PSYCHOLOGICAL REVIEWfsnagle.org/files/anderson1971integration.pdflearning, perception, judgment,...

PSYCHOLOGICALREVIEWVOL. 78, No. 3 MAY 1971

INTEGRATION THEORY AND ATTITUDE CHANGE *

NORMAN H. ANDERSON2

University of California, San Diego

A theory of information integration is applied to attitudes and social judgments,based on a principle of information integration. For quantitative analysis,a simple but general algebraic model of judgment is used, in which each infor-mational stimulus is characterized by two parameters, scale value and weight.Functional measurement procedures are employed to derive equal-intervalscales of parameter values. Exact tests based on analysis of variance are givenfor four applications of the model, and these applications are reconsideredunder the further restriction imposed by the averaging hypothesis. Qualita-tive comparisons are made to several other theories of attitude change. Ten-dencies toward balance and congruity are shown to be consequences of theprinciple of information integration. Critical tests between integrationtheory, and balance and congruity theories are also suggested. Similar com-parisons are made to summation theory, logical-consistency theory, assimila-tion-contrast theory, and similarity-attraction theory. Molar and molecularanalyses of communication structure are considered briefly and the analysisof inconsistency resolution within integration theory is also discussed. Finally,it is noted that integration theory has had reasonable success in the areas oflearning, perception, judgment, decision making, and personality impressions,as well as attitude change. It may thus provide a beginning to a unifiedgeneral theory.

Attitude change stands out from most continually impinge on the person, in lifeareas of experimental psychology in the or in the laboratory, and he must integratenature of its stimuli. In even the simplest them with one another as well as with hisinvestigations of attitudes and opinions, prior opinions and attitudes. Social judg-the stimuli typically carry information at a ments are typically based on a cumulationcognitive level not often reached in other of various pieces of information, sometimesareas of research. Informational stimuli of the most diverse nature. Factual and

!This work was supported by grants from the hearsay evidence, rumors, prestige associ-National Science Foundation (GB-6666) and the ations, gesture and appearance, may alla^lS'the SSal tt>» Menfaf bear on the final attitude. Information in-Health to the Center for Human Information Pro- tegration is thus fundamental in attitudecessing, University of California, San Diego. This change.paper owes much to many people. I wish to express .my enduring appreciation to David A. Grant and Gough, Kenneth Hammond, Reid Hastie, ClydeCarl I. Hovland who stimulated my interest in the Hendrick, Chester Insko, Martin Kaplan, Jacquesmethod and content of this work. I owe special Kaswan, Howard Leventhal, Theodore Newcomb,thanks to Sam Himmelfarb and Rhoda Lindner for Ramon Rhine, Milton Rosenberg, Ralph Rosnow,detailed, insightful criticism, and to Robyn Dawes Marshall Segall, Jim Shanteau, Marvin Shaw, Pauland Robert Wyer for many helpful comments. I am Slovic, Raymond Smith, and Warner Wilson.also indebted for comments, not always heeded, on a Requests for reprints should be sent to Normanparticular points by Donn Byrne, Don Campbell, H. Anderson, Department of Psychology, UniversityGerald Clore, Rudolf Cohen, Harry Gollob, Philip of California, San Diego, La Jolla, California 92037.

171

© 1971 by the American Psychological Association, Inc.

172 NORMAN H. ANDERSON

In previous research, the writer has-beenworking on a general theory of informationintegration. Experimental applicationshave ranged from personality impressionformation to decision making and psycho-physical judgment. The present papergives a more detailed exposition of integra-tion theory in attitude change, developingfurther the theme of some of the first re-ports in this research program (Anderson,1959a; Anderson & Hovland, 1957) and ofmore recent work (Anderson, 1968a).

INTEGRATION THEORY

Integration Model

A basic distinction in the present formu-lation is that between weight and value.Each piece of information is represented bytwo parameters: a scale value, s, and aweight, w. The value is the location of theinformational stimulus along the dimensionof judgment. The weight represents thepsychological importance of the informa-tion. It is important to note that both sand w will depend on the dimension of judg-ment as well as the individual. For sim-plicity, only a single dimension of attitudeor judgment will be explicitly considered.The same piece of information may havequite different value and importance ondifferent dimensions, or for different indi-viduals on the same dimension.

The theoretical model used in most of thiswork can be written as a weighted sum:

R = C + Z wiSi. [1]i—a

Usually, R is taken to be the overt response,measured on a numerical scale. In somecases, however, R might be considered asthe attitude underlying an overt yes-nodecision. The summation in Equation 1 isover all relevant informational stimuli.The contribution of Stimulus *' is just itsweight W{ times its value 5,. The constant,C, allows for an arbitrary zero in the re-sponse scale and will not be explicitly con-sidered here. The first term in the sum,TOO-JO, represents the initial opinion, prior toreceiving the informational stimuli.

Two basic algebraic operations, addingand multiplying, are involved in the inte-gration model. In simplest form, the totaleffect of any one informational stimulus isthe product of its weight and its scale value.The total effect of two or more informa-tional stimuli is the weighted sum of theirscale values. These two algebraic opera-tions correspond to two classes of experi-mental manipulations in attitude experi-ments as noted below.

Despite its simple nature, the algebraicjudgment model has considerable flexibil-ity. It includes adding, averaging, sub-tracting, dividing, and multiplying models,as well as proportional-change and linearoperator models. Special cases have beenstudied by numerous investigators in variedareas as cited here and elsewhere (Ander-son, 1970a; S. Rosenberg, 1968).

Empirical Support

The writer's program of research in in-formation integration has been based on asystematic exploitation of the algebraicjudgment model. A substantial portion ofthe work has dealt with personality impres-sions (see Anderson, 1968a), including thestudy of stimulus interaction and configuraluse of cues (Anderson, 1965b; Anderson &Jacobson, 1965; Lampel & Anderson, 1968;Sidowski & Anderson, 1967). Other appli-cations include decision making (Anderson& Shanteau, 1970; Shanteau, 1970a), psy-chophysical judgment (Parducci, Thaler,& Anderson, 1968; Weiss & Anderson,1969), illusions (Anderson, 1970b; Massaro& Anderson, 1971), learning (Anderson,1969b; Friedman, Carterette, & Anderson,1968; Himmelfarb, 1970), and attitudechange (Sawyers & Anderson, 1971).

The integration model has done well,both qualitatively and quantitatively. Itrests upon a substantial data base. Al-though a major part of the supportingexperimentation has been done with per-sonality impressions, the same principlesmay be expected to apply to the more tradi-tional communication-persuasion paradigm.Indeed, personality impression formationinvolves attitude change toward a particu-lar individual and can be viewed as a min-

INFORMATION INTEGRATION AND ATTITUDE CHANGE 173

iature attitude change situation. Eachtrait adjective corresponds to a communi-cation whose weight can be controlled byattributing it to various sources, for in-stance, or by manipulating its reliability.The development of personality impres-sions and attitudes both involve the inte-gration of information into evaluative judg-ments that have social relevance. Fromthe present standpoint, an a priori distinc-tion between them would be artificial.

Valuation and Integration

The two fundamental operations in inte-gration theory are valuation and integra-tion. Valuation, in model terms, involvesthe determinants and the measurement ofthe w and 5 parameters. Integration com-prises the ways in which the several stimuliare combined. The judgment task mayaffect the integration rule and certainly willaffect the valuation process. In general,however, valuation and integration mayconveniently and effectively be kept sepa-rate as long as the stimuli do not interact.

When the stimuli do interact, valuationand integration will become interlinked.As a working rule, it will be assumed herethat stimulus interaction primarily affectsthe valuation process, and that the changedparameter values are then employed in theintegration.

Most of the experimental work to datehas used the assumption that the w and svalues for an informational stimulus remainconstant, regardless of what other stimuliit may be combined with. This is conven-ient in tests of the model, particularly in theearly stages of development. Fortunately,the assumption that the stimuli do not in-teract seems to be justified in an importantgroup of situations.

More interesting though more difficultproblems arise in the many situations inwhich context-induced changes may occur.Primacy effects (Anderson, 1965b; Asch,1946), positive context effects (Anderson,1966a; Kaplan, 1971), discounting effects(Anderson & Jacobson, 1965; Lampel &Anderson, 1968; Schumer & Cohen, 1968),and differential weighting (Oden & Ander-son, 1971) have all been studied in personal-

ity impressions with some theoretical suc-cess. Such problems of configural cue usageare even more important in the generalstudy of attitude change as the latter dis-cussion of the source-communication rela-tion will show.

The problem of stimulus configuralityalso bears directly on the problem of cogni-tive structure. A personality impression,for example, or even a trait adjective, ob-viously has a more complex cognitivestructure than can be represented on asingle dimension. A multidimensional rep-resentation would do better, of course, andthe present development may be consideredas applying to each of several dimensions inturn.

However, the undoubted success of thedimensional view in psychology can lead topreoccupation with a restricted set of prob-lems, and to a possibly artificial view ofcognitive structure. Information integra-tion, for example, may itself occur at a morebasic level than the judgment, and the lat-ter may be merely the valuation of thestructure along the specified task dimension(Anderson, 1967). The standard dimen-sional view will be used in this paper, butits probable limitations need particular at-tention in the study of stimulus interaction.For example, the data suggest that affectiveand semantic inconsistency produce aboutequal discounting (Anderson & Jacobson,1965). In inconsistent combinations, theresponse must be based on the stimulusconfiguration, and it is problematic howfar standard dimensional representationsof the stimulus will go.

Application to Attitude Change

In attitude change, the source-communi-cation-issue schema developed most exten-sively by Hovland and his associates (e.g.,Hovland, 1957; Hovland, Janis, & Kelley,1953) provides a useful way to organizemany problems. A communication fromsome source provides information that isrelevant to the person's attitude or opinionon some issue. The effective stimulus isthen the source-communication combina-tion. The present use of two parameters,weight and scale value, to represent the


source-communication parallels the ap-proach of Anderson and Hovland (1957).

The scale value of the source-communica-tion corresponds to its position on the atti-tude dimension. For many purposes, thiscan be taken as the position advocated bythe source-communication. This value willbe primarily determined by the semanticproperties of the communication, as theyare interpreted within the person's valuesystem. Conceptually, it is sometimes use-ful to consider the scale value as the attitudethat would be left unchanged by the com-munication.

The weight parameter is more importanttheoretically than the scale value becauseof the many determinants of the weight. Aprimary determinant of Wi will be character-istics of the source. Thus, source status,reliability, and expertise will all affect w,-.Moreover, WQ, the weight parameter of theinitial opinion, will reflect personality char-acteristics, such as persuasibility, as well asego involvement and strength of prioropinion. In addition, the evidence indi-cates that primacy and recency effects areto be interpreted in terms of the weightparameter as discussed later.

Because of its close relationship withfunctional measurement, integration theoryemphasizes a more quantitative approachto communication-persuasion processesthan has been usual in attitude theory.Traditional approaches have been more con-cerned with qualitative analysis of valua-tion than with integration per se. Sincefunctional measurement opens up possibili-ties for direct measurement of the stimuli,the present approach is less exclusivelyconcerned with qualitative analysis. More-over, because the theory rests on a principleof information integration, the experimentalprogram has emphasized the study of in-formation variables in the stimulus. Aswill become apparent, some of the tradi-tional problems of attitude theory are par-ticularly amenable to analysis within aconceptual framework based on informationintegration.

Functional Measurement

The power of the algebraic judgmentmodel has depended on the concomitantdevelopment of a theory of functional mea-surement. This scaling theory makes itpossible to get the equal-interval scalesthat are needed in the quantitative testsof the model. The basic ideas of functionalmeasurement were given in two earlypapers (Anderson, 1962a, 1962b), and amore systematic exposition in psychophysi-cal judgment is given in Anderson (1970a).A brief sketch will be given here; the latertheoretical applications will exhibit func-tional measurement in action.

A central idea of functional measurementis that measurement scales are derivativefrom substantive theory. Measurementthus involves three simultaneous problems(Anderson, 1970a, Figure 1): (a) Problem 1—to measure the subjective stimulus valueson equal-interval scales; (b) Problem 2—tomeasure the subjective response value on anequal-interval scale; and (c) Problem 3—tofind the psychological law that relates thesubjective values of stimuli and response.All three problems are to be solved together.That this can sometimes be done quitesimply is shown in previous experimentalwork using functional measurement pro-cedures (e.g., Anderson, 1962a). Theseprocedures are illustrated in the nextsection.

Nearly all the experimental work in this researchprogram has used numerical response measures suchas ratings. But rating scales may be only ordinal,while the exact tests of the model require an equal-interval scale. Functional measurement allowstransformation of an ordinal scale into an equal-interval scale on the response side. Functional scaleson the stimulus side can then be obtained. The alge-braic judgment model is used as the scaling frame sothat the validity of the scales depends on the validityof the model. Substantive theory and measurementtheory are thus cofunctional in development.

