A Simple Representation of the Contingent Structure of Knowledge

ABSTRACT - The concept of knowledge-as-constructed is described and a method of measurement is presented which represents its contingent character. An application to consumer knowledge of the health implications of food is presented.

Citation:

John Deighton (1987) ,"A Simple Representation of the Contingent Structure of Knowledge", in NA - Advances in Consumer Research Volume 14, eds. Melanie Wallendorf and Paul Anderson, Provo, UT : Association for Consumer Research, Pages: 12-16.

Advances in Consumer Research Volume 14, 1987      Pages 12-16

A SIMPLE REPRESENTATION OF THE CONTINGENT STRUCTURE OF KNOWLEDGE

John Deighton, Dartmouth College

[John Deighton is Assistant Professor of Business Administration, Amos Tuck School, Dartmouth College, Hanover, New Hampshire.]

ABSTRACT -

The concept of knowledge-as-constructed is described and a method of measurement is presented which represents its contingent character. An application to consumer knowledge of the health implications of food is presented.

INTRODUCTION

The modeling of belief or knowledge has a long history. It includes early attempts to model extensive domains such as Abelson and de Solla Pool's (1965) model of the 1960 presidential election voter and Abelson's (1973) model of the beliefs of Barry Goldwater, or more limited domains such as the mind of the restaurant user (Shank and Abelson, 1977). Some models take a complex view of knowledge as a map of causes (Bougon, Weick and Binkhorst 1977) or propositions (Lindsay and Norman 1977), while others, such as those in the tradition of perceptual mapping, merely seek to model the similarity aspect of object knowledge.

The issue is currently a lively one in consumer research. Knowledge content and structure have been implicated in many consumer phenomena: in the selection and encoding of new knowledge (Johnson and Russo 1984, Taylor and Crocker 1980), in information search (Punj and Staelin 1983, Bettman and Park 1980), and in information retrieval during choice or problem solving (Sternthal and Craig 1982, Srull 1986). The ability to identify and represent what consumers know about a market simply and efficiently is, clearly, a desirable measurement skill.

It is important to be specific in using the term knowledge. It can be used quite broadly, as Shank (1980) does when he defines it as that which is necessary to operate successfully within a system. In that sense a sunflower might be said to "know" where the sun is. In this paper, a narrower sense is meant. A distinction can be made (Anderson 1976, Ryle 1944) between propositional knowledge (relating to the properties of objects, concepts, or events) and procedural knowledge (embedded in behavior and relating to rules of action or conduct). Our concern is with declarative knowledge - the knowledge consumers can supply when questioned. It is also important to specify whether the concept to be measured is knowledge-in-memory or knowledge-as-constructed. The content of memory is the concept implicated in much research in information processing, but it is not the topic of this paper. We are concerned with the sum of what is in memory and what the subject can readily construct by inference operating on the contents of memory: the product of a computational, as distinct from retrieval, process (Brucks and Mitchell 1981, Dacin and Mitchell 1986, Wyer and Srull 1985).

Why measure this concept? Unlike knowledge-in-memory, which is usually found as a mediating concept in accounts of consumers' cognitive processes, ours is an indicator of an initial or terminal state. Change in knowledge-as-constructed (within subjects) can reveal that a knowledge-altering process such as learning or persuasion has occurred, and differences in knowledge (across subjects) can reveal differences in what consumers know in different segments of the market.

A representation is necessarily approximate: it must be parsimonious both in what it requires of the data collection task and in what aspects of the phenomenon are selected for inclusion in the representation. The aspects of knowledge which might be taken as important (listed in what we speculate to be the order of their accessibility to the modeller) are:

- The objects of knowledge that populate the domain.

- Relations of similarity among the objects, including their hierarchical (categorical) structure.

- Relations of dominance (e.g. preference) among the objects.

- Attributes and properties of the objects.

- Relations of contingency among the attributes, including their hierarchial (subset-superset) structure.

- Relations of causality among the attributes.

This paper describes a method of collecting and summarizing consumer knowledge with respect to the first five aspects. The method is similar to that employed in D'Andrade's (1976) analysis of U.S. beliefs about illness. The structure which it produces is an alternative to a positioning map, which represents only the first four aspects. The innovation here, by comparison with maps of perception and preference, is to be able to show that some attributes are subordinate to. or contingent on the presence of, others.

