ll of the quals signs n the quationsmust e readwith slightgrain f salt, since we can hardly xpect hat any dichotomous ocial sciencemeasure f relative eprivation ouldyield heprecise robabilities redicted,given nherent ifficulties f measurement. hus, technically, he equals signsshould be read as "is a linear function f." However, ince the use towhich hetheory illbe put s limited o comparing ocialsystems n terms fmore r essdeprivation, ather han stimating xactproportions, he ualifica-

tiondoesnot ffect hefollowingrguments.In short, ll of the parameters mplied y the theory may be deduced fromthe distribution f deprivation n the ub-classes.

EXAMPLESFROM THE AMERICANSOLDIER

We shallconsider leven pecific xamples f relative eprivation easoning.Merton nd Kitt list nine n their ssay (MK pp. 43-45). In addition wediscovered ne more, nd divided heir xamplenumber into two parts. Weshalluse the MK numbering, ddingnumber 0 for ur erendipitous iscoveryand dividing umber into 6 a. and 6 b. Of the eleven, t is our belief hat thetheory uccessfully ormalizes en.This, of course, s not amazing, s this sprecisely hat he heory asdesigned odo.

We will begin with our failure MK number ). The Research Branchauthors ay:

With higher evels of aspiration han the esseducated, he better ducated man had moreto lose in his own eyes and in the eyes of his friends y failure to achieve some sort ofstatus n the Army. Hence, frustration as greater for him . . . (AS I, p. 153)

The authors ere treat n intra-personal omparison, ot an inter-personalone, and thus fall more within he boundaries f the Festinger heory hanthe theory f relative deprivation. he argument s thus irrelevant o thetheory, ot ontradictory.



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Let us begin with the three implest ases (1, 2, and 10). In each only asingle artitioning s considered n addition o deprivation, nd the dependentvariable s of the type onsidered n inference from ur theory.

MK 1. Married nd Single DraftedMenThe Research Branch uthors ctually se two rguments n this ase, only

one of which follows rom ur model.Since Merton nd Kitt reproduce henon-model rgument e can begin by introducing nother uotation rom hesamepage:

A further lement must have been important sychologically o those married men whowere drafted. The very fact that draft boards were more liberal with married than withsinglemen provided numerous xamples to the drafted married man of others n his shoeswho got relatively etter breaks than he did.... Hence, the married man, on the average,was more ikely to come into the army with reluctance nd, possibly, sense of injustice.(AS I, p. 125)

In terms f the theory, he authors' rgument may be put as follows: hevalue of P is greater or ingle han for marriedmen; therefore is greaterfor married men than for single; consequently, ince feelings f relativedeprivation mong hedeprived ncreasewith Q (inference ), drafted married

menwillbemore ikely o experience elative eprivation.MK 2. Highand Low Education nd Reactions oDraft

The argument ere s exactly hesame as in case 1, the critical uotationbeing:

On the average, the non-high school man who was inducted could point to moreacquaintances conceivablyno more entitled o deferment han himself, who, nevertheless,had been deferred n occupationalgrounds.

MK 10. Ageand Reaction othe DraftAlthough ot cited n the Merton nd Kitt essay, hefollowing xample s

almost dentical:. . . a larger proportion f older men than of younger men got deferment n the draft ..

thus providing he older soldiers, ike the married oldiers, with ready made examples ofmen with comparable backgrounds who were experiencing ess deprivation. AS I, p. 126)

The interpretation ouldbe the ame as in the previous woexamples.Examples1, 2, and 10 not only eem o fit hetheory, ut they lso suggest

twomore nferences bout relative eprivationngeneral.9. If a given ocialcategorization s correlated ith objectivedeprivation,

relative eprivation ill be more frequent mong the deprived n the morefavored ategory.





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TABLE 2Promotion, ongevity, nd Education

Promoted Not Promoted

High ongevity LowEducation a bHigh ducation c dLowEducation e fLow Longevity HighEducation g h

in cell "h" than n cell"f" (i.e., the correlation etween ducation nd relativedeprivation oes not disappear when ongevity s partialed ut).

In the following able we can list the out-group ells with which ach ofourgroups O NOT compare.