Functional measurement may be contrasted withThurstonian scaling in several respects, two of whichshould be noted here. First, the Thurstonian ap-proach is largely concerned with stimulus scaling,which is traditionally seen as a preliminary to thesubstantive inquiry. Such an approach has its at-tractions, but it bases the substantive investigationon a separate scaling theory of uncertain validityand relevance. Many workers, as a consequence,have attempted to develop "measurement free"


methods that use only rank-order information. Thepresent approach, in contrast, treats scaling andtheory as inherently interlinked at every level ofconsideration.

A second difference between functional measure-ment and Thurstonian scaling is in the treatment ofindividual differences, a problem of some import-ance in attitudes and opinions. As is well known,Thurstonian paired-comparison scales of attitudinalstimuli almost necessarily rely on pooled group data.Most people will have clear preferences, and the re-sultant 0-1 probabilities disallow scaling at the indi-vidual level. Group scales (Bock & Jones, 1968,pp. 1-2) have normative and sociological value, as inCoomb's (1967) replication of Thurstone's (1927)scale of seriousness of offenses. However, their rolein the study of psychological processes is severelylimited. Functional measurement has the importantadvantage that it can operate directly at the levelof the individual.

Conceptually, the response scaling feature (Ander-son, 1962b, 1970a; Bogartz & Wackwitz, 1970, 1971)is essential to functional measurement. The logic ofthis approach rests on "using the postulated behav-ior laws to induce a scaling on the dependent vari-able" (Anderson, 1962b). Indeed, it would not bepossible to consider this approach as a general theoryof measurement without systematic methods fortransforming ordinal response measures to an in-terval scale. Experimental illustrations are givenin Anderson and Jacobson (1968) and Weiss andAnderson (in press).

For the kinds of situations considered in thisarticle, however, there is increasing evidence thatordinary rating procedures can provide intervalscales simply and directly, at least with reasonableexperimental precautions (e.g., Anderson, 1967;Himmelfarb & Senn, 1969; Shanteau & Anderson,1969). In this article, therefore, it will be assumedthat the observed response is on an interval scale.This assumption is directly testable since an inade-quate scale would tend to disconfirm the model pre-dictions. Conversely, if the model does fit the data,response scale and model are jointly validated.

From the experimental standpoint, an importantmethodological feature of functional measurement isthe use of stimulus combinatorics. Each informa-tional stimulus is systematically placed in severaldifferent combinations. This experimental strategyembodies a direct approach to the substantive prob-lem of stimulus integration. Happily, it also allowsthe effect of the given stimulus to be factored outand scaled. Extensive use is made of factorial de-signs, therefore, with analysis of variance a principaltool.

Conjoint measurement (Krantz & Tversky, 1970;Luce & Tukey, 1964) has certain similarities to func-tional measurement, but as a matter of principle re-stricts itself to rank-order data. Its principal virtueseems to be that it can provide rank-order tests ofgoodness of fit for certain models. That virtue by-passes the response scaling problem, which couldcertainly be advantageous, though practical difficul-ties seem to have limited the use of these techniques

(Tukey, 1969; Zinnes, 1969). Functional measure-ment, in contrast, enables one to use whatever metricinformation is in the overt response. In that sense,the difference between functional and conjoint mea-surement parallels that between parametric and non-parametric tests (Anderson, 1961a). At a morefundamental level, the functional measurement ap-proach makes measurement theory an integral partof substantive psychological theory. As one conse-quence, it has the flexibility needed to cope with non-additivities caused by averaging processes and cer-tain kinds of stimulus interactions.

MATHEMATICAL APPLICATIONS

This section details several applicationsof the integration model, and much of it canbe skipped initially. After the next twosubsections, therefore, and the initial re-marks on the averaging hypothesis, it maybe desirable to go to the main section of thepaper, Relations to Other Theories.

Basic Integration Rules

The applications below all rest on twokinds of experimental manipulations: ofthe weight parameter and of the scale value.These correspond to three basic integrationrules. The first is a multiplying rule whichspecifies the total effect of a communicationto be the product of its weight and its value.The rationale for this multiplying rule canbe illustrated by considering any method ofmanipulating weight. Source credibility,for example, does not of itself produceopinion change, but only affects degree ofacceptance of the communication. A de-crease in source credibility would thus actby attenuating the effect of the communi-cation.

The second basic integration rule specifiesthat two communications will follow somekind of adding rule, as in Application 1 be-low. An adding-type rule is intuitivelyattractive and has been employed in someform in almost all attempts at quantitativeanalysis.

However, there is considerable evidencefor an averaging rule instead of an addingrule. Mathematically, the two rules haveconsiderable similarity, though the aver-aging rule tends to be more difficult to workwith. In many cases, the two rules makethe same prediction, but they disagree


markedly in some important situations asdiscussed under Averaging Theory.

Psychologically, adding and averagingare quite different. In a strict addingmodel, the informational stimuli can becompletely independent in their action.In contrast, averaging always implies somedegree of cognitive interaction because theweight of any one informational stimulusnecessarily depends on all the others. Ac-cordingly, averaging is considered as a thirdbasic rule and considered separately in thenext section.

A comment on terminology may helpavoid some ambiguity in the use of theterms "adding" and "averaging." Becausethey make the same predictions under cer-tain conditions, there may be neither neednor basis to make a distinction. In manyof the published papers that have employedone or the other model, no distinction hasbeen necessary. In line with mathematicalusage, therefore, the term adding will beused generically to include both strict add-ing and averaging models. When the dis-cussion is to be restricted to one or theother, this will be indicated. The resultsof the following four applications do not allhold for averaging models as discussed inthe next main section on averaging theory.

Application 1: Variation in s

This application is appropriate when two(or more) communications that have differ-ent scale values on a given issue are com-bined. In the experiment cited below, forexample, the communications were para-graphs that described good and bad actionsof United States Presidents.

It is assumed that the communicationsare presented according to a Row X Col-umn factorial design as illustrated in Table1. The row and column factors each corre-spond to one source, and the levels withineach factor correspond to communicationsattributed to the row source and columnsource, respectively. The source may beonly implicit, when the communications arepresented as historical fact, for example.

Under an adding model, the theoreticalentry in each cell of the design is

[2]

Here WR and Wo are the communicationweights associated with the row and columnsources; s^i is the scale value of the com-munication coming from Source R in row i;Sa is the scale value of the communicationfrom Source C in column j. Each opinionis thus considered as the resultant of threeinformational stimuli: the two communica-tions and the initial opinion. The initialopinion will be assumed equal to zero, asimplification that does not affect the con-clusions.

Equation 2 imposes two assumptions:The first is that the communications do notinteract or change scale value when com-bined. The second is that the row weight,WR, is constant over rows and analogouslyfor the column weight. Since WR repre-sents the joint effect of the row source andthe row communication, this virtually re-quires that each row communication havethe same natural weight and that sourceand communication do not interact.

These restrictive assumptions should bekept in mind when designing an experiment.They are, however, more restrictive thannecessary for an adding model. Applica-tion 4, below, allows the weights to varyacross rows and/or columns and still yieldsexact predictions.

Test of fit. For this design, the modelmakes a very simple prediction: each tworows differ by a constant. For example,the difference between rows 1 and 2 in eachcolumn of Table 1 is WR(SKI — ̂ 2)-

If the model is correct, then the raw datashould show a very simple pattern. Graph-ically, the three rows of data should plot asthree parallel curves except for samplingerror. An example based on Table 1 isgiven in Figure 1 in the next section. Sta-tistically, this means that the Row X Col-umn interaction is zero in principle andnonsignificant in practice. Thus, regularanalysis of variance provides a simple andpowerful test of goodness of fit.

It may be reemphasized that this paral-lelism test can be made directly on the rawdata. The person receives the two informa-tional stimuli and then makes his responseon a numerical scale. The test is made di-rectly on these responses. Separate esti-


TABLE 1

INTEGRATION MODEL ILLUSTRATED FOR TWO-COMMUNICATION FACTORIAL DESIGNWITH VARIOUS COMMUNICATIONS ATTRIBUTED TO EACH OF Two SOURCES

A. Formal model expressions

Source R(WR)

Communication RlCommunication R2Communication R3

M

Source C(wc)

Communica-tion Cl

VlRSRi + WcSciWRSB.2 + WCSCIviRSm + wcsci•UIB.SR + wcsci

Communica-tion C2

WRSRI + WcSmWRSR2 + WCSC2

WRSRS + WCSC2WR^R + wcsci

Communica-tion C3

WRSRi + Wc*C3WRSR2 + 1VCS03WRSRS + WcScz1VRSR + WCSC3

Communica-tion C4

WRSRI + WCSGIWRSR2 + WCSCtWRSRS + WcSCiTORSR + wcsct

M

WRSRi + WC$CWRSR2 + WcScWRSR3 + WCSCWRSR + WcSc

B. Numerical example

Source C(wc = 2)

SRI = 1sm = 2Sns = 6

M

Sd = 1

3485

?C2 = 2

56

107

soi = 3

78

129

Set = 6

13141815

M

78

12

mates of the scale values of the communica-tions are not required. This is invaluablein attitude research because prior scalingof the communications is often undesirableor infeasible.

Application 1 has special interest becauseit holds when the communications are pre-sented in strictly serial order as is typicalof attitude change situations. The rowfactor then corresponds to the first com-munication, the column factor to the sec-ond communication, etc. Applications ofsuch serial-factor designs have been madein a number of other areas (e.g., Anderson,1964d; Shanteau, 1970a; Weiss & Ander-son, 1969). Under certain conditions, it ispossible to construct the serial-positioncurve knowing only the response at the endof the sequence.

Functional scales. A striking property ofthe integration model is that it provides amethod for scaling the communications. InTable 1, the column means are linear func-tions of the sa,

Rj = + [3]

where the mean row value, Sa, is a constant.The observed column means, therefore, are

estimates of the communication values onan equal-interval scale.

This is illustrated in the numerical ex-ample in the lower half of Table 1. Thecolumn means are twice the column scalevalues plus 3; the row means are the rowscale values plus 6. These interval scaleshave arbitrary zero and unit and are uniqueonly up to a linear transformation. Thisneeds to be kept in mind for scaling pur-poses; more than two row stimuli wouldordinarily be needed to estimate any scalevalues for the row stimuli. Of course, nomore than two rows are needed for the testof fit, and two rows suffice for scaling undercertain conditions when the same stimuliare used in each factor of the design (e.g.,Weiss & Anderson, 1969).

These results are not restricted to two-way designs but hold for any number offactors. The first experimental applicationof functional measurement (Anderson,1962a) used a three-way design for person-ality impressions.

Experimental example. Figure 1 showsan experimental test of integration theory.Subjects judged general statesmanship ofvarious United States Presidents, each de-


4

o 2sz

o 0

? 6LLJ2

4

2

0

" I = 1.56E = 2.05

M+

1 =11.67E = 1.66

M+

1=2 ,13E = 0.94

H

I = 0.06E = 1.33

IT

FIG. 1. Mean attitude toward United States Presidents produced by pairs ofinformational paragraphs. (Equal weighting model predicts parallelism forthe 2 X 2 design in each panel. Mean squares for interaction and error denotedby I and E. H, M+, M~, and L denote paragraphs of highly favorable, moder-rately favorable, moderately unfavorable, and very unfavorable information.)(Reprinted from an article by Barbara K. Sawyers and Norman H. Andersonpublished in the May 1971 Journal of Personality and Social Psychology. Copy-righted by the American Psychological Association, Inc., 1971.)

scribed by two paragraphs based on histori-cal sources (Sawyers & Anderson, 1971).Very positive, mildly positive, mildly nega-tive, and very negative paragraphs are de-noted by H, M+, M~, and L. Each panelshows a 2 X 2 design which should obeythe parallelism prediction. Parallelismseems to hold fairly well except that thediscrepancy was significant in the topcenter panel.

Adding and averaging models make thesame parallelism prediction in this experi-ment and are not distinguishable from thesedata. However, subsequent work appearsto rule out the adding model for Presidentjudgments.

The parallelism test is made directly onthe raw response and does not require actualestimation of the scale values. Normativeratings were used to class the paragraphs asH, M+, M-, or L, but the only function ofthese categories was to separate the datacurves in order to allow potential nonparal-lelism to appear. It should be noted thatthe 2 X 2 design is frequently not conven-

ient or usable for functional scaling. How-ever, the primary purpose of this experi-ment was to test the model rather than scalethe stimuli.

Application 2: Variation in w

This application is similar to the first,but with manipulation of the weight param-eter instead of the scale value. This appli-cation would be appropriate for studyingthe combined effects of two different sources.Since it can provide an interval scale of theweight parameter, it may be especially use-ful in the analysis of the many determin-ants of source effects.

A factorial design is employed, as in Ap-plication 1, but with the roles of w and sinterchanged. Each factor corresponds toone communication; the levels within eachfactor correspond to different sources towhich the communication is attributed.For a two-way design, the model becomes

Rtj = w0s0 + WK.-SH + wcysc, [4]

parallel to Equation 2.