To illustrate this distinction, consider that a positioning nap can record that a subject knows that, in the domain of animals, possession of feathers and ability to fly are strongly associated. However such a representation cannot identify whether the subject believes that feathered animals are a subset of flying animals, or that flying animals are a subset of those with feathers, or in fact that bats and ostriches make it impossible to specify any hierarchial relation at all. A representation that reveals contingency can be said to have generative capacity. It can predict the answers a subject would give to new questions, and responses to new objects.

BACKGROUND TO THE STUDY

The aim of this study was to represent and contrast two "ideologist regarding diet and health. We wanted to examine how the beliefs of a group of health food consumers differed from those of a group who had been converted from this pattern of beliefs to those espoused by a rather more radical nutritionalist, Nathan Pritikin (1979). Three subjects in the study held a pattern of beliefs which we took to be representative of the patrons of health food stores. They were concerned about good nutrition and avoided junk foods. They expressed a preference for vegetable oils over animal fats, and nuts and whole grains over sugary snacks. Two other subjects had previously held similar views, but had been influenced by the writings of Pritikin. He challenges some of the tenets of health store dogma. Specifically, Pritikin proposes cutting back all fat intake, whether vegetable or animal, and claims that most people eat more protein than they need. Many conventional health foods, such as nuts, cheese, and soybean products, are held by Pritikin to be either unnecessary or harmful to health.

All five subjects were de m graphically similar: middle income American women aged 30-45 with families. Their backgrounds too were similar, and it should be acknowledged that they were chosen for similarity of values to minimize problems of aggregation.

The contrasting beliefs of these two groups could have been shown by collecting ratings of propositions such as the health value of specific foods, or by mapping perceptions and preferences of the items. These analyses, however, would have said nothing about differences between the groups due to differences in the hierarchial or contingent structures of their ideologies.

OBJECTS AND PROPOSITIONS

The first problem posed by the task of representing knowledge is to define the domain to be represented. Some exogenous rule, in this case "knowledge about diet and health," implies a set of objects, in this case foodstuffs, about which subjects have propositional knowledge. The semantic content of the terms was captured by using the sentence frame method (D'Andrade, 1976). A sentence frame is an open proposition which designates properties that subjects hold to be true, false, or inapplicable for each term. An example of a sentence frame is the statement, "It is important to eat a little/some _____ every day."

Both the objects of knowledge and the sentence frames were selected from a large number of statements about diet and health offered by subjects in informal interviews. Interviewer Judgment was used to choose object terms and sentence frames which seemed to be well understood by all subjects and which spanned the semantic domain. Thirty object terms and 30 frames were entered into the quantitative phase of the analYsis.

In the quantitative phase, each subject was shown each sentence frame and, with each object inserted in succession into the blank space in the frame, was asked to agree or disagree with the resulting proposition. A matrix of 30 objects by 30 frames resulted, in which agreement was coded 1 and disagreement or inapplicability were coded 0.

The aim of the study was to record consensual knowledge within each of the two groups. We wanted, therefore, to use only terms and frames whose meanings were shared across both groups, and we discarded objects on which respondents disagreed, or frames which failed to show differentiation among objects, based on row and column variances. Exhibits 1 and 2 showed the 23 objects and 24 frames which were retained for further analysis.

EXHIBIT 1

LIST OF FOOD TERMS

EXHIBIT 2

SENTENCE FRAMES

EXHIBIT 3

THE SIX POSSIBLE CONTINGENCY TABLE FORMS WHICH ARE SIGNIFICANT AND CONTAIN ONE OR MORE EMPTY CELLS

Among the 276 two-by-two contingency tables constructed within each group of subjects from all possible pairs of sentence frame properties, were many tables with zero cells. Exhibit 4 shows, for the group of Pritikin ideologues, the set dependencies among the frames in the form of a lower-half matrix.

EXHIBIT 4

DEPENDENCIES AMONG SENTENCE FRAMES

This matrix can be reduced further in several ways. First, equivalence relations permit pairs of properties to be replaced by single properties, since what is true for one element of the pair holds for the other, too. Second, where transitivity exists in subset-superset relations, the number of relations which have to be portrayed in the representation is limited to the principal ordering.

GRAPHICAL PRESENTATION

Exhibits 5 and 6 show knowledge structures for Pritikin believers and health food store patrons respectively. They depict ordered nets in which the subset-superset structure of food terms is indicated by arrows running from subordinate to superordinate members. Terms always belong to classes above them to which they are connected by an arrow.