Now, the difference n the relative eprivation f any two groupsmust bedue to those groupswhich re used as comparisons y one and not the other,since the common comparisons ave no effect n differences n relativedeprivation. et us then onsider ur twopairs ofcells:

The difference etween b" and "d" is that the b's comparewith -f, nddo not compare with g-h; while he d's compare with g-h, nd not e-f. Now,the uthor's ssumption hat hecorrelation etween ducation nd promotionholds within ongevity roups mounts o saying that there re more pro-moted n g-h than there re in e-f. This means, hen, hat the d's (who DOcompare with g-h, and not with e-f) are more ikely to compare with apromoted erson nd hence experience elative eprivation. he same argu-ment can be applied n each of the levels of the table, with the followinggeneral nferences.

11. If A and B are socialcategories n the comparison ystem, nd A has aconsistent elationship ith deprivation hen evels of B are introduced s atest variable, A will have a correlation ith relative eprivation ithin othlevelsof B. the correlation eingopposite n sign to the correlation etweenAand objective eprivation.

This, n turn, illgenerate hefollowingnferences:12. If A and B are social categories, nd (a) the correlation etweenA

TABLE3Non-In-Group Comparisons

Group Not an In-Group Comparison

d e,f,b g,hh a, ,f c, d



RELATIVEDEPRIVATION 289

and objectivedeprivation iffers n size or sign within evelsof B and (b)within specific evel of A there s no correlation etween B and objectivedeprivation, here will be a correlation etweenB and relative deprivation

within he evelofAspecified y 2.MK 8 and 9. Race,Region, nd Deprivation

Inference 2 may not appear to be intuitively lear, but it is the implicitargument sedby the Research ranch uthors n their nalysis f race, egion,and deprivation.

These are really he same example nd may be summarized s follows:... the psychological alues of Army ife to the Negro soldier n the South relative to

the Southern Negro civilian greatly exceed the psychologicalvalues of Army ife to theNegro soldier n the North relative o the Northern Negro civilian. AS I, p. 564)

Considering nlyNegroes, hefollowing ill re-state heargument n termsof our heory:

1. The correlation etween ivilian-soldiernd objective eprivation ariesby region. n the North to over-state heargument omake the point clear)the correlation s negative soldiers re more deprived han civilians); whilein the South the correlation s positive (soldiers are less deprived than

civilians).2. There s no difference n the objectivedeprivation f Negro soldiers ntheNorth nd Negro oldiers n the outh.

Thus, according o inference 2, there will be a correlation etween egionand relative eprivation mong oldiers, ven though heir bjective epriva-tion s no different.

ExampleMK 7,which oncerns ank, ongevity, nd promotion, s identicalin ts ssumptions ith xample and the onclusion ollows rom nference 1,

given the author's mplicit ssumption hat there s a correlation etweenlongevity nd promotion ithin ach rank. We shall not then discussthis ndetail.

MK 4. Combat nd Overseas erviceOur last multi-variable ase,MK 4, is of a different ature, nd therefore,

should e examined n somedetail.The problem s that f explaining hy hereis only small differencen the ttitudes f soldiers tationed n the U. S. andnon-combat roops verseas, espite definite ifference n objective epriva-tion. The Research Branch uthors nalyze the problem s follows:

In general, t is, of course, rue that the overseas oldier, elative o soldiers till at home,suffered greater break with home ties and with many of the amenities of life in theUnited States . . . But it was also true that, relative to the combat soldier, the overseassoldier in rear areas of an active theater) not in combat and not likely to get nto combatsuffered ar ess deprivation han the actual fighting man. (AS I, p. 172)



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Rather han wo social" categories, his xample onsiders wo deprivationcategories-being overseas and being in combat. Their cross-partitioningwould ive he following:

TABLE 4Combat ndStation omparisons

Combat Non-Combat

U.S. - aOverseas b c

One of the combinations combat soldier n U. S.) does not occur em-

pirically. ow, et us consider oldiers n the c" cell. Their n-group ompari-sons will be "b" and "a," and other c's." That is, in comparing hemselveswith ther verseas oldiers, hey will nclude hose n combat, nd in compar-ing themselves ith other non-combat oldiers hey will include hose n theU. S. When they ompare with a's" they will suffer elative eprivation; utwhen they comparewith "b's" they will enjoy relative gratification. hus,the existence f the "b" cell tends o offset he relative eprivation roducedby the comparisonwith "a's." Now, according o the theory t least, this

solace s not available to those n the "a" cell, since for hem b" is an out-group omparison, nd the theory ssumes hat only comparisons ith peoplein the ame ogical lasses produce elative eprivation r gratification.