The assumptions of Equation 4 are ana-logous to those of Equation 2, though per-haps more easily satisfied in practice. Therow communication is assumed to have thesame scale value regardless of which sourceit is combined with, and similarly for thecolumn communication. The weight ofeach communication depends on the sourceand will in general be different in each rowand column. Finally, as in all these ap-plications, it is assumed that the combiningof two stimuli within any cell of the designdoes not change the parameter values.

For a strict adding model, the analysis isidentical to that of Application 1. If thedata satisfy the model, therefore, they pro-vide equal-interval scales of the weightparameters. This application may thusbe useful in the analysis of source effects,though it should be recognized that it as-sumes a strict adding model.

Application 3: Variation in both w and s

Application 1 was concerned with howtwo communications are combined, andApplication 2 with how two sources com-bine. Application 3 is concerned with howone source and one communication com-bine. It may be particularly useful whenonly a single source-communication can begiven.

Mathematically, Application 3 is inter-esting since it rests on a multiplying modelinstead of an adding model. As a conse-quence, the model analysis requires somenew developments. A two-way factorialdesign is used again, but with the row factorrepresenting different sources and the col-umn factor representing different communi-cations. The model then becomes

TABLE 2HYPOTHETICAL DATA FOR SOURCE X COMMUNICA-

TION DESIGN TO ILLUSTRATE FUNCTIONALMEASUREMENT FOR A MULTIPLYING MODEL

= W0s0 + [5]

where wBl- is the weight of the source in rowi, and SGJ is the value of the communicationin column j. In contrast to Applications 1and 2, there is only one communication ineach cell of this design. The assumptionsrequired by Equation 5 are that the weightparameters depend only on the row and thescale values depend only on the column.

Equation S is a multiplying model, sincethe initial opinion term is just an additive

1234

MEstfe)

Communication

1

986S70

2

141286

101

3

2924149

194

4

2420128

163

5

4436201228

7

M

2420128

constant. Functional measurement formultiplying models has been discussed forpsychophysical judgment (Anderson,1970a), and it has been used to scale sub-jective probability and utility in decision-making experiments (Anderson & Shan-teau, 1970; Shanteau, 1970b). The sameapproach may be used here.

The hypothetical data of Table 2 willillustrate the procedure. Each entry is tobe considered as the attitude resulting fromone combination of source and communica-tion. The first step is to test whether thesedata follow the multiplying model of Equa-tion 5.

Test of fit. Testing the model would bestraightforward if the communication scalevalues were known. Plotting the entries inany one row as a function of the SGJ would,if Equation 5 was correct, yield a straightline with slope wRi. Although the icy arenot known, this idea provides the basis forsolving the problem.

A simple graphic solution may be ob-tained as follows. First, two communica-tions are assigned arbitrary values: inTable 2, the first two communications havebeen assigned the values 0 and 1 in the lastrow of the table. The observed means forthese communications, 7 and 10 in the table,are plotted as a function of these assignedscale values. These two points define astraight line, and each remaining communi-cation mean is then marked on this line atits proper elevation. The downward pro-jection of this point on the value axis is aprovisional estimate of the scale value of


that communication. Thus, if 19 is markedon the line joining 7 and 10, its projectionon the value axis, namely 4, is a provisionalestimate of the scale value of Communica-tion 3. In the same way, the scale values ofCommunications 4 and 5 are estimated as3 and 7 in the last row of the table.

The final and critical step is to plot thedata of each separate row as a function ofthese provisional scale values. If the modelis correct, these row curves will form afamily of diverging straight lines. Devia-tions from this pattern would infirm themodel.

To supplement this graphical test, anexact statistical test is also available byappropriate use of analysis of variance.Since the model predicts nonparallel curves,the Row X Column interaction is nonzero.However, if the model is correct, all theinteraction is concentrated in the LinearX Linear component, and the residual in-teraction should be nonsignificant (Ander-son, 1970a, p. 157).

Two extensions of this application de-serve mention. The first adds on a secondtwo-way design so that each cell containstwo such source-communication combina-tions. The analysis would then be similarto the duplex bets studied in Anderson andShanteau (1970). Another extension addson a third factor representing a secondsource variable so that each communicationis attributed to two sources. This wouldbe useful in the theoretical analysis ofsource combinations.

Functional scales. Verification of themodel simultaneously validates the pro-visional scale values used in testing it.Indeed, Equation 5 implies directly thatthe column means of the Source X Com-munication design are a linear function ofthe communication values, SGJ. Similarly,the row means are a linear function of thesource-communication weight, wm. Themarginal means of the factorial design thusprovide equal-interval scales of the stimu-lus parameters. The multiplying model isjust like the adding models in this respect.

Application 4: Variation in both w and s

The last application is a generalization ofApplication 1 in which a different source-communication is allowed in each row andin each column. It may thus be applicableto situations in which the communicationinteracts with the source, as in studies ofsource expertise.

A two-way factorial design is used again.The strict adding model then implies that

+ WmSRi + WcjScj, [6]

in which different weights and values areallowed in each row and in each column.The only restrictive assumption is that therow and column stimuli do not interactwhen combined in any cell. However,source and communication in any given rowor column may interact in any manner.

Even in this general case, the addingmodel still makes the parallelism prediction,Analysis of variance can thus be appliedjust as in Application 1. There is a loss inprecision since the functional scales do notseparate the weights and the scale values.Nevertheless, the row means still measuresomething useful, namely, wntSRi, which isjust the total effect of the given communi-cation.

Applications 1 and 4 bear a close relation.In practice, the row weight in Equation 2might depend on the scale value of thecommunication. It could not then be con-sidered as a constant, W-R, but would needto be taken as a variable, WR,-. The addingmodel predicts parallelism in either case. Inan averaging model, however, the analysisbecomes more difficult as will now be seen.

AVERAGING THEORY

There is increasing evidence for the im-portance and ubiquity of averaging pro-cesses in information integration. Thisfinding has fundamental importance in inte-gration theory. It affects every aspect ofan experiment, from general design andprocedure to theoretical interpretation.The critical evidence will be briefly noted,and then the four applications discussedabove will be considered from the averagingstandpoint.


Averaging versus Adding

Two main experimental paradigms havebeen used for critical comparisons betweenaveraging and adding. First, adding mildlypolarized to highly polarized stimulus in-formation decreases response polarity (An-derson, 196Sa; Anderson & Alexander,1971; Hendrick, 1968; Lampel & Anderson,1968; Manis, Gleason, & Dawes, 1966;Levin & Schmidt, 1970; Oden & Anderson,1971). This result eliminates a directadding formulation, though it might besaved by postulating a contrast effect.Thus, an adding model would predict adecrement if mildly favorable informationreceived a negative evaluation in the con-text of highly favorable information. Itseems doubtful that such contrast effectsplay an effective role with verbal stimuli(e.g., Anderson, 197la, 1971b; Anderson& Lampel, 196S; Kaplan, 1971; Tesser,1968; Wyer & Dermer, 1968), but thepossibility cannot yet be ruled out.

The second result is that adding informa-tion of the same value typically makes theresponse more extreme; this is the familiarset-size effect. Qualitatively, the set-sizeeffect accords with an adding process,though no adding formulation has yet givena quantitative account. More seriously,the set-size effect eliminates a simple aver-aging model in which a constant stimulusmean would produce a constant response.

The present averaging formulation ac-counts for the set-size effect by the use ofan initial opinion. The set-size function isthen a growth curve of somewhat differentform for serial presentation (Anderson,1959a) than for simultaneous presentation(Anderson, 1965a). In this form, the aver-aging model can give a good quantitativeaccount of the set-size effect (Anderson,1967).

This last point bears emphasis in tworespects since it has sometimes been mis-interpreted. First, the averaging formula-tion can account for both incremental anddecremental effects of added information,so there is no need to postulate two pro-cesses. Second, the averaging formulationhas given exact, quantitative accounts

of both the incremental and decrementaleffects.

An interesting appearance of the set-sizeeffect can be seen in an argument of M. J.Rosenberg (1968), who makes the plausibleargument that a given piece of informationthat could produce considerable opinionchange if the issue was new and unfamiliarwould have little effect if the issue was oldand familiar. Rosenberg interpreted thisargument against averaging as well as add-ing. However, it accords with the averag-ing set-size function on which the oldopinion, based on a considerable accumula-tion of information, would be near asymp-tote. More precisely, the old opinion, beingbased on much more evidence, would havea much greater weight parameter than thenew opinion. In the averaging formulation,the weight of the given piece of informationmust then be much less relative to the oldopinion, since the weights must sum to one.

Averaging Assumptions

Mathematically, the difference betweenadding and averaging models is simple.Adding models impose no constraints onthe weight parameters, whereas averagingmodels require the weights to sum to one.

Averaging always implies stimulus inter-action because of this constraint on theweight parameters. In an adding model,the effect of any one stimulus may be inde-pendent of the other stimuli. But in anaveraging model, the effect of any onestimulus is inherently dependent on thewhole set of information. In a certainsense, therefore, an averaging model hasgestalt qualities, since the role of each partdepends on the whole.

For present purposes, therefore, the as-sumption of no interaction will be used tomean that each stimulus has a natural orabsolute weight which, together with itsscale value, is constant across stimuluscombinations. The effective weight of eachstimulus is then its absolute weight dividedby the absolute weights of all the stimuliin the given combination. In this way,each application considered above is di-rectly convertible to an averaging model


by dividing by the sum of the weights, andthis procedure will be followed here.These effective or normalized weights sumto one for each stimulus combination.Mathematically, it is often convenient touse unnormalized weights at intermediatestages in the calculations or derivations.

Application 1

For this application, the weight WR wasassumed constant across rows, and theweight We was assumed constant acrosscolumns. Equation 2 then implies that thesum of the weights, w0 + WE + We, isconstant, the same in each cell of the design.Dividing each predicted attitude by thisconstant is equivalent to changing the unitor range of the response scale. Since thescale unit is arbitrary, adding and averagingare not distinguishable under the given as-sumptions. Both predict parallelism, andboth yield interval scales of the stimuli.

This equivalence of the two models dis-appears as soon as the weights vary acrossrows or columns. Not much is lost underthe adding model; it still predicts parallel-ism as discussed under Application 4 above.But since the sum of the weights will nowvary from cell to cell of the design, theaveraging model predicts systematic devi-ations from parallelism.

Because of this complication in the aver-aging analysis, experimental precautions tohelp ensure equal weighting may be worth-while. Of course, this may not be possiblewhen the stimuli vary naturally in weight.In the personality-impression task, for in-stance, the response to a combination ofmoderate and extreme negative adjectivesis displaced toward the extreme (Anderson,1965a, 1968b; Anderson & Alexander,1971).This directional result is consistent withthe hypothesis that the extreme adjectiveshave greater natural weight and is one pieceof evidence that favors the averaginghypothesis.

Application 2

The averaging model is quite differentfrom the strict adding model in this design.

Written as an averaging model, Equation 4becomes

(w0 + WE. + wCj). [7]

Since the denominator varies from cell tocell of the design, the parallelism predictionwill not hold. The deviations from parallel-ism will still show a systematic pattern,however, depending on the pattern ofweight parameters. The expected form ofthe nonparallelism can be studied by usingEquation 7 to determine how the differencebetween any two rows varies with columnweight. The mathematical analysis isfairly straightforward but too detailed toinclude here.

To illustrate the matter, consider a square designfor which the weights in row i and column i are equal.Suppose that the weights are arranged in increasingorder of magnitude, from left to right across columns,and from top to bottom down rows. Finally, assumethat wo, the weight of the initial opinion, is zero.(The design provides a partial check on this last as-sumption, since it implies that the entries in everycell along the main diagonal are constant, equal tothe simple mean value of the row and column com-munications. If wo is not zero, then averaging theorypredicts a trend along the main diagonal from so to-ward the mean of sn and so.)

In this design, the global shape of the set of pre-dicted curves is similar to a correlation ellipse, trun-cated at either end. Above the diagonal, the rowcurves converge to the right ; below the diagonal, therow curves converge to the left. The overall trendis upward if the column communication has greatervalue, downward if the row communication hasgreater value. The magnitude of the trend dependson the difference between the values of the row andcolumn communications. If these are equal, thenthe predicted response is the same in all cells.

A simple experimental realization of this illustra-tive design would be available with the personality-impression task. The row and column communica-tions would correspond to two sets of personality-trait adjectives describing a single person. Weightcould then be manipulated by specifying the occupa-tions of the sources (Rosenbaum & Levin, 1968,1969), for instance, or by otherwise varying thereliability of the information.

Application 3

Under the averaging hypothesis, Equa-tion 5 becomes

+ WRiSCj*)/(wt> + C8]


If w0 is zero, then J?,-y equals the scale valueof the communication regardless of thesource weight. This might seem odd, butwith no other basis for opinion, the com-munication must be taken at face value.Since this case is mathematically trivial, itwill be assumed that w» is not zero.