Superficially, the structures look quite different. The Pritikin group classify the target foods into two sets without overlapping membership: a set of unhealthy foods and a natural set. For the health food group there are also two sets, but they are not mutually exclusive: the respondents are not as extreme in their typing of foods, and allow more exceptions. Animal fats, in particular, bridge the gap between good and bad for this group. They are associated with heart risk but also with growth of young bodies.

There are, however, many similarities apparent in the structures. Both groups are suspicious of foods which taste good, so that the gross structure in both cases reveals unhealthy/good-tasting foods as one organizing concept and naturalness as another. The health food group classifies relatively few foods as unhealthy. Even foods seen as heart risks are not all termed unhealthy. Consequently unhealthiness cannot be a superordinate concept, nor can its contingencies be clearly revealed. The Pritikin group has a much larger category of unhealthy foods, and a more comprehensive "theory" of the sources of unhealthiness is thus revealed. This structure of beliefs parallels almost precisely its beliefs about the determinants of good taste.

Pritikin's doctrine, as it is revealed in this analysis, is an account of the roots of unhealthy diet. Health food dogma, by contrast, has more to say about healthiness. While several sub-structures, such as naturalness, health food stores, and the contribution of protein to growth, are similar in the two representations, the subordinate position of "healthy" in the Pritikin responses, and its superordinate position in the health food responses, is a clear point of difference.

We have been treating these maps as representations of implicit theories of food in general. Another way to use them is as guides to the meaning of specific food items - to examine the contingent beliefs associated with one food item at a time. For example, differences in the meaning of tofu between conventional health food consumers and those influenced by Pritikin's teachings may be inferred by comparing the paths in which the item is implicated. For the health food group, tofu is a healthy product, similar in many respects to desirable foods, but rejected simply because of taste. If its flavor could be changed, it might be liked. (Think, for example, of Tofutti.) For the Pritikin group the product is enmeshed on the wrong side of the structure. It is associated with vegetable oil (it is made of soybean curd) and its rejection is based on a web of related beliefs which would each have to be altered before it could be regarded as healthy.

The study supplies some tentative evidence of the method's reliability. Individual measures of the structure of knowledge for members of each of the two ideological groups were constructed, and did not differ materially from the aggregate measure. Thus the method was not unreliable across subJects in this test. The more important question, however, is whether another researcher, working independently, would have found the same structures as this investigator found. Although the choice of objects and frames is clearly subjective, there is little reason to suspect that the method is not objective beyond that point.

It must be emphasized, however, that the representation is a function of the objects in the stimulus set. Some relations of contingency hold only for the objects presented to the subjects, and exceptions capable of voiding some of the dependencies would not be hard to find. Only as the size of the object set approached the population of all possible objects would the representation become valid, but the data collection task would have become intolerable long before then.

The method requires categorical Judgments from the respondents. They must decide whether an object does or does not belong in a sentence frame. The method cannot cope with subjects who are uncertain or believe the proposition holds only some to the time. This problem may not be as serious as it seems. By appropriate wording of the sentence frame, by adding "usually" or "I think", most scaled responses can be made categorical. On the positive side, the respondent's task is considerably simplified by the fact that the interviewer seeks categorical rather than interval scaled or probabilistic responses.

EXHIBIT 5

CONTINGENT STRUCTURE OF KNOWLEDGE FOR PRITKIN GROUP

EXHIBIT 6

CONTINGENT STRUCTURE OF KNOWLEDGE FOR HEALTH STORE GROUP

CONCLUSION

This paper has presented a methodology for representing what consumers know (or can easily infer, because this is a representation not of memory but of knowledge) about a domain. The method has several attractive features. The data collection task is not very demanding, involving a series of categorical judgments. Analysis is objective and straightforward. While the resulting representation is more complex than say a mapping of similarity or dominance data, the display reveals contingency as well as proximity.

The method is proposed as an indicator of learning, or of knowledge differences among consumer segments, in academic consumer research and in applied studies of persuasion and influence. Its validity for the x purposes remains to be established. This study did no more than report some evidence of face validity: subject groups with known differences in ideology yielded knowledge structures which were different in plausible ways. It will be necessary to investigate whether this indicator converges with other measures of learning or knowledge to establish its worth more solidly.

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