We may summarize hepreceding ections y saying hat nferences hichfollowdeductively rom he assumptions f the theory ave enabled us toformalize hearguments sedby the ResearchBranch uthors n eight f theelevenexamples ollected n the Merton-Kitt rticle. Furthermore, lthoughwe can not claim complete odification y any means, he analysishas sug-

gested that relative eprivation ypotheses, s here formulated, an be for-malized nd codified hrough hewellknown ystems ordeducing onclusionsfrom he nter-relationships f correlations. his property f the theory houldmake t amenable otesting ith survey" ypedata as well s through xperi-mental echniques.

Onlyone of the examples n The American oldier reats ttitudes owardsan out-group s the dependent ariable, although these attitudes re asimportant n the general heory s relative eprivation nd relative ratifica-

tion. xample may be summarized s follows:MK 5. Officersnd Men

. . . the less the differential etween fficers nd men in the enjoyment f scarceprivileges-the xtreme asebeing hat of actual combat-the ess ikelywas the enlistedman obecritical f the fficers.... AS I, p. 181)




The dependent ariable ere s what we have called relative ubordination,"and the expected robabilities re givenby inference in the theory.

The problem s to assess n more formal erms what s meant by "the less

the differential." his may meaneither he bsolute evelof deprivation n thesystem r the correlation etween he category nd deprivation. ow, ac-cording o inference , the thing we are interested n is PA X QNA.If differ-ential means correlation nly, ncreasing he correlation, hile holding heabsolute evel of deprivation onstant, mounts o adding the value of PA,subtracting rom he value of PNA and thus adding to the value of QNA.

Obviously he product A X QN;Amust ncrease s "discrimination" gainstthe A's increases. What, on the other hand, happens f we mean "absolute"

difference n deprivation?We can think f this effect s adding a certainprobability o both PA and PNA,thus subtracting t from QNA. If we thinkof this ddition s X, the new formula orrelative ubordination mong heA's becomes:

RS = (PA + X) (QNA - X) -- AQNA+ QNAX - PAX -X2

The valueof this formula ill be decreased whenever AX + X2 is greaterthan QNAX,or whenever A + X2 is greater han QNA.The exact circum-stanceswill vary with the value of X, but it is clear that even when X isvery mall f both PA and PNAare greater han 50, addition f a constantto both probabilities ill ower he relative ubordination f the A's. In shortwe may conclude hat, whendeprivation ates re high n both lasses, ddinga constant o the deprivation f both groupswilldecrease elative ubordina-tion. Thus, both definitions f "differential" end to support the authors'informal easoning.

We can now dd the followingnferences:13. When the total rate of deprivation s held constant, elative ubordina-

tion varies directly with the correlation etween he social category ndobjective eprivation.

14. When correlation s held constant, aising he deprivation robabilitiesin both ocial classes equally will decrease he amount f relative ubordina-tion f (a) the ncrement f deprivation s quite arge nd/or b) deprivationrates nboth lasses were uite high nitially.

MK 6b. Fairness

Example6 b. is the famous omparison etween ttitudes oward romotionin the Air Forceand the Military olice.The Research Branch uthors eginwith hefollowing:

Air Corpsmen tended o take a dimmer iew of promotion pportunities ormen ofability n the Army han id the Military olice .. chances f promotion n the MilitaryPolicewere bout the worst n any branch f the Army-among his ample f men n



292 SOCIOMETRY

the Army one to two years, only 24 per cent of the MP's were noncoms as compared with47 per cent of the Air Corps men. AS I, p. 251)

Considering histo be anomalous, heauthors dvance the following rgu-ment:

But consider high school graduate or college man in the Military Police with Armylongevity f one to two years. The chances of his being a noncom were 34 out of 100.If he earned the rating, he was one of the top third among his fellows. f he failedto earn the rating, he was in the same boat with two thirds of his fellows with equalschooling.Contrast him with the Air Corps man of the same education and longevity. hechances of the latter's being a noncom were 56 in 100, based on the proportions n thissample at this time. f he had earned a rating, o had the majority of his fellows n thebranch, nd his achievement was less conspicuous han n the MP's. If he had failed to earn

a rating, while the majority had succeeded, he had more reason to feel a sense of personalfrustration, hich could be expressed s criticism f the promotion ystem... (AS I, p. 251)