The analysis under the averaging hy-pothesis parallels that of Application 3above except in one respect. If Equation8 is averaged over rows, the marginal col-umn means are a linear function of the com-munication values. In practice, this meansthat the observed column means may beused as provisional estimates of the scalevalues in the bilinear test of fit. To thedegree that the model is validated, the col-umn means may be considered as intervalscales of the communication values.

The one change required by the averag-ing constraint comes in the estimation ofthe weight parameters. In the simplemultiplying model, the slopes of the bilin-earized curves are proportional to theweights, w-ni ; with the averaging constraint,they are proportional to Wfu/(wRi + w0).

Application 4

Only one case of Application 4, one thathas considerable importance, will be con-sidered in detail. The model for this casemay be written,

(w0 + WR + Wcy). [9]

This is the averaging form of Equation 6under the added restriction that the rowweight is constant.

Figure 2 illustrates the difference be-tween the adding and averaging models.These plots are for a 3 X 4 design forwhich the communication scale values arethose listed in Table IB. The left panel iscalculated on the assumption that the rowand column weights both equal one. Thesethree curves are parallel. The right panelis calculated on the assumption that therow weight is one, but that the columnweight increases with scale value as speci-fied in the figure legend. These curves arenot parallel.

Despite this nonparallelism, the rightpanel of Figure 2 shows two regularities.The first is qualitative: the curves converge

Q_o

cc.o

6 -

5

4

3

2

1

R3

SC3 SC4 Sr S'C4

FIG. 2. Illustration of parallelism prediction with equal weighting in leftgraph, nonparallelism with unequal weighting in right graph. (Each point isthe predicted opinion resulting from two communications whose scale valuesare given in Table IB. In the right graph, the weight of the row communicationis 1, while the weight of the column communication increases with scale valueaccording to the formula, 1 + .2soj-)


toward the right, that is, as the scale valueincreases. This illustrates a general con-vergence prediction of the differentialweighting model : Whenever the weights ofthe informational stimuli are directly re-lated to their magnitudes, this same con-vergence pattern will be obtained. If thedesign were extended to include stimuliwith negative values, this pattern wouldreappear as a convergence from the middletoward the left. Bilateral asymmetrywould reflect differential weighting of posi-tive and negative stimuli.

The second regularity in the right panelof Figure 2 is quantitative; the differencebetween any two row curves is a constantmultiple of the difference between anyother two row curves. This can be seenmore readily by reference to Equation 9.The difference between the first two rows is

— RU = — SRI)/(w>0 + wn Cj). [10]

If the difference between the first and thirdrows is expressed similarly, the ratio ofthese two differences is

(Rv - Rii)/(Rti - Rn~)= (SR2 — SRI)/(SRS - SRI), [lla]

which is constant, independent of columns.Equation lla can thus be rewritten,

(Rv - Rii) = a(Rv

= 1,2,- [lib]

where a is a constant. This result holds ingeneral so that any two sets of row differ-ences should plot as straight-line functionsof each other. This property could be usedas a rough graphical test of fit.

Another graphical test, somewhat sim-pler, can be obtained by plotting the en-tries in each column as a function of therow means. The model implies that eachcolumn should plot as a straight line exceptfor sampling error.

An interesting extension of bilinearity analysis(Anderson, 1970a, p. 157) provides an exact statisti-cal test. The computing procedure given there maybe followed exactly with these modifications. Firsta reduced data matrix is obtained by subtractingthe column mean from all entries in each column.This has the effect of reducing Equation 9 to the

form of a simple multiplying model. All furthercalculations are done in terms of this reduced matrix.The comparison coefficients for rows are just the rowmeans, since the grand mean is zero. To get thecomparison coefficients for columns requires a detour,since all column means are zero in the reduced ma-trix. For this purpose only, the sign of all cell en-tries is ignored; the column comparison coefficientsare then obtained as in the cited reference as columndeviations from the grand mean in this temporarymatrix of absolute values. These comparison co-efficients allow calculation of the Linear X Linearcomponent of the interaction. The residual inter-action should then be nonsignificant. Its df equals(r — 2)(c — 1) — 1, where r and c are the number ofrows and columns; the initial reduction of the datamatrix loses one degree of freedom per columnthrough estimating an additive constant in eachcolumn.

The error term requires a brief comment. Thewithin-cells error would be used for both the LinearX Linear component and the Residual interactionfor the case of independent groups in each cell and,typically, for single subject analysis as well. Re-peated-measurements designs, with each subject inall conditions, are more complicated. If the analy-sis is to be made over subjects, the above procedureneeds to be applied to each subject. The overallRow X Column interaction is split into LinearX Linear and Residual components using the meansof the individual comparison coefficients. In paral-lel, the Subject X Row X Column interaction issplit into Subjects X Linear X Linear, and SubjectsX Residual. Each component of the overall inter-action is then tested against its interaction withsubjects.

Two functional scales are also available.If Equation 9 is averaged over columns, itbecomes a linear function of the row scalevalue, SRJ. As in Application 1, the rowmarginal means provide an equal-intervalscale of the values of the row communica-tions.

Furthermore, Equation 10 indicates thatthe row difference is an inverse measure ofthe column weight, ivcj- Thus, the recipro-cals of the row differences can provide aninterval scale of the column weight param-eter as shown in Equation 12:

WCj =— — SE2)/[12]

The optimal statistical procedure for esti-mating these weights is not known, how-ever.

Differential Weighted Averaging

In the application just considered, theweight parameter was allowed to vary arbi-


trarily as a function of the scale value.There is increasing evidence that such dif-ferential weighting is more the rule than theexception (Lampel & Anderson, 1968;Oden & Anderson, 1971), and differentialweighting seems especially likely in attitudechange experiments. It is fortunate, there-fore, that some direct analyses and estima-tion methods are possible.

The importance of this result can be il-lustrated by the date ratings of Lampeland Anderson (1968) which illustrate thata cognitive interaction of some complexitycan be handled simply. Boys described bya photo and two personality-trait adjec-tives were rated as coffee dates by collegegirls. The data provided a critical test ofaveraging-adding in favor of averaging.In addition, the Adjective X Photo inter-action was very large, with the adjectiveshaving a greater effect with a positive thanwith a negative photo. This was inter-preted as a discounting effect: girls do notwant to be seen dating unattractive boysno matter how nice they are; as their physi-cal appearance improves, their personalitycharacteristics become more important.In theoretical terms, then, the weight ofthe photo is inversely related to its value.

In this experiment, the adjectives corre-spond to the rows, the photos to the col-umns of Application 4. Figure 1 of thecited article plots two difference curvesanalogous to Equation 10. The uppercurve is almost exactly a constant multipleof the lower curve, in agreement with Equa-tions lla and lib.

Conjunctive and disjunctive models (e.g., Coombs,1964; Torgerson, 1958) can also be represented asdifferential weighted averaging models. The stand-ard conjunctive model sets a criterion on each ofseveral dimensions. Only if the criterion is exceededon all dimensions simultaneously is a positive deci-sion made. The present approach would replace thecriterion by a weighting function that had highweights below some threshold region, diminishing tolower weights at higher levels of the scale value.Because the averaging model requires the weightsto sum to one, any stimulus variable that fell belowthe criterion could dominate the response and pre-vent a positive decision. The averaging model thusprovides a more general and flexible analysis. Inparticular, it replaces the somewhat artificial pointcriterion by a band or region.

It should also be noted that scaling is an integralpart of psychological theory in the present approach.The standard treatments of conjunctive and dis-junctive models, in contrast, assume that stimulusscale values are already at hand. But if weight andscale value are inversely related, as in the date-rating experiment, this critically affects the scalinganalysis.

It has been suggested that a strict adding modelshould have been applied to the main data of thedate-rating experiment. The observed interactionsthen would be interpreted as an artifact of a merelyordinal response scale, to be eliminated by appropri-ate monotone transformation (Anderson, 1962b;Bogartz & Wackwitz, 1970; Kruskal, 1965). Thissame argument holds more generally for the aver-aging analysis of Application 4. A convergenceinteraction could reflect a nonlinear output function(Bogartz & Wackwitz, 1970, 1971) rather than a realaveraging effect. Because of their simplicity, strictadding models have been favorites in abstract mea-surement theory, and they have many mathemati-cally convenient properties. However, the empiricalevidence summarized under Averaging versus Add-ing above raises considerable doubt about the vali-dity of strict adding models.

RELATIONS TO OTHER THEORIES

This section compares integration theorywith several other theories of attitudechange, mainly those that have attemptedsome degree of quantitative analysis. Themain purpose of these comparisons is toshow how integration theory handles vari-ous traditional problems in attitude theory.

Balance Theory

As an organizing concept, a principle ofinformation integration has certain ad-vantages over the principles of balance andcongruity (Anderson, 1968a). Criticalcomparisons by Lindner (1970, 1971) havesupported integration theory. This sectionwill illustrate the theoretical comparison inmore detail. Since the most extensive at-tempt to relate balance theory to attitudechange is that of Feather (1964, 1967), onlyhis development will be considered here.A recent review of balance theory is givenby Zajonc (1968). Mention should also bemade of the work of Wiest (1965), who hasattempted to quantify the strengths of therelations, and of Newcomb (1968), whohas attempted to give a more realistic def-inition of balanced states.


S R

Case 3 Cose 4

FIG. 3. Communication graphs, with S, C, I, and R denoting Source, Com-munication, Issue, and Receiver. (Solid lines denote a positive association orattitude; broken lines denote a negative attitude.)

Feather bases his analysis on the graphdiagrams studied by Cartwright and Har-ary (1956) and illustrated in Figure 3. Thesolid arrow connecting C to I means thatthe communication (C) is favorable towardthe issue (I) in each of the four cases. Simi-larly, the solid arrow connecting S to Imeans that the receiver (R) considers thesource (S) to be favorable toward the issueprior to receiving the communication. Thesolid line connecting S to C simply meansthat the communication comes from thesource. The initial attitudes of the receivertoward the issue and the source are denotedby s0 and 70) respectively. These featuresare the same in all four diagrams.

Attitude toward issue. For each diagramin Figure 3, the receiver gets two pieces ofinformation about the issue: the initialstand of the source and the favorable com-munication from the source. For simplic-ity, it will be assumed that the prior standof the source has already been integratedand become part of So- The integrationequation for the attitude after receipt ofthe favorable communication is then

] r- j ~ ~]

a weighted sum or average of the initialattitude, So, and the scale value of the com-munication, SG. The effective weight, Wi,of the communication will depend on prop-erties of the source and communication asdiscussed elsewhere.

The four cases in Figure 3 differ accord-ing as initial attitudes of the receiver to-ward the source and issue are positive

(solid arrow) or negative (broken arrow).These will now be discussed in turn.

Case 1: Here the receiver's initial attitudeis positive toward the source, negative to-ward the issue. Figure 3 then representsan unbalanced structure, and balancetheory postulates a tendency to restorebalance. In integration theory this tend-ency is not a postulate but a deduction. InEquation 13, s0 is negative, because theinitial attitude toward the issue is negative,but both Wi and SG are positive. Accord-ingly, Equation 13 implies directly thatthe postcommunication attitude will beless negative, perhaps even positive.

This is no more than common sense, ofcourse, but integration theory differs frombalance theory in two important ways.First, the final state need not be balanced;the postcommunication attitude may bepredictably negative. Second, integrationtheory allows a quantitative analysis of themagnitude of attitude change and its de-pendence on various stimulus parameters.It thus takes into account the strengths ofthe relations which balance theory is unableto handle satisfactorily.

Case 2: Here the receiver's initial atti-tudes toward source and issue are bothpositive. Since there is no imbalance in thediagram, balance theory has no basis onwhich to predict a change in attitude.

Integration theory does predict a change,following Equation 13. Under the averag-ing model, moreover, the changed atti-tude will be more positive or less positive,according as Sc, the communication value,


is more or less positive than 5o, the initialattitude.

Case 3: Here the receiver is initiallynegative toward source and issue both asindicated by the broken arrows in Figure 3.Since the SRI triad is balanced, balancetheory again lacks a basis on which to pre-dict a change in attitude.

Under integration theory, the theoreticalanalysis depends on whether Wi is positiveor negative. That Wi may be positive evenwith a negative source is indicated by thepositive attitude change found with lowcredible sources (see Hovland et al., 1953;McGuire, 1969). If iv\ is positive, then thereceiver's attitude toward the issue will be-come less negative. Indeed, it may evenbecome positive, thus converting a bal-anced state to an imbalanced state.

Case 4: Here the receiver has a negativeattitude toward the source but is positivetoward the issue. This unbalanced statecould become balanced if either the receiveradopted a positive attitude toward thesource, or else a negative attitude towardthe issue. Balance theory does not predictwhich will occur.

For integration theory, the theoreticalanalysis again depends on whether w\ ispositive or negative. If Wi is negative, thereceiver's attitude toward the issue will be-come less positive, and hence more bal-anced. However, if Wi is positive, then thereceiver's attitude toward the issue becomeseven more positive, increasing the imbal-ance. As in Case 3, this allows a criticalqualitative test between balance theoryand integration theory.

