Brunswik's Lens Model: a Review and Extension to Consumer Research

Shelley R. Tapp, Indiana University
ABSTRACT - This article extends the lens model research of cognitive psychology to the study of consumer behavior. The author posits a probabilistic relationship between the attributes which a product possesses and the post-purchase satisfaction which the consumer derives from the product. Also it is posited that consumers learn to utilize probabilistic cues with varying degrees of validity.
[ to cite ]:
Shelley R. Tapp (1984) ,"Brunswik's Lens Model: a Review and Extension to Consumer Research", in NA - Advances in Consumer Research Volume 11, eds. Thomas C. Kinnear, Provo, UT : Association for Consumer Research, Pages: 103-108.

Advances in Consumer Research Volume 11, 1984      Pages 103-108


Shelley R. Tapp, Indiana University


This article extends the lens model research of cognitive psychology to the study of consumer behavior. The author posits a probabilistic relationship between the attributes which a product possesses and the post-purchase satisfaction which the consumer derives from the product. Also it is posited that consumers learn to utilize probabilistic cues with varying degrees of validity.


Marketing literature increasingly refers to the probabilistic relationship between the consumer's perceptions of a product's attribute levels and the satisfaction (utility/ preference) which the consumer then experiences from that product. Monroe (1971) examined the probabilistic link between price and the utility which consumers receive from a purchase, emphasizing the important role of price as a cue which substitutes for all the other knowledge which the consumer would like to have about the product but cannot acquire from the purchase environment. Eliashberg (1980) also acknowledged that most consumer decisions are made under conditions of uncertainty. He pointed out that most models tested in consumer literature assume that the consumer has complete and accurate knowledge not only of outcomes of decisions but also of all of the important attributes characterizing the decision situation. Meyer (1981) recently has proposed a model of multiattribute decision-making which seeks to recognize the probabilistic nature of attributes as cues to preference of consumers for certain products.

This article examines the issue of attributes as probabilistic cues in a way which has not been utilized by other researchers in marketing. Rather than focusing on the stochastic nature of the consumer's final decision as Monroe does, or on the probability distributions generated by possible brand choices as the Eliashberg and Meyer articles do, the model proposed in this study aids the researcher in his investigation of how attributes are perceived by the consumer and how they are utilized in the purchase decision. Thus the emphasis of the model describe in this paper lies in the processes with which consumers learn about and utilize attributes as cues to post-purchase satisfaction rather than modeling the choice of a brand as an holistic bundle of attributes. Thus emphasis is placed on the role of learning as it influences consumer decision waking in an uncertain environment.

Simon (1959) recognized that "classical theory is a theory of a = choosing among fixed and known alternatives, to each of which is attached known consequences. But when perception and cognition intervene between the decision-maker and his objective environment, this model no longer proves adequate. We need a description of the choice process that recognizes that alternatives are not given but must be sought; and a description that takes into account the arduous task of determining what consequences will follow on each alternative (p. 272)." Such a model was proposed by Edward C. Tolman and Egon Brunswik (1935) to explain the relationship of an individual to an uncertain environment and the means by which the individual learns about, and makes decisions in, such an environment. With minor modifications, this model can be used to explain the manner in which a consumer learns about and utilizes attributes as probabilistic cues in a purchase situation.

The literature of cognitive psychology has produced experimental results in the field of multiple cue probability learning which have important implications for research into consumer decision making. Finally, this model not only provides a basis for a conceptual understanding of the consumer's use of uncertain information but also offers suggestions for empirical research into such issues as consumer perception of attributes, information search, and information utilization.

Before examining the model itself, it is important to clarify how this approach differs from other conceptualizations of consumer decision and purchase processes which also attempt to include uncertainty in some conceptual fashion. The most notable of these streams of research include the stochastic models of consumer behavior (Bass 1974 and Jones 1971) and the linear learning model (Kuehn 1962; Bennett and Mandell 1969; Jones 1970; Lilien 1974; Aaker 1970; and Aaker and Jones 1971). In both these research streams the uncertain variable which is modelled is the purchase itself rather than any attribute of the product. With the lens model, it is the relationship of the presence of a certain attribute to the postpurchase satisfaction of the consumer which is viewed as probabilistic. This probabilistic nature of the attribute arises from several factors. One possible cause is the consumer's inability to judge the level of the attribute accurately: for example, durability is difficult to ascertain for many products without the opportunity to use the product over time. Another example of sources of uncertainty about the relationship of the attribute to postpurchase satisfaction occurs when the consumer has limited experience in a buying situation and therefore has a limited or faulty perception of the relationship of significant attributes and postpurchase satisfaction. Whatever the source, it is this relationship between attributes and postpurchase satisfaction which the lens model, as applied to consumer behavior, investigates.