In our terms, he authors re comparing wo separate ubsystems theymakeno claim that Air Forcemen comparewith Military olice) in terms ffairness the survey uestion was "Do you think soldier with bility has agood chance for promotion n the Army?"). Now, according o the theory(Inference ), unfairness hould qual 2PQ. SinceP equals 34 in the MilitaryPolice, nd .56in the Air Force, he expected unfairness" s as follows:

TABLE 5ExpectedProportion xperiencing eelingsof Unfairness

Air Force .49Military olice .45

Two aspects of this nterpretation eserve omment. n the first lace, thedistribution f 2PQ is curvilinear, eaching ts peak whereP = Q = .5, and

declining teadily s P moves oward or 1.That is, we find formal ustifica-tion or Merton nd Kitt's troubled ootnote:. . .it is scarcely probable that this relationship between actual mobility rates and

individual satisfaction with mobility chances holds throughout he entire range of varia-tion.... Presumably he relationship s curvilinear, nd this requires he sociologist o workout toward the conditions nder which the observed inear relation fails to obtain. (MK, n.p. 54)

The secondpoint worth oting s that the ResearchBranch uthors o not

use our argument, ut onewhich s, n terms f the theory, nvalid.They saythat n the Air Force the promotedwere ess happy and the non-promotedmoreunhappy han n the Military olice. Then they mplicitly ssumethatthe questionnaire tem they re considering easures ersonalhappiness ndthat the sum of happiness s greater n the Military olice.According o thetheory, his an not be so, for ccording oinferences and 2 the proportion




of relatively eprived lways qualsthe proportion elatively ratified. ence,an increase n one s always ccompanied y an increase n the other. f, how-ever, ne assumes, s we have done, hat he dependent ariable s "fairness,"

not deprivation-gratification,he onclusions f the uthors re congruent iththe heory nd with he data n all instances.

SOME SPECULATIONS ON SUB-GROUP FORMATION

While our theory was designed o codify he examples n The AmericanSoldier, s in all formalizations, he scheme s capable of generating largenumber f additional ypotheses. n particular, he theory will suggest omeaspectsof the structure f simple ocial systems which re not considered nThe American oldier, which ypically oncentrates n sub-group ifferencesrather han characteristics f the system s a whole.While the following sonly ne of a number f questionswhich an be treated with he theory, t mayserve o llustrate ome f tspossibilities.

Anypopulationmaybepartitioned n numerous ays, n terms f education,age, sex, hair color, ntroversion, tc., etc. In some of these nstances, helogicaldivision s also associated with recognized ocial divisions, s in thecase of religious ub-groups r political arties. n other nstances, n equallyimportant istinction, .g., a personality rait, will not produce ociallyrec-ognized ub-groupings. ur theory uggests omehypotheses bout conditionswhichwillproduce elf-consciousub-groupings.

To begin with, et us assume, by fiat, that sub-grouping ill be mostprominent n a social system when: (a) members f the particular ub-groupconsider hemselves o be very different rommembers f the out-group, nd(b) members f the sub-group onsider hemselves obe very imilar o eachother. These, of course, orrespond o our variables of social distance nd

in-group airness.We can then ay that sub-grouping ill reach a maximum hen: (a) in.group airness s at a maximum nd (b) out-group istance s at a maximum.Now, o far, ur new theory s true by definition i.e., tautological).However,wecan begin oedgeout on a limb by askingwhat conditions houldproducehigh ub-group onsciousness.

Since ll of our variables re nter-related, e can write he xpected mountof sub-group onsciousnesss a function f a number f different ariables.

Let us consider simple ystem n which he partitions onsist f depriva-tion and a singleother ocial category.Now, despite ll the words we haveused to describe uch a system, ll the information nvolved s given by asimple four-fold able in which deprivation s cross-tabulated gainst thesocial characteristic f interest. Now, the four numbers n the table canthemselves e thought f as functions f the two marginals" i.e., the number



294 SOCIOMETRY

of persons n the ocial categories nd the number f persons eprived n thesystem) nd the degree f correlation r association n the table. f we thenconsider system n which he numbers f A's and NA's are equal, we canthen derive the degree of sub-group onsciousness and any other variablein the theory) s a function f (a) the total evel of deprivation n the ystemand (b) the randomness r correlation n the distribution f deprivation e-tween he wo ub-groups.