Attitude toward source. Integration theory ana-lyzes attitude toward the source in much the sameway as just illustrated for attitude toward the issue.In the diagrams of Figure 3, there are three relevantinformational stimuli, including the receiver's priorattitude toward the source. Thus, the communica-tion attributed to the source constitutes a piece ofinformation about the source; as such it has a cer-tain weight and scale value. The same holds for theinitial stand attributed to the source. Both thesepieces of information are then to be integrated intothe receiver's initial opinion about the source, andthe integration process is assumed to be essentiallythe same as for the issue.

There are, however, important differences in de-tail, especially in the valuation process, that reflectthe asymmetry of the source-issue relation. That

the source favors the issue does not mean that theissue favors the source, for instance. In addition,the valuation process will depend on the dimensionof judgment. In particular, the parameters of theinformational stimuli will be different if the receiverjudges the position of the source on the issue thanif he makes an evaluative judgment of the source.

Evaluation of the communication. Judgments ofthe communication, such as its position on the issue,or its fairness, will of course depend in detail on thecontent and structure of the communication. Theywill also, as is well known, depend on the attitude ofthe receiver and his valuation of the source, and thisdependence will be discussed briefly.

If the receiver is asked to judge the position of thecommunication on the issue, he has two main piecesof information to rely on. One is his opinion, ex-plicit or inferred, about the source's stand on theissue independent of the communication. The otheris the content of the communication per se. Underthe simplest theoretical analysis, the judgment ofthe communication will then be a weighted averageof these two pieces of information. Loosely speak-ing, the judgment might be considered a compromisebetween what the source actually said and what thesource was expected to say; certainly this is a rea-sonable strategy from the subject's view.

From this standpoint, the theoretical analysis ofthe communication parallels that just given forjudgments of the issue. For instance, if the initialattitude toward the source is negative, the communi-cation will ordinarily be seen as less positive whenattributed to the source than when considered alone.Here as before, a tendency toward balance arises asa deduction from integration theory.

This simple averaging analysis does not allow forthe seeming fact that the judged position of a com-munication may also depend on the receiver's atti-tude toward the issue. This is a complicated prob-lem (see Kiesler, Collins, & Miller, 1969, pp. 264 flf.)that will be briefly considered under Assimilation-Contrast Theory, below.

Judgments of the fairness or plausibility of thecommunication have also been considered (see, e.g.,Brigham & Cook, 1970; McGuire, 1969). The gen-eral finding is that communications more discrepantfrom one's own position tend to be judged as lessfair. This commonsense result merits a common-sense explanation: if the receiver is at all attached tohis own position and considers it correct, he willnaturally judge a discrepant communication as in-correct, hence misleading, and hence unfair. Atthe same time, many experimental studies of opinionchange do not involve firm opinions, and in suchcases fairness would not necessarily be affected.Thus, it seems more promising to look for a sociallearning base for such evaluations rather than aprinciple of balance.

Summary comments. The main conclu-sion from the preceding analysis is that atendency toward balance may be derivedfrom a principle of information integration.


Further, the integration principle is moregeneral since it also accounts for opinionchange in balanced situations. Only cer-tain illustrative situations have been con-sidered, of course, but much the same analy-sis would seem to apply to the numerousother graph structures considered byFeather (1967).

Integration theory has additional ad-vantages. Feather (1964, 1967) has notedthat major unresolved problems in balancetheory include allowing for the strengths ofrelations, for the importance of the issue,as well as for individual differences. Theseproblems are handled in a natural way, interms of the w and s parameters of integra-tion theory. Moreover, functional mea-surement technique is specifically orientedtoward measurement at the level of theindividual.

Heider (1958) has stated that "Formula-tion in terms of equifinality [balanced endstate] is more parsimonious than formula-tion in terms of single conditions andeffects [p. 207]." Integration theory takesthe opposite road to parsimony, stressingthe primary importance of detailed analy-sis, both theoretical and experimental, ofstimulus conditions and their effects.

Congruity Theory

Congruity theory (Osgood & Tannen-baum, 1955; Tannenbaum, 1967, 1968)postulates an averaging model of the formof Equation 1 (S. Rosenberg, 1968). It is,however, a very specialized averagingmodel, since it requires the weight param-eters to be specific functions of the scalevalues or polarities of the stimuli. For twostimuli of values si and $2, congruity theorypostulates that Wi = S i \ / ( \ S i \ + \ s ^ \ ) ,w2 = |s2|/(|si| + |sa |) . This formulationmakes the weight increase with the scalevalue, which would be reasonable in manysituations. It also requires a neutral stimu-lus to have zero weight, which is clearlywrong.

In the present formulation, the weightparameter can depend on factors other thanstimulus value. For instance, one can ex-perimentally manipulate the credibility orreliability of the information without

thereby affecting its scale value. This indi-cates that congruity theory has an inade-quate conceptual base. Moreover, con-gruity theory has not been able to handlethe set-size effect, in which the additionof information of equal value increases theextremity of the response (e.g., Anderson,1959a, 1965a, 1967). An extensive discus-sion of this and related problems is givenby Smith (1970).

Tannenbaum (1967) has recently dis-cussed two experiments that he interpretsto support congruity theory and to infirman information-processing approach. How-ever, both experiments can be treated as2 X 2 designs for which integration theorypredicts zero interaction, in agreement withthe data. An earlier experiment by Tann-enbaum and Norris (1965) also showed anonsignificant interaction, though there thetheoretical analysis is less clear.

In one experiment (Tannenbaum, 1967,Table VI), each condition contained onemessage from a positive source, one mes-sage from a negative source. The fourconditions differed in that they containedtwo positive messages, two negative mes-sages, or one of each polarity. The inter-action term would apparently not have ap-proached significance, in agreement withintegration theory. The data imply a nega-tive weight for the negative source, thoughthis may reflect the covariance adjustment.

In the other experiment, the four experi-mental conditions received either the sameor different messages, from either the sameor different sources. In an informationalanalysis, redundant information requires aredundancy parameter, in this case forsame-versus-different message as well as forsame-versus-different source. These re-dundancy parameters need not be evalu-ated, but can be incorporated directly in theformal model. The adding model then pre-dicts zero interaction, and the averagingmodel makes approximately the same pre-diction. Tannenbaum's data (1967, TableV) show a very small interaction term thatwould evidently not have been significant.

Neither experiment, therefore, poses anydifficulty for information integration theory.Indeed, integration theory goes beyond


congruity theory to make quantitative pre-dictions in both cited experiments.

Integration theory implies that congru-ity, like balance, will generally increase.A congruity principle, or at least a congru-ity tendency, is thus a deduction from amore general principle of information inte-gration. The detailed supporting analysisfor this claim has already been given in thediscussion of balance theory. Here it maybe noted that integration theory avoids afundamental criticism raised by Abelson(1963). If a positive source makes a posi-tive statement about some issue, the evalu-ation of source and issue will approach eachother. The cause, according to congruitytheory, is a pressure toward congruitywhich exists as long as the source and issueevaluations are unequal. This makes itawkward to explain why complete congruityis seldom if ever obtained. For integrationtheory, there is no difficulty. The changeis effected by the information in the com-munication; once this is absorbed, nofurther change is implied and there is noreason to expect complete congruity be-tween source and issue.

Assimilation-Contrast Theory

The present theory of opinions and atti-tudes is in large part a theory of socialjudgment. Although this section is meantto compare integration theory with otherquantitative formulations, comparison withassimilation-contrast theory (Sherif & Hov-land, 1961; Sherif, Sherif, & Nebergall,1965) is appropriate since it also empha-sizes judgmental processes. Summariesand evaluations of their theory have beengiven by Insko (1967) and Kiesler et al.(1969). Here the two approaches will becompared in the context of an interestingrecent experiment by Rhine and Severance(1970).

Rhine and Severance studied three vari-ables: source credibility, ego involvement,and discrepancy between the person's ini-tial attitude and the position advocated bythe communication. For a single com-munication with weight w\ and value s1(

the postcommunication attitude can bewritten as

R = WOSQ + [14]

where s0 is the initial opinion, with weightw0. In an averaging model, the weights arerequired to sum to one. This effect can beachieved by letting w\, and Wo = 1 — w\ bethe relative weights. Then Equation 14can be rewritten as

R = [15]

From Equation 15, the change in attitude isseen to be just w\(si — SQ). Accordinglythe theoretical analysis devolves on thedeterminants of "w\ and of (s\ — SQ).

Source credibility will affect w\. A morecredible source would correspond directlyto a larger value of w\ and would producemore attitude change.

Ego involvement was defined by choiceof issue, either the proposed tuition increasein the University of California, Riverside,where the experiment was run, or the de-sired size of the city park in Allentown,Pennsylvania. For this particular manip-ulation, ego involvement corresponds tow0, the strength of the initial opinion.Thus, Wi would be lower for the higherlevel of ego involvement and less changewould occur.

The discrepancy variable, (si — s0), wasmanipulated by using three different dollaror acre values in the communications givento different groups. With no further quali-fication, Equation 15 predicts that amountof opinion change will be a linear function ofthe discrepancy, (si — s0). This was foundto hold for the parks issue though not onthe tuition issue.

Integration theory includes a process ofinconsistency discounting (Anderson &Jacobson, 1965) in which inconsistent, in-formation is given decreased weight. Forexample, a communication attributed to ahighly credible source would tend to be dis-counted if it was inconsistent with the per-son's previous opinion about the source'sposition. In the same way, a communica-tion will tend to be discounted when it isinconsistent with fact or with the person'sown previous opinion on the given issue.


Accordingly, the predicted effect of thediscrepancy variable needs to be consideredin the light of the experimental task. Forthe parks issue, the subjects were told thatthe average park size was 20 acres for acity with a little less than half the 106,400population of Allentown. The highest ad-vocated figure was 240 acres which wouldnot be expected to evoke any inconsistencyreaction. On that basis, the obtained linearrelation between advocated change and ob-tained change is in accord with expectation(Anderson, 1959a; Anderson & Hovland,1957). Theoretically, linearity is a directconsequence of the averaging hypothesis.

The highest advocated increase in tuitionwas $600 which was very high, especially inview of the long tradition of free tuitionthat prevailed prior to the present state ad-ministration. For the tuition issue, Wiwould decrease as (si — 5o) increased. Thepredicted change, being the product ofthese two factors, would accordingly in-crease at first and later decrease as Si be-came more discrepant from 5o.

The inverted-U relation obtained for thetuition issue by Rhine and Severance, aswell as similar results obtained by others(e.g., Aronson, Turner, & Carlsmith, 1963;Bochner & Insko, 1966), is thus consistentwith integration theory. It should benoted, however, that a firm prediction ofthe later decrease depends on having suffi-ciently large values of the discrepancy vari-able. Rhine (personal communication,1970) has suggested that this was the caseon the ground that the discrepancies ex-tended well into the latitude of rejection.

In their Table 5, Rhine and Severancelist five predictions about attitude changeand conclude that assimilation-contrasttheory accounts for three of these whiledissonance theory accounts for two. Inte-gration theory, on the analysis just given,agrees with the data in all five cases. Thisanalysis is post hoc, of course, but it is notad hoc; no special assumptions were madein applying the integration model. Rhineand Severance also provide data on sourceand message evaluation that may be ana-lyzed in the manner indicated in the sectionon balance theory.

Inconsistency discounting is central inthe present analysis of the discrepancy vari-able. Almost all other theories of attitudechange postulate some process that has thesame general effect (see Insko, 1967, Ch.3). None of these is too satisfactory, sincetheir application depends more or less oncommon sense. Integration theory has oneadvantage, since it can make definitequantitative predictions about the effects ofcombining two communications.

The heavy dependence of the Sherif-Hovland ap-proach on concepts of assimilation and contrast is oftheoretical concern for several reasons (see Insko,1967; Kiesler et al., 1969; Upshaw, 1969). Assimila-tion-contrast is considered again later, and only twopoints will be made here. Both bear on a problemmentioned in the discussion of balance theory;namely, the effect of a person's own opinion on hisjudgment of the position of a communication.

Sherif and Hovland claim that people with strongopinions tend to see communications that portraymarkedly different opinions as even more discrepantthan they "really" are, a contrast effect. Suchclaims are beset by interpretational difficulties.Denning the "real" position of the communication interms of responses of other people is a dubious pro-cedure. Within functional measurement theory,the scale value of the communication is unique toeach person; that one person's evaluation differsfrom that of another does not mean that either hasdistorted the position of the communication. Thisview is consistent with Upshaw's (196S, 1969)explanation in terms of a variable zero point in thejudgment scale. In general, comparisons betweendifferent populations can be most difficult (Ander-son, 1963), and this is no less true when the popula-tions are single people.