As Castellan (1977) suggests, multiple cue probability learning (MCPL) tasks are representative of the type of open-decision situations which daily confront humans in natural settings. The study of MCPL tasks in cognitive psychology revolves around the linear estimation problem which originated in the works of Egon Brunswik. This "problem" essentially, is the judgment process in which probabilistic cues from the environment are related to some criterion. Early research in this area (Anderson 1969; Hammond, Hursch, and Todd 1964; Hoffman 1960; Hoffman, Slovic, and Rorer 1968; and Slovic, Rorer and Hoffman 1971) examined probabilistic cues in the area of clinical judgement In such research, the symptoms of the patient constitute cues which the clinician uses to identify the disorder which the patient has. However, the symptoms which the clinician observes are only probabilistic cues of the nature of the patient's disorder. The thrust of research in cognitive psychology has been to discover how clinicians deal with the probabilistic nature of the cues which form the basis of their diagnoses. The model, developed by Brunswik, which cognitive psychologists apply to such decision situations is illustrated in figure one. Brunswik compared the model's configuration to that of a convex lens which explains the model's common name, the "Lens Model."

In figure one, Ye represents the true state of some natural phenomenon (also referred to as the distal variable). This true state is not immediately available to the subject but must be gauged through the subject's utilization of cues in the environment which indicate the true state of the phenomenon. These cues have a true correlation with the distal variable, Pei, which indicates how predictive of the distal variable the cue actually is. The subject integrates perceptions of the correlation between the cues and the distal variable, Psi, to form an estimate of the true state of the phenomenon, Ys. The correlation between Ye and Ys, called "achievement" by Brunswik, is a measure of the accuracy with which the subject utilizes cues in order to apprehend the distal variable: the higher the correlation between Ye and Ys, the more accurately a subject perceives the relationship between the cue and the distal state. Although these cues are probabilistic, the subject can learn to utilize these cues more accurately (Campbell 1966).

Castellan (1977) defines the validity of a cue in the following manner. Assume that an experimental subject has been asked to predict, from a set of cues, the occurrence of two events, E1 and E2. In every trial of the experiment, the researcher provides the subject with a value from each of" binary cue dimensions. From the cues presented the subject predicts A1 or A2. A prediction Ai is accurate if event Ei occurs. If Ci is a value of the ith cue, P(Ci), the probability with which Ci is presented on any trial, and if event Ei occurs on any trial with probability P(Ei) = si, then, if P(Ei/Ci) is the probability that event Ei will occur given Ci and P(Ei/Ci) is the probability that event Ei will occur after presentation of the other value of the binary cue. The probability of Ei's occurrence can be defined as:


The validity of a cue, its product-moment correlation with the event, is defined as 0 thusly


Obviously o2 equals zero when the cue is totally independent of the event and one when they are perfectly predictive of each other.




A minor redefinition of terms suffices to apply this conception of the individual's perception and integration of probabilistic cues to the arena of consumer decision raking. Let Ei be the satisfaction (positive reinforcement, preference, etc.) which the consumer derives from the use of a product. Then Ai becomes an implicit prediction of Ei, if Ai is conceptualized as the consumer's purchase of the product. That is, the consumer purchases a product under the assumption that he will derive satisfaction from it. This expectancy that satisfaction will result from the purchase act is occasioned by the consumer's integration of the cues in his environment which indicate the ability of that product choice to give satisfaction. These cues are the attributes of the product and all attributes of the selling situation which might influence the buyer's postpurchase satisfaction (for example, service or warranty provisions, trade-in policies of the retail outlet). While the model above focused on the simpler binary cue situation, obviously the model can be extended easily to account for a-dimensional cues. For a set of" three dimensional cues where each Cij (i-l, 2, 3, ...," and j-l, 2, 3) is presented with probability P(Cij ), then the conditional probability of event Ei given presentation of cue Cij is PtEi/Ci:). The probability of event Ei (that is, that the consumer will experience satisfaction, or positive reinforcement, from his purchase) then equals:


and is determined by n equations. The squared validity follows the formula:



The first important implication of the Brunswik Model lies in its insistence on the examination of the validity with which the consumer utilizes cues. Much marketing research has focused on which attributes consumers use to make purchase decisions (notably research into the Fishbein and extended Fishbein Models and research into conjoint and analysis-of-variance models of attribute use). However this research has neglected the critical question of how accurately the attributes which consumers use do indeed predict postpurchase satisfaction. While some might believe that the importance weights which these approaches derive might reflect the validity of the attribute as a cue, these concepts are entirely different as a simple example will illustrate. The attributes which characterize the fidelity of a stereo system are obviously important attributes for a consumer to consider when making a stereo purchase. Undoubtedly most consumers would rank these characteristics high on an importance scale. However, many consumers are insensitive to improvements in fidelity beyond a certain point and thus may overemphasize these attributes in paper-and-pencil experimental situations such as conjoint research procedures. However, this impaired achievement, in Brunswik's terms, on paper-and-pencil research tasks may have a realistic counterpart in in-store sales situations. There consumers are often presented with promotional materials which explain that higher signal-to-noise ratios are better indicants of "quality" or listen to salespeople explain that the lower the wow-and-flutter of the system, the better. Using these decision rules provided by the salesman or promotional materials, the consumer may purchase a stereo system possessing a higher degree of fidelity than he can actually appreciate.

The legacy of probabilistic functionalism in such a case demands the examination of the level of validity which exists in this selling situation between the consumer's use of fidelity as a cue to satisfaction and his actual ability to predict satisfaction for that consumer of those attributes. Such research would focus on comparing the consumer's use of fidelity as a cue to post-purchase satisfaction with the actual ability of this particular set of cues to predict satisfaction. Such an investigation would require examining the consumer's sensitivity to improvements in fidelity through actual tests of the sensitivity and reliability of his judgments of the difference in the sound of receivers with varying levels of fidelity performance. Then the actual predictive ability of such cues for that consumer could be compared with the consumer's use of the cue in a conjoint or anova-type presentation.

Rather more important than the question of the validity with which consumers utilize cues is the question of how they learn to utilize various cue patterns and configurations. This research in cognitive psychology can be loosely compared to the lengthy research stream in marketing concerning what combinatory rules consumers utilize in reaching overall preference decisions with respect to multiattribute products (Pras and Summers 1975; Alpert 1971; Cohen, Fishbein and Ahtola 1972; Heeler, Kearney, and Mehaffey 1973; Wilkie and Pessemier 1973). However, the key question here is not whether the consumer does indeed use linear or non-linear, compensatory or noncompensatory models to combine several attributes into an overall preference judgment. Rather, psychologists have attempted to discover in laboratory settings whether cues which are related to the distal variable in positive or negative linear relationships are easier for subjects to learn to use than those related in nonlinear relationships. Other experimental questions investigated by cognitive psychologists include how configurations of cues affect learning, when does information overload occur when multiple cues are present, do subjects generate hypotheses as to the relationship of the cues to the distal variable or do they acquire heuristics which they sample randomly when confronted with a probabilistic situation in order to determine the relationship between cue and distal variable (Einhorn 1970; Brehmer 1974; Sniezek and Naylor 1978; Muchinsky and Dudycha 1974; and Brehmer 1976).