Given uch a system, he expected roportion n the total populationwhoare characterized s "in-group onscious" i.e., whose omparisons ead themto define hemselves s unlike he out-group nd like the in-group n termsof deprivation) s as follows:

(P2A) * (QNA + Q2A) * (PNA + P2NA) * (QA + Q2NA) . (PA)2

If we take a simplemeasure f correlation,2 t turns ut that what we getmaybe summarized y the following raph.

The vertical xis indicates he probability hat a person drawn t randomfrom he system will be "in-group onscious," while the horizontal xis in-dicates the degree f correlation. t the left we find he most extreme is-

crimination gainst the A's, at the right he most extreme iscriminationagainst heNA's, whilepoint R in the center ndicates purely andom is-tribution. ach deprivation evel generates separate parabola except thatthe distribution s symmetrical, uch that the results or 20 are the same as.80; .30is the ame as .70,and so on. We may draw the following onclusionsfrom his:

15. Sub-group onsciousness ncreases s the correlation etween he socialcategory nd deprivation ncreases, egardless f the total evelof deprivation

in the ystem.16. Sub-group onsciousness ecreases s total deprivation eparts rom 50toward ither or 1.00, regardless f the degree f correlation etween hesocial ategory nd deprivation.

In a less formalway we can say that our theory uggests hat the way tocreate ub-groups s to start rewarding hemdifferentially nd keep the totallevel of reward n the system near .50; while conversely he way to lowersub-group onsciousness s to treat both groups equitably and move the

2 t should be noted that the exact results f such an analysis will vary with the writer'sdefinition f "correlation." he one we used was as follows: At each level of total depriva-tion, we defined n increase n correlation s an increase n the value of PA. We set themaximum s the maximum for PA, the minimum s the minimum A could reach for thatlevel of total deprivation, nd then plotted the intervening oints o that equal changes nPA produced qual changes n "correlation."




CaT 1

Probability

1.000.901

Total Deprivation.80

.70 am

*30

*20 olOor .90

0l.

_1.00 4n o

CORRELATION

reward evel to an extreme f either eneral deprivation r general gratifica-a pair struggling ver a toy. They either rovide nother oy or remove hetion. This, of course, s what parents f smallchildren o when heyobserveonly oy, imultaneously emovingny correlation nd pushing hedeprivationlevel toward ne or the other xtreme. ur inferences hus ppear ntuitivelyagreeable, lthough xperimental onfirmation ould add somewhat o our

confidencen the heory.However, ur interest ere s not in sub-group onsciousness tself, butrather n noting hat this s only one of a number f problemswhich an beanalyzedusing hetheory f relative eprivation. or instance,we could ookfor he factors nderlying ifferences etween he two ocial categories n theamount of sub-group onsciousness; we could predict he occurrence f ananomie-like tate defined y the probability hat ego will feel different romboth heout-group nd from he n-group; r wecould ook t a variablewhich

might redict mobility spirations etween he groups, uchas the probabilitythat gowill feeldifferent rom is in-group nd like the out-group. n short,the theory ppears capableof generating number f hypotheses hichhavenot been discussed n The American oldier or in this essay. Thus, again wenote hefamiliar onclusion hat n attempt o attain losure hrough odifica-



296 SOCIOMETRY

tion usuallyproducesmore new questions han t answers. uch, apparently,is the ask nd nevitable rustration f theory onstruction.

Manuscript eceived: pril 1, 1959Revisedmanuscript eceived: uly , 1959

James . DavisNational pinion esearch enterUniversity f ChicagoChicago 7, llinois

REFERENCES

1. Festinger, ., "A Theory of Social Comparison Processes,"Human Relations, 1954, VII,117-140.

2. Merton, R. K., and A. S. Kitt, "Contributions o the Theory of Reference Group Be-havior" in R. K. Merton and P. F. Lazarsfeld, Continuities n Social Research,Studies in the Scope and Method of "The American Soldier," Glencoe, ll.: TheFree Press, 1950, 40-105. (Hereafter we will designate he essay by "MK.")

3. Stouffer, . A., E. A. Suchman, L. C. DeVinney, S. A. Star, and R. M. Williams, Jr.,The American oldier: Adjustment uring Army Life, Princeton, N. J.: PrincetonUniversity ress, 1949. (Since this work will be repeatedly ited n our analysis,wewill refer o it hereafter s "AS Vol. I.")

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A Formal Interpretation of the Theory of Relative Deprivation