It is also possible that such displacement effectsrepresent composite judgmental processes. For ex-ample, the overt judgment of the communicationmay be a weighted average of its position on theissue, and of the felt position, or perhaps of the socialevaluation of the person to whom the statement isattributed. For many political and social issues,such a judgmental process would appear to produce"contrast" for positions far from that held by thejudge, and "assimilation" for positions near thatheld by the judge. On this basis, apparent contrastin evaluation of discrepant communications wouldbe expected from Dawes' (1971) finding that personswith opposite points of view are thought to be moreextreme than they are in fact. A related model foran assimilation effect has been applied to componentjudgments in impression formation with some suc-cess (Anderson, 1966a; Kaplan, 1971).

Similarity-Attraction Model

An extended series of experiments byByrne and his associates (see Byrne, 1969)


has supported, under certain experimentalconditions, the hypothesis that interpersonalattraction is a linear function of proportionof similar attitudes. In the typical experi-ment, the subject receives a form purport-ing to describe the attitudes of a stranger onpolitical affiliation, drinking, and similarissues. These forms are constructed to havespecified numbers of attitudes that aresimilar and dissimilar to the attitudes of thesubject. The subject's response is a ratingof how much he would like the stranger.

This interpersonal attraction task isquite similar to the personality-impressiontask studied by the writer (Anderson, 1967;Byrne, Lamberth, Palmer, & London,1969). It is appropriate, therefore, to askhow integration theory might apply to theinterpersonal-attraction task. Of the num-erous interesting results, only one or twocan be considered here.

From the view of information integrationtheory, each item on the form constitutes apiece of information about the stranger,much the same as a trait adjective. Assuch, it has a weight and a scale value alongthe dimension of judgment. Let wp and spbe the weight and value of an item markedsimilar, and let wa and sn be the weight andvalue of an item marked dissimilar. Sup-pose there are N items altogether of whichk are marked similar. Under the addingmodel, the theoretical expression for theattraction response is then

R = kwpsv + (N - k)wnsn. [16]

If the number of items marked similar isincreased by one, k would be replaced byk + 1 in this equation. The change inresponse is then the difference,

AR = — wnsn [17]Since AJ? does not depend on k, it followsthat R is a linear function of k, and hencealso of k/N, the proportion of similar items.Under the given assumptions, therefore,Byrne's linearity result is consistent withprediction from integration theory. Moredirect empirical support has been obtainedby Kaplan and Olczak (1970) who em-ployed a factorial integration design as inApplication 1.

The adding model of Equation 16 restson the assumption that the similar itemshave equal value and weight, and so alsofor the dissimilar items. If these assump-tions do not hold, the linearity predictiondoes not follow. However, it would stillbe possible to use Application 4 of the addingmodel to get a parallelism prediction.

If the averaging model holds, the rightside of Equation 16 must be divided by thesum of the weights, kwp + (N — k)wn.The linearity prediction then holds only ifwp = wn. Deviations from linearity wouldthen be expected to the degree that similarand dissimilar items are differentiallyweighted. This possibility deserves furtherconsideration since the personality-traitstudies argue for an averaging model.

Two important differences between inte-gration theory and Byrne's formulationcan be illustrated in the Byrne and Rhamey(1965) experiment. In addition to the in-formation about the stranger's own atti-tude, the subjects also received informationabout the stranger's evaluation of the sub-ject's own intelligence, adjustment, etc.To handle two sources of information, theattraction equation was modified so that

attraction toward X is a positive linear functionof the sum of weighted positive reinforcements(Number X Magnitude) received from X dividedby the total number of weighted positive andnegative reinforcements received from X [Byrne &Rhamey, 1965, p. 887].

This differs from the integration model inseveral respects. For instance, the scalevalues, which correspond to their "rein-forcements," do not appear in the denomin-ator of the integration equation.

The Byrne and Rhamey experiment hasspecial interest, since it employed a two-way design in which the interaction wassignificant, contrary to the simple integra-tion model. Inspection of their datasuggests that the interaction results from adiscounting of the attitude-similarity infor-mation in the context of the favorable eval-uation of the subject. The value of theircontrol condition in supporting this inter-pretation deserves particular mention as auseful methodological device.


It should be noted that Byrne and Rha-mey also predict no interaction (see Table5, Byrne & Rhamey, 1965). That they gota close fit to the linear function despite theinteraction illustrates the limitations ofregression analysis discussed in the nextsection.

The second difference between integra-tion theory and Byrne's formulation is morefundamental. As illustrated in the abovequotation, Byrne considers the attitude-similarity items to be reinforcing stimuli.Integration theory considers them to beinformational stimuli, a view that is sup-ported by the work of Himmelfarb andSenn (1969) on judgments of social class.

This distinction between informationalstimuli and reinforcing stimuli would holdno less in real social situations. From thepresent view, giving praise or blame doesnot necessarily act as a reinforcing stimulusfor the attraction response to the source;it may simply provide an informationalstimulus which is integrated into the opin-ion about the source. In applicationsto learning (Anderson, 1969b; Anderson &Hubert, 1963; Friedman et al., 1968), inte-gration theory thus appears as a cognitive,information-processing theory somewhat inthe sense of Tolman rather than an S-Rreinforcement theory in the sense of Hullor Skinner.

Summation Theories

Certain kinds of integration tasks evi-dently require strict adding rather thanaveraging models. For example, the valueof a commodity bundle might be taken asthe sum of the values of its components(e.g., Bock & Jones, 1968; Gulliksen, 1956),possibly with a law of diminishing returns(Shanteau, 1970b). The addition of onecommodity to the bundle would thus in-crease the total value. For attitude changealso, an adding process is intuitively at-tractive, on the analogous argument thatthe addition of favorable informationshould increase the favorableness of theresponse.

The most vocal attempt to support anadding model for attitude change has beenmade by Fishbein and his associates.

Triandis and Fishbein (1963) used a per-sonality-impression task to compare asummation model with congruity theory.Mean correlations between observed andpredicted were .65 for the summation model,.53 for congruity theory. Two later ex-periments (L. R. Anderson & Fishbein,1965; Fishbein & Hunter, 1964), also onpersonality impression formation, showedsimilar support for a regression model overthe congruity model.

For some reason, this disconfirmationof congruity theory was generalized to in-clude all averaging models on the one hand,and all balance-consistency theories on theother. But congruity theory is a veryspecialized averaging model as alreadynoted. Moreover, general balance theorycarries no commitment to adding or aver-aging (Abelson, 1968a, p. 123; Anderson1968a). M. J. Rosenberg (1968) alsodiscusses this matter.

One further piece of evidence was givenby Fishbein and Hunter (1964). Withserial presentation of personality adjectives,they found that the addition of adjectivesof essentially equal value increased the ex-tremity of the response. This set-sizeeffect contradicts the simplest form of anaveraging model. However, essentiallythe same result had been obtained in previ-ous work on attitude change (Anderson,1959a) and was interpreted to result fromthe averaging in of an initial opinion.Later work has supported this interpreta-tion (e.g., Anderson 1965a, 1967; Anderson& Alexander, 1971; Hendrick, 1968; Oden& Anderson, 1971).

It should be emphasized that a quantita-tive model can be used to good purpose inan essentially qualitative way as exempli-fied by the summation formulation used byM. J. Rosenberg and by Peak. Theirmeans-ends formulation looks at the con-sequences or properties of an issue or object.Each consequence is considered to have acertain value for the person (analogous tothe present 5 parameter), and also a "per-ceived instrumentality" (Rosenberg, 1960)or "judged probability" of occurrence(Peak, 1955) (analogous to the present wparameter). Attitude toward the issue or


object is then simply 2ws, an adding form-ulation that seems to be conceptuallysimilar to that used by Fishbein (see Insko,1967, pp. 136, 197). Rosenberg tested thisformulation by using posthypnotic sug-gestion to change attitudes on certain issues,and found associated changes in the corre-sponding w and 5 values. Although thiswork has been criticized on the ground thathypnosis is even less understood than at-titude change, there is no doubt about itsgreat interest and potential.

Regression-Correlation Formulations

Much work on information integration,especially in clinical judgment, has restedon multiple regression and correlationanalysis (e.g., Goldberg, 1968; Hammond,Hursch, & Todd, 1964; Hoffman, 1960;Meehl, 1954, 1960; Triandis & Fishbein,1963; Tucker, 1960; Wishner, 1960; Wyer,1969). This approach has suffered fromtwo serious shortcomings.

In the first place, the correlation-regres-sion analyses that are reported seldom in-clude a test of fit of the linear regressionmodel. It might seem that high correla-tions between predicted and observed arerelevant evidence. However, very highcorrelations are virtually guaranteed bythe usual experimental designs, even witha seriously defective model (Anderson,1962a). Adequate assessment must attendto the discrepancies from the model predic-tions.

That discrepancies from an adding modelcan be important despite high correlationsis illustrated in Sidowski and Anderson(1967). Subjects judged the desirabilityof working at certain occupations in cer-tain cities. An adding model was applied,and the correlations between predicted andobserved were .986 and .987 in two experi-ments ; yet there was a sizable interactionlocalized at the occupation of teacher inthe least desirable city. Similarly, themodel-data correlation for the date ratingsdiscussed above (Lampel & Anderson,1968) was .985 despite a strong AdjectiveX Photo interaction. Even in an experi-ment designed specifically to produce alarge configural effect (Anderson & Jacob-

son, 1965, Condition 2), the correlation was.977. In all these experiments, the dis-crepancy was clearly visible as a nonparallel-ism, and was readily picked up by theanalysis of variance.

Thus, the present approach leads to adifferent view from that of Goldberg's(1968) review of linear models in clinicaljudgment. Goldberg considers three inter-pretations of the general finding that hu-man judges are seldom better than linearprediction models, and suggests the mostattractive interpretation to be that judgesreally behave configurally but that thelinear regression model is so powerful thatit obscures the real configural processes.The results cited in the previous paragraph,as well as related work, point to a fourthinterpretation: A linear-type integrationmodel holds in many situations, but thereare certain conditions that produce configu-ral response; further, analysis of variancehas ample power to detect configuralitywhen it occurs (Anderson, 1969a; Slovic,1969).

The second difficulty with regression-cor-relation is more fundamental. Regressionanalysis typically proceeds under twoscaling assumptions: that the stimulusvalues are known, and that the overt re-sponse is on an equal-interval scale. Theseassumptions naturally come under suspi-cion if the linear regression model does notfit well. Nonlinearity may be nothingmore than an inappropriate stimulus scale.For if the ostensible stimulus scale is notequal interval, then a linear function of thetrue subjective values will appear to benonlinear. Similarly, apparent configural-ity may not represent true interaction butonly an inappropriate response scale (An-derson, 1961a, 1962b; Bogartz & Wackwitz,1970). Without a theory of measurementto support the scaling assumptions, inter-pretations in terms of nonlinearity or con-figurality rest on uncertain ground. Theadvantage of functional measurement the-ory is that it gives a unified approach tothese problems.

This brief discussion should not obscurethe great usefulness of regression analysisin certain practical prediction problems.


As Yntema and Torgerson (1961) indicate,systematic discrepancies from a simpleadditive rule of combination may not beserious in certain man-machine systems.Much of the work on clinical judgment canbe viewed from a similar standpoint ofpractical prediction. Unfortunately, thereseems to be an overwhelming temptationto generalize from product to process, thatis, from prediction to understanding. Goodprediction does not imply good under-standing, as the correlation coefficientsquoted in the third paragraph of this sub-section show. When the main concern isto understand the psychological processesthat underlie the judgment, any systematicdiscrepancy may be meaningful and impor-tant.

It should also be emphasized that it ispossible to apply regression analysis to thequestion of goodness of fit, as well as to themeasurement question. Analysis of vari-ance and multiple regression are both ap-plications of the general linear hypothesisof mathematical statistics and have con-siderable similarity. However, the typicalregression design corresponds to a highlyconfounded factorial design; therefore, dis-crepancies from prediction are generallydifficult to localize and interpret. More-over, nonindependence of the beta weights(Darlington, 1968) can complicate the stim-ulus scaling. On the other hand, regressiondesigns can be very efficient, since they re-quire far fewer observations than a com-plete factorial design. An attempt to applymultiple regression to attitude measure-ment has been made by Ramsay and Case(1970), though their approach assumesthat the stimulus values are known andfails to supply a test of fit. Some work onextending functional measurement to re-gression analysis has been done by Bogartzand Wackwitz (1970, 1971).

Logical-Consistency Theory

That human reasoning does not obey formal syl-logistic logic is well known. It is also well knownthat formal syllogisms are only a small part of logic,so perhaps human reasoning might accord withsome more general logic model. This interestingpossibility has been studied by McGuire in a seriesof articles (e.g., McGuire, 1960, 1968) on a logic

model for probabilistic beliefs. The basic postulateis that subjective probabilities or beliefs must beconsistent with one another in such a way that theyobey the laws of mathematical probability theory,though they may otherwise have any relation to theobjective probabilities.

McGuire has applied this logic model in bothqualitative and quantitative ways. The qualitativeapproach assumes that the tendency toward logicalconsistency is complicated by other factors, such aswishful thinking, and is concerned with Socraticeffects, cognitive structure, and related problems.The quantitative approach, which has been adoptedby Wyer and Goldberg (1970) and Wyer (1970), as-sumes the basic postulate, that subjective probabili-ties obey mathematical probability theory, is ex-actly true. Only this quantitative approach will beconsidered here.