For example, Brehmer's experiments of 1974 seem to indicate that subjects experience great difficulty learning nonlinear relationships between probabilistic cues and the distal variable, particularly in identifying and utilizing cues which have an inverse U relationship to the distal variable. If such relationships occur commonly in the purchase environment then the public policy implications are immense. Recall the example presented earlier in which the relationship of increased fidelity of stereo components to postpurchase satisfaction (utility, etc.) was called into question. Remembering that, beyond a certain point, improvements in fidelity are undetectable Dy the normal listener, the relationship which must exist between fidelity and post purchase satisfaction must be an inverse U function given that the cost of the component increases with the fidelity. Beyond that upper limit then, the consumer is paying more and more for differences in quality which he cannot possibly perceive. If consumers have the difficulty reported by Brehmer learning such relationships and applying them in their judgment processes, then how effectively will they make decisions in this product category? Another fruitful ares of study then, could be the examination of the types of relationships occurring between common product attributes and consumer satisfaction or preference and the ability of consumers to learn to use various cue functions. A further example of important theoretical and empirical research which should arise out of the consideration of attributes as probabilistic cues is the manner in which consumers perceive configural patterns of relationships between attributes in a multi-attribute product and how they achieve global preference Judgments. As in the work of Estes (1972) with cues used in clinical diagnosis, the marketer could examine whether when presented with multi-attribute products, the consumer processes information about the predictiveness of a-tributes taken as individual cues to the satisfaction or utility which he will receive from the purchase or whether the consumer attends to patterns of attributes as probabilistic cues of the outcome of the purchase. Such examination could shed new light on the classic research into the consumer's use of price as an indicant of quality.

A recent article by Holbrook and Moore (1981) attempts such an investigation. The authors examined the effect of verbal product descriptions versus schematic diagrams on consumer ratings of various sweater designs. They found evidence that consumers do react to attribute configurations. Therefore, they suggest that additive models of consumer judgments of aesthetic goods include interaction terms. This study demonstrates the necessity of examining possible configural effects on consumer judgments.

In another paper, Holbrook (1981) uses the Lens Model to integrate the compositional and decompositional approaches of modeling consumer judgments. As part of his analysis he investigated the question of the effects of nonlinear cue relationships on consumer judgments. However, Holbrook concludes that his subjects' judgments could be adequately explained by a simple additive model without interaction effects. His conclusion that cue configurality is not important in his subjects' judgments of the musical stimuli presented cannot be generalized beyond his specific research. Only two levels of each of the musical variables were presented to the subjects. Because only two levels of each of the variables were presented to each subject, it is not unreasonable to suggest that the subjects were able to utilize simple monotonic functional relationships to make their preference decisions. Future research into configural effects on consumer judgments will require that the features under study be varied across several levels.


The absence of objectively verifiable ways of measuring the true correlation, Pei, of the attribute to the consumer's post-purchase satisfaction constitutes the greatest limitation of the Brunswik model when extended to consumer research. Brunswik's original research concerned the degree of achievement when subjects were placed in estimation tasks which involved such specific activities as the estimation of the height of a building or its distance from the subject (Brunswik, 1944)- For such a task, it is possible to determine the true validity of a variety of cues which the subject might utilize in the estimation task. It is also possible to determine the cue utilization, Psi, and, therefore, the degree of achievement in such a learning task can be measured objectively and with great certainty. This results from the existence of an objectively verifiable true state of the phenomenon involved in the estimation task. A building has a definite height. It is some measurable distance from the subject. Thus a criterion exists which is independent of the subject; that is, the research may establish the true state of the phenomenon without reference to the subject.

This simply is not the case with the type of research which the marketer wishes to perform. Whether we investigate the subject's post-purchase satisfaction with a product, or the utility which he derives from its use, or the degree to which he feels that the product fulfills the purpose for which it was purchased, we may only gauge the degree of achievement by relying on the subject's perception of his satisfaction. A major problem arises from our enforced dependence on a subjective distal variable. The subject's perceptions are governed by a host of psychological phenomena, among which are cognitive dissonance, impression management issues, or the inability to report psychological processes accurately. All of these phenomena can result in the subject's inaccurately reporting either his degree of satisfaction with the product or the manner in which he combined his perceptions of the product's attributes to reach his purchase decision. Thus, the marketing researcher lacks an objectively derivable criterion to determine the true state of the distal variable.

Another limitation to the use of the Brunswik model in consumer research concerns the validity with which the typical experimental paradigm for multiple cue probability learning can be said to represent the experience of the consumer in the purchasing environment. MCPL experiments to only utilize numerous trials (200 learning trials in the Deane et al., 1972 study; 200 trials in the Todd and Hammond 1965 study; and Kuylenstierna and Brehmer, 105 learning trials in the 1981 study). These experiments and others not cited demonstrate that simple functional relationships between cue and criterion may be learned after only a few trials. However, complex functional relationships may not be learned by the subject after as many as 4,000 trials even when feedback has been provided after each trial (Goldberg 1968). Consumers purchase only a few types of products with this frequency. Services, such as restaurant or fast-food outlets, gasoline at various types of retail outlets, etc., and consumer nondurables, such as foods, over-the-counter medications, etc., constitute the kind of products which might be purchased frequently enough to make the experimental paradigm utilized in MCPL research a valid representation of the consumer's learning process. However, published research exists which indicates that choice processes for such products may be routinized to the extent that little prepurchase search or evaluation occurs on the consumer's part (Wells and LoSciuto 1966; Ward 1974, and Frank and Massy 1970). These studies indicate that very little comparison of brands occurs in the store and suggest that the consumer used some process other than the comparison and evaluation of different products on several of their attributes to arrive at the purchase decision. This would be a serious obstacle to the use of this model if the researcher wished to utilize it to predict specific brand choice in a purchase situation. However, if the objective of research into consumer learning processes has as its objective to understand how the consumer perceives attributes then it would not be invalid to expose the consumer, in the laboratory, to more product comparisons than he would actually make in a realistic purchase situation. If the researcher wishes to investigate the consumer's cognitive processing of the various functional relationships which attributes may exhibit with respect to some post-purchase evaluation, then his aim is different from that of the experimenter who wishes to predict which brand the consumer will actually purchase. Research of the second type demands as much external validity as possible from the experimental setting. For research of the first type, validity of the judgments about the attributes is maintained by exposing the consumer to actual product samples and ascertaining his response.


The major problem in designing experiments which will allow marketers to investigate the manner in which consumers utilize probabilistic attribute cues lies in the construction of criterion tests to determine the actual validity of the attribute as a cue to satisfaction in the real use environment. While the paper-and-pencil approach of conjoint and anova paradigm investigations into multiattribute attitude models can be defended as somewhat representative of various types of promotional materials which consumers utilize in information search, such methods can only provide the lens model researcher with the cue utilization, ¦sis side of the model presented in figure one. In order to measure the consumer's level of achievement or the validity with which the cue is utilized, the researcher must be able to determine, under conditions which replicate more closely the actual conditions of use of the product, how accurately individual attributes under study predict satisfaction (utility/ preference) for the product. This requires longitudinal studies which allow the researcher to gather data about the consumer's satisfaction with a recently purchased product. Such research is more costly than prepurchase attitude studies utilizing product descriptions and consumer ratings. However, it could be feasibly accomplished within a diary panel paradigm. Such research would provide insight not only into how accurately the consumer chooses products from which he will gain satisfaction but also into how dissatisfactory product choice affects his subsequent decision processes.

The Lens model lends itself to the study of many different subjects. One research issue which has recently been raised in conJunction with this model is that of whether consumers' evaluation models are essentially additive or interactive. The 1981 Holbrook study, cited previously, tested this question and found no evidence for cue configurality (that is, interactive processing of attributes). As suggested above, it is possible that the subjects were able to apply simple monotonic preference functions to the bi-level attributes and combine these additively. Whether they could maintain this additive process in the face of more levels per attribute is questionable.

A better test of cue configurality would adopt Holbrook's experimental method and expand it in the following manner. One set of subjects would hear 16 recordings manipulating Holbrook's four factors on two levels. Using a randomized block design, a second group of subjects would be exposed to subsets of the 81 treatments achieved by varying each of the four factors on three levels. Subjects' ratings of the musical stimuli, on scales such as those used in the Holbrook study, would be subjected to dummy-variable regression. As in the case of Holbrook's 1981 study, it is unlikely that an interaction effect will prove significant for those subjects who are exposed to the four-factor-two-level completely crossed treatments. However, testing the hypothesis of no interaction for the treatments created by increasing the number of levels should result in failure to accept the null of no significant interaction effect. That is, the researcher should detect configural processing as the researcher increases the number of levels associated with each attribute.


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