To facilitate comparison with integration theory,only the following law of probability theory will beconsidered:

PB = PA.PBIA + PA-PB/A: [18]

Here PJL, PA', and PB are the probabilities of A,not-^4, and B; FBI A and PB/A' are the conditionalprobabilities of B, given A and not-^4. The logi-cal-consistency model does not require subjectiveprobabilities to have any relation to objective prob-abilities (e.g., expectation of success need not equalits true probability). But it does require that sub-jective probabilities be consistent among themselvesin the manner specified by Equation 18.

That one's beliefs on any given, restricted set ofissues ordinarily exhibit a fair degree of consistencyis a matter of common observation. But whethersuch a set of beliefs will obey Equation 18 of thelogic model is not easy to determine. As a precau-tion, the investigation might be limited to beliefsystems that the person himself felt to be consistent.When some new fact or argument threatens a theo-retical position, the belief system may be at leasttemporarily deranged.

Naturalistic observation. Testing the logic modelin a naturalistic setting rests completely on the mea-surement of the subjective probabilities. If the fiveseparate terms of Equation 18 can be measured, thenit is fairly straightforward to test between PB as ob-served and predicted. An absolute measurementscale is required, however, and it is unclear that therating scales that have been used in the experimentalwork are even equal-interval scales. Shanteau(1970b) has found sizable differences between prob-ability ratings of words such as probably, unlikely,etc., and their functional scale values. Correlation-regression analysis has the same shortcomings in thiswork that were discussed previously.

The use of ratings as measures of subjective prob-ability seems especially problematic for the condi-tional events that occur in the logic model. Theimplication, "If abortion is infanticide, then itshould be prosecuted like other murders," (if A,then B) presumably ought to get a high PBIArating; but probably such ratings would be stronglyaffected in many people by their belief in the pre-


mise or the conclusion (Lefford, 1946; McGuire,1968).

Equation 18, unfortunately, may be insensitiveto such biases when the beliefs are extreme. If PA,the belief in the premise, is near zero, bias in PB/Awill have little effect. This illustrates that the logicmodel may yield reasonably good predictions evenwhen it is seriously wrong. Of course, even if theratings of the conditional events are not valid, thatdoes not necessarily infirm the logic model. Theperson's internal cogitation may be perfectly con-sistent with Equation 18 without his being able toassign valid ratings to the events.

Two brief comments should perhaps be added onthe use of such probability ratings. First, the pro-cesses that underlie such ratings may be of consider-able interest and worth closer study in their ownright. Second, there are many purposes for whichan equal-interval scale is not needed. Random as-signment allows comparison between different ex-perimental treatments even with an ordinal scale(Anderson, 1961a, 1963). Similarly, McGuire's(I960) interesting work on the Socratic effect doesnot necessarily require an interval scale.

Experimental analysis. If integration theory canbe applied to these probability judgments, a radicalsimplification of the measurement problem is possi-ble. Accordingly, the blanket assumption is madethat all five terms in Equation 18 follow this formu-lation. Since PA, PA>, and PS presumably follow anaveraging rather than an adding model, some carewould be desirable to ensure equal weighting of thecommunications. For the two conditionals, PB/Aand PB/A', a multiplying model would seem appro-priate, though the overt ratings themselves mightfollow an averaging model.

The main question to be considered is whether thelogic model and the integration formulation are mu-tually consistent. Application 1, in which two com-munications are given in a factorial design, will beused for this purpose. This reflects a key experi-mental change from the work of McGuire (1960) andof Wyer and Goldberg (1970); the use of two com-munications in a factorial design provides the lever-age for a critical comparison.

Two cases need to be considered. The first caserests on the assumption that the communicationshave no effect on the conditionals, PB/A or PB/A-, butonly affect belief in A, A', and B. By assumption,these beliefs follow the integration model and sub-stitution of the theoretical expression from Equation2 into Equation 18 yields the following predictionsfor.?*:

BU + + WOSCJ)PB/A+ V>O'SOJ')PB/A: [19]

This expression is additive in the manipulatedscale values. The joint application of the logicmodel and integration theory thus implies zero in-teraction in these predicted values of PB- Since thisagrees with the assumption that the judgments ofPB obey the integration model, the logic model isconsistent with integration theory in this case.

This test, it should be emphasized, can be madedirectly on the raw ratings of PB- The problems ofmeasuring the four terms on the right of Equation 18have been completely bypassed. Furthermore, be-cause of the response scaling feature of functionalmeasurement, only an ordinal response scale isstrictly necessary for judgments of PB- This testdoes depend on getting communications that do notaffect the conditional probabilities, but that shouldbe straightforward, at least if the logic model iscorrect.

As the second case, suppose that one or bothcommunications also affect belief in PB/A and/orPB/A'- This could be arranged experimentally by anappropriate mixture of arguments. Equation 19must then be changed by substituting in these theo-retical expressions as well. This done, the predictedvalues of PBU no longer obey the parallelism predic-tion. This contradicts the original assumption thatthe averaging model applies to PB- In this secondcase, therefore, integration theory and the logicmodel are inconsistent: if PB obeys the averagingmodel, the logic model cannot hold.

Both cases are needed for a proper critical test.Although the first case does not distinguish betweenthe models, it is necessary to show that at least oneof the models may be correct. The personalityadjective task has various advantages as an experi-mental situation. The conditional probabilitieswould then depend on the implicational similarity ofthe traits.

One essential difference between the two ap-proaches is in the conceptualization of the attitudechange process for PB- In the integration model, theinformational stimuli are considered to bear directlyon PB- In the logic model, these changes occur in-directly, mediated by changes in PA, PB/A, etc. Inthe logic model, the exact analysis of Equation 19depends on whether PB/A and PB/A' follow an aver-aging, adding, or compound averaging-adding model,but some simple predictions about matrix rank areavailable.

Bayesian statistics. Modern developments inmathematical statistics have emphasized personalprobability and Bayesian statistics (Edwards, Lind-man, & Savage, 1963; Savage, 1957). The Bayesianapproach has close parallels with logical-consistencytheory. Part of its interest lies in its emphasis onthe revision of statistical probability in the light ofnew evidence, analogous to opinion change. Al-though the Bayesian development is a strictly statis-tical theory, considerable experimental work hasbeen done using it as a normative model of how menought to process probabilistic information (seeEdwards, 1968; Peterson & Beach, 1967; Slovic &Lichtenstein, 1970).

It is the fate of normative theories that men do notbehave as they normatively ought. Aside from theubiquitous order effects, the response is usuallymuch more "conservative" than is statistically cor-rect. Several explanations of "conservatism" havebeen given (Edwards, 1968), including misperception,misaggregation, and response bias.


In terms of integration theory, misperception andmisaggregation would both correspond to weightparameters different from the statistically optimalvalues. Since integration theory is descriptiverather than normative, it is directly concerned withthe determinants of the weights (Shanteau, 1970a).Nonoptimal weighting in the Bayesian binomialinference task would be no more surprising than innumber averaging (Anderson, 1964d, 1968d), butdeviations from a statistical standard, however im-portant they might be in practical decision prob-lems, seem unlikely to say much about psychologicalprocesses. In the present approach, accordingly,the emphasis is on getting a theoretical frameworkthat is psychologically congruent to the behavior.

The response bias interpretation has recently beensupported by DuCharme (1970). Of itself, responsebias would not necessarily be serious, since themethods of functional measurement could be usedto rectify a distorted response scale. However, thework of Shanteau (1970a) suggests a more funda-mental response problem. The standard bookbag-and-poker-chip task used in the Bayesian researchasks for inference judgments of the probability thatthere are more white than red chips in a populationsampled one chip at a time. Shanteau comparedsuch inference judgments with estimation judgmentsabout the proportion of white chips in the popula-tion. No difference was found between these twoconditions, and Shanteau 's careful experimentalwork indicated that both instruction conditionsproduced estimation judgments. Shanteau's re-sults may thus invalidate the Bayesian interpreta-tion of the binomial inference experiments.

Proportional-Change Model

The proportional-change model for attitudechange (Anderson, 1959a; Anderson & Hovland,19S7) postulates that the amount of attitude changeis proportional to the advocated change :

Si = Jo + + (1 — w)sa, [20]

where $v and si are the opinions before and after re-ceipt of a communication with value so and weightw. An analogous postulate was used in learningtheory by Hull (1943). An extensive mathematicaldevelopment was given by Estes and Burke (1953)and Bush and Mosteller (19SS) for discrete choicetasks, and by Anderson (1961b, 1964a, 1964b) andRouanet and Rosenberg (1964) for continuous re-sponse tasks. In these models, the weight parameterrepresents the learning rate.

In its original form, the proportional-changemodel has not been very successful. In learning, thecritical tests are the sequential dependencies (An-derson, 19S9b; Atkinson & Estes, 1963). The fail-ure of stimulus sampling theory of probabilitylearning has resulted from its inability to accountfor these dependencies (see e.g., Anderson, 1960,1964c, 1966b; Anderson & Grant, 1957, 1958; Ander-son Si Whalen, 1960; Friedman et al., 1968; Jones,1971).

Attitude change experiments, in contrast to learn-ing experiments, typically involve only a few "trials."As a consequence, the weight parameter will changeover successive communications (Anderson, 1959a).A related difficulty arises in Abelson's (1964) gen-eralization of the Anderson-Hovland model to groupinteraction situations which, under fairly generalconditions, predicts that everyone in a given groupwill eventually reach the same opinion. Thisdifficulty can be avoided if the communications aretreated as informational stimuli. A given communi-cation then loses its effectiveness over successiverepetitions since it conveys no new information.

The present serial integration model includes theproportional-change model as a special case and hasconsiderably greater flexibility. A principal ad-vantage is its ability to allow for changes in theweight parameter over a sequence of informationalstimuli. Complete serial position curves, whichmay include both primary and recency components,thus become available (e.g., Anderson, 1964d,1965b; Shanteau, 1970a; Weiss & Anderson, 1969).

SOURCE AND COMMUNICATIONPARAMETERS

The weight and value parameters areproperties of the source-communicationcombination. Much work on attitudechange is not concerned with source effectsand there may not even be an explicitsource. When paragraphs about UnitedStates Presidents are given as historicalfact (Sawyers & Anderson, 1971), the con-cept of source is relevant, but it resides atlarge in the cultural-experimental context.At the other extreme, the source may beexplicit and its nature an integral part ofthe communication.

The valuation problem is interesting inits own right, and it is also relevant to thevarious design applications that have beenconsidered. The problem is complex, de-pending heavily on the situational details,and a brief discussion necessitates somewhatcavalier treatment. The following roughanalysis should be useful in many cases andis given to illustrate some of the mainpoints without explicit concern for itsevident limitations.

Molar Analysis

To begin, it seems reasonable to expectthat within limits the scale value will be in-dependent of the source. There are im-portant exceptions, of course, especially


when the source is an integral part of thecommunication. In oral presentations, forexample, warmth of voice and gesturecould become attributes of the communica-tion and affect its scale value. However,the scale value corresponds to the positionof the communication on the issue. In asubstantial part of attitude change research,this position is conveyed by the semanticcontent of the communication and shouldbe independent of the source.

Determination of the weight parameteris markedly more complex as shown bynumerous experimental studies summarizedin McGuire's canonical chapter on attitudechange (McGuire, 1969, pp. 177 ff.).Some communications, based on consis-tency or affective arguments, can have acompletely source-free weight, but in mostcases the weight will depend importantlyon the source. The source may be merelyimplicit, defined by the cultural-experi-mental situation, or source weight may beexplicitly varied. The weight will also de-pend on specific properties of the communi-cation such as clarity and redundancy.

Both the source and the communicationwill thus contribute to the weight param-eter. If these contributions are indepen-dent, as might be expected in some situa-tions, it would be of interest to know howthey combine. The most plausible hy-pothesis would seem to be a multiplyingmodel, though a composite adding-multi-plying model might prove necessary.

Of course, source and communicationmay interact with each other, and with theissue as well, in determining the weightparameter. A communication at variancewith a source's known position on the issuemight be partially discredited or discounted,that is, given a lower weight. Source ex-pertise would also interact with the issue;an engineer would presumably be moreeffective on pollution control than on nar-cotics addiction.

Application 4 of the averaging model maybe especially useful in the analysis of sourceeffects and interactions. For example, agiven communication could be attributedto different sources in different columns ofthe design. In each case, source and com-

munication could interact in any way. Theinterval scale of the weight parameterwould then provide an assessment of thesource-communication-issue interactions asreflected in the weight parameter.

Molecular Analysis

Thus far, the communication has beentreated as a unit with a single weight andscale value. However, it will usually havea more or less complex structure, contain-ing various separate statements and argu-ments, and its molar effect will itself resultfrom information integration. The follow-ing classification is neither novel nor com-plete, but it indicates how a molecularanalysis might proceed.

Means-ends assertions constitute onegreat class of persuasive arguments (seeMcGuire, 1969, pp. 153 ff.). The sourceasserts that a certain action or belief willproduce a good or avoid an evil, therebymodifying the acceptance of that action orbelief. Each such argument is a subcom-munication, and indeed a source-communi-cation-issue instance. The issue is the goodor evil end, and is the primary determinantof the value of the subcommunication. Theweight parameter will reflect the impor-tance of the end, and also the persuasiveproperties of the source and communicationthat link means and end. On this analysis,which is similar to that of Peak (1955) andRosenberg (1956), each means-end argu-ment counts as one piece of information tobe integrated into the overall opinion.

The other class of persuasive argumentscan be called inferences. Letters of refer-ence, for example, are usually amplifiedlists of personality adjectives. To judgethe intelligence or motivation of someonedescribed as level-headed requires an un-certain inference about the parameters ofthe given information with respect to thespecified dimension of judgment. Bothweight and scale value would be determinedprimarily by the semantic-actuarial rela-tions between level-headedness and intelli-gence or motivation. Source characteristicswould also affect the valuation process ofcourse.


Bare assertions by the source, "I dis-liked the movie," and "I consider HarryTruman one of the greater United StatesPresidents," have received considerablestudy as prestige suggestions. These maybe considered inferences even though theinference may be a conditioned response ofacceptance or rejection. Such statementshave their weight determined by the sourceand their scale value by the semantic con-tent of the assertion. With a design basedon two prestige sources, Application 1would provide a straightforward test of theintegration model.

Consistency arguments may fall intoboth classes. "If you consider self-reliancea virtue, then you should allow your chil-dren more freedom" requires an assessmentof the force of the implication. A means-end evaluation is also needed. Some con-sistency arguments are simple direct in-ferences, however.

This classification bridges the molar tothe molecular. It is thus one approach tothe detailed processing and integration ofcomplex communications. Many communi-cations will not stand a simple dissection,of course, but the total effect of those thatdo may be simple functions of the compo-nents. Suppose that WI,W<L,-• • , are theweights and si,s%, • • • , the scale values of thecomponents of some communication. Aver-aging theory then implies that the scalevalue of the whole is the mean value of theparts,

t, [21]

and that the weight of the whole is the sumof the weights of the parts,

w = Z w,-. [22]

Equation 22 has interest as an adding rulewithin averaging theory. Inconsistency orredundancy among the components couldaffect their weights, of course. Theoreti-cally, Equations 21 and 22 should still applywith these altered weights.

COGNITIVE CONSISTENCY

Cognitive consistency is central in atti-tude structure, and many current theoriesof attitude change take some consistency

principle as their basic postulate and pointof departure. The popularity of this ap-proach is to be seen among the 84 chaptersof Theories of Cognitive Consistency: ASourcebook (Abelson, Aronson, McGuire,Newcomb, Rosenberg, & Tannenbaum,1968). The variety, interest, and impor-tance of the questions that have been raisedby the consistency theorists are impressive.

But as the basis for a general theory ofattitudes, a consistency postulate seems tobe inherently inadequate. Much attitudechange does not involve inconsistency res-olution but only straightforward integra-tion of information (Anderson, 1968a;Lindner, 1971). New information, includ-ing another's opinions and arguments, mayalter attitudes and actions in the absenceof any imbalance, incongruity, dissonance,or any other inconsistency. If this is cor-rect, then a consistency principle is inher-ently too limited to support a general theoryof attitudes. Just this limitation seems tobe reflected in the conceptual insufficienciesof the various consistency principles, aswell as in the problems that have arisen inattempts at quantitative treatment. Muchof the difficulty seems to result from forcingthe consistency principle into situationsthat do not involve inconsistency.

The present approach has developeddifferently, beginning with situations thatdo not require inconsistency resolution.The logic of this attack is straightforward.Inconsistency among the informationalstimuli will affect their parameter values.The test of a simple averaging or addingmodel, though it requires some care, isstraightforward if the stimulus parametersare constant. But if they vary across con-text, the analysis is markedly more difficult.It then becomes difficult to distinguishparameter changes from alternative inte-gration rules. And it is also difficult todistinguish basic defects in the model fromshortcomings in the experimental techni-ques.

The success of the averaging model withconsistent information makes it possible tointerpret deviations produced by integra-tion of inconsistent information (Anderson& Jacobson, 1965). Moreover, success in


the simpler situations helps validate theexperimental techniques and the analyticalprocedures. The development of functionalmeasurement theory, in particular, and theuse of numerical ratings as equal-intervaldata have been central in this work. Thesupport that this methodology has re-ceived in the simpler tasks provides part ofthe basis for attributing psychologicalmeaning to discrepancies from the simplemodel in other situations (e.g., Lampel &Anderson, 1968; Oden & Anderson, 1971;Sidowski & Anderson, 1967; Slovic, 1969).

Inconsistency Resolution

Mechanisms for resolving inconsistencyhave been studied by numerous writers(e.g., Abelson, 1959, 1968b; Adams, 1968;Aronson, 1968; Feather, 1967; Festinger,1957; Gollob, 1968; Hardyck & Kardush,1968; Kaplan & Crockett, 1968; Kelman &Baron, 1968; McGuire, 1966, 1968; Weick,1968). The present analysis has varioussimilarities to previous treatments, thoughperhaps with some advantages in precision.

The most direct method of resolving in-consistency is in the valuation operation. Ifthe informational stimuli are inconsistent,changes either in their meaning or in theirimportance could reduce the inconsistency.In the integration model, changes in mean-ing would be reflected as changes in s\changes in importance would be reflected aschanges in w.

Attitude change experiments may explic-itly or implicitly involve judgments ofsource and communication as well as theissue. The valuation process then becomesmore complex as may be illustrated by con-sidering an unpleasant communication at-tributed to a respected source. For thecommunication itself, the evidence belowsuggests that w will decrease but that s willremain constant. The decrease in w mayresult from revaluing the source or from in-consistency discounting, equivalent here todissociating source and communication.At the same time, the communication con-stitutes a piece of information about thesource. To the extent that it is not dis-counted, it will decrease the scale value of

the source according to the analysis givenin the section on balance theory.

Other mechanisms for resolving incon-sistency will not be considered here, but itshould be noted that the relation betweenvaluation and integration needs closeranalysis. The present discussion has im-plicitly viewed valuation as preceding inte-gration. This is too simple a view: incon-sistency can only exist as a consequence ofan attempted integration. Valuation andintegration must then proceed concurrentlyand a more molecular analysis is needed todelineate the temporal course of the totalprocess.

Within the present framework, however,the two main modes of inconsistency resolu-tion are change in meaning and change inweight. The evidence on these two modeswill be discussed briefly to illustrate someof the problems.

Change of Meaning

The hypothesis that words change mean-ing as a function of context has great intu-itive appeal. Certainly, it is true undercertain conditions, as for words that havedistinct alternative meanings (Anderson,1968c). However, whether words with asingle principal meaning change as afunction of context is doubtful and cer-tainly not well supported by existing data.Various lines of evidence have been con-sidered, but none gives very convincingevidence for change of meaning in thiscase.

Evidence from primacy. One line ofevidence that has received considerablestudy is the primacy effect in personalityimpressions first noted by Asch (1946).If good and bad traits are presented inserial order, the earlier traits have greaterinfluence on the overall impression. Aschinterpreted this in terms of change of mean-ing, as though the subject was selecting outthose shades of meaning of the later wordsthat would fit better with the earlier words(Anderson, 1965b; Asch, 1946). However,an extended series of experiments has pro-vided little support for this view (seeAnderson, 1965b, 1971a). Instead, it ap-pears that the later adjectives keep a fixed


scale value but get lower weight. Whetherthis results from discounting or attentiondecrement, however, is not yet completelyclear (see Hendrick & Costantini, 1970).

In other work, Asch (1948) has arguedthat political statements change theirmeaning when attributed to differentsources. These results, however, can beaccounted for directly in terms of integra-tion theory. It is only necessary to assumethat the subject is attempting to judge theposition of the source on the issue. For thishe has two pieces of information: the state-ment itself and his prior opinion of thesource's position. His judgment will be acomposite or weighted average of these twoinformational stimuli and hence will varydirectly with his opinion of the source.In this judgmental interpretation, it is notnecessary to assume that the statementchanges in any way.

Component judgments. Further supportfor a judgmental view comes from work onjudgments of the single items of a combina-tion. If subjects are asked to judge thelikableness of each separate trait in a persondescription, there is a positive contexteffect: the rating of each trait shifts from itscontext-free value toward the values of theother traits (Anderson, 1966a; Anderson &Lampel, 1965). The obvious interpreta-tion is that these judgments directly re-flect change in meaning. Beyond plausibi-lity, there is no satisfactory evidence forchange of meaning, and the alternative hy-pothesis of a generalized halo effect isequally plausible. The available evidence(Anderson, 1971a; Kaplan, 1971) supportsthe judgmental view.

Contrast and assimilation. The conceptsof contrast and assimilation have beenwidely but uncritically used in social psy-chology. Such effects, if real, would cor-respond to changes in meaning or scalevalue Assimilation, however, may resultfrom composite judgmental processes asalready suggested, and it is well known thatcontrast effects may be artifacts of the re-sponse language rather than changes instimulus value. Even with psychophysicalstimuli such as lifted weights, contrast ef-fects are not always obtained (Anderson,

1971b; Schiffman, Goldstein, & Aroksaar,1970).

The problem of contrast with verbalstimuli has been considered by numerousworkers (e.g., Anderson & Lampel, 1965;Campbell, Lewis, & Hunt, 1958; Dawes,1971; Manis, 1971; Parducci, 1965; Segall,1959; Upshaw, 1965). It seems clear thatmost observed contrast effects stem largelyfrom response language usage, not fromtrue change in stimulus value. Dawes'(1971) report has special interest in thisrespect because it indicates that people withopposite views are perceived as more ex-treme than in fact they are. In addition,some evidence suggests that true stimuluscontrast may be obtained under certaincircumstances. Even if that is true, how-ever, it does not justify the use of responsemeasures that are severely contaminatedby artifacts.

Judgmental context. The scale value of aword will certainly depend on the dimen-sion of judgment. Masculinity is more de-sirable in men than women, for instance.This case is like that of words that havemore than one principal meaning, andillustrates the role of the judgmental con-text in the valuation process. Similarly,the scale value of lighthearted would bedifferent in judgments of likableness thanof dependability.

Change of Weight

Discounting refers to decreased weightingowing to interaction among the informa-tional stimuli. If a new piece of informationis inconsistent with the old, the inconsis-tency can be reduced by assigning it lessweight or importance. Direct evidence forinconsistency discounting in the personal-ity-impression task is given by Andersonand Jacobson (1965) and Schumer andCohen (1968). An important study usingmore realistic stimuli that bears on dis-counting processes has been made by Bug-ental, Kaswan, and Love (1970). Outlierdiscounting has also been studied (An-derson, 1968d). Moreover, the simplestform of redundancy interaction (e.g.,Brewer, 1968; Dustin & Baldwin, 1966;Schmidt, 1969) would also correspond to


decreases in weight. In contrast to thechange of meaning hypothesis, then, thechange of weight hypothesis seems to be onfirm ground.

Stimulus interaction might possibly in-crease weight parameters. No evidenceseems to exist, though increased weightingmight occur when two stimuli form somenatural unit. Chalmers (1969) has arguedfor both incremental and decrementalweighting in personality impression forma-tion by analogy with facilitation and inter-ference in verbal learning. (It should benoted that Chalmers used the term, changeof meaning, to refer to changes in the weightparameter.)

Discounting has received relatively littlestudy, and that mainly with indirect mea-sures, though an attempt to extend dis-counting analysis has been made by Schii-mer and Cohen (1968). Direct subjectiveestimates of importance would be most de-sirable, and some very tentative evidencefor the usefulness of importance ratings isgiven in Anderson and Alexander (1971).Validation of such importance ratingswould be especially valuable for configuralanalysis, since it is evident that discount-ing must depend on the configural patternof the stimuli.

CONCLUDING COMMENTS

A distinctive feature of integration theoryis its basis in a functional theory of mea-surement. Scaling thus becomes an organicpart of the substantive investigation. Thescales are developed and used directly inthe substantive problem, and their validityrests on the validation of the psychologicallaw. In some sense, this must be true ofany measurement theory, but typically thescaling problem in psychology has been con-sidered separately, to be accomplished as amethodological preliminary. In functionalmeasurement theory, stimulus and responsescaling and the psychological law are co-functional in their development.

Integration theory is especially concernedwith situations that require putting to-gether several pieces of information. Suchsituations are not unique to opinions andattitudes. Learning, perception, judg-

ment, and decision making also involveinformation integration. There should bea unified theory that covers all these areas.The present formulation has shown someinitial promise in each of these areas,and it may provide a basis for the develop-ment of a unified general theory.

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(Received August 24, 1970)

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