# Brunswik's lens model

Brunswik's lens model is a conceptual framework for describing and studying how people make judgments. For example, a person judging the size of a distant object, physicians assessing the severity of disease, investors judging the quality of stocks, weather forecasters predicting tomorrow's weather and personnel officers rating job candidates all face similar tasks. In each case, they must use whatever information is at hand ("cues") to make an inference about some unknown quantity. The cues for judgment are analogous to a lens through which the person views an unknown object.
Egon Brunswik developed the lens model as a representation of his theory of probabilistic functionalism, which describes how people function in an uncertain world. On one side of the lens is the environmental system that is the context for judgment. The other side of the lens is the cognitive system. The core of the lens model is the assertion that understanding judgment requires study of both sides of the lens.
The lens model is used to study multiple-cue judgments made under conditions of uncertainty and complexity. The person has several "cues" (i.e., items of information, or indicators) to rely on, and the cues are imperfect, fallible, indicators of an unknown attribute of some entity. Such judgments are pervasive and difficult.

## Elements of the lens model

As the lens model has been adapted and applied for various kinds of judgments, it has appeared in different versions that differ from Brunswik's original in form but not in substance. A modern version used by Cooksey incorporates into Brunswik's original model later developments from Hammond's Social Judgment Theory (Figure 1).
The lens model represents the essential symmetry (the "principle of parallel concepts.") between the environment (left side of the model) and the person (right side of the model).
The cues (X$_i$) together make up the "lens" They are "proximal" because they are directly available to the person making a judgment. In the case of weather forecasting they would include today's temperature and other weather data. In the case of predicting college GPA, cues might include high school grades and test scores.
The lines from the cues converge on the object or event on the left that is the target of judgment. It is "distal," that is, it is not directly available to the person but must be inferred from the available cues. The criterion (Y$_e$) is the true value of the attribute that is being judged. The criterion might be tomorrow's observed high temperature or the actual college GPA of an applicant upon graduation.
Lines from the cues also converge on the judgment (Y$_s$) at the right. This is a person's inference about the unknown attribute based on the known cues.
The lines between the criterion and the cues represent "Ecological validities," that is, the strength of the relations between the cues and the criterion. Similarly, the lines between the cues and the judgments represent "Cue utilizations," that is, the strengths of the relations between each cue and the judgment.
The lines between the cues (r$_{ij}$) indicate that the cues themselves are not independent of each other. Typically they are correlated with one another.
The arc between the criterion and the judgment is achievement, or accuracy. It is typically measured by the correlation (r$_a$) between Y$_e$ and Y$_s$.
"Zones of ambiguity" exist between the cues and both the criterion and judgment. According to Hammond et al., p. 272:
   Knowledge of the environment is difficult to acquire because of causal ambiguity -- because of the probabilistic, entangled relations among environmental variables. Tolman and Brunswik called attention to the critical role of causal ambiguity in their article "The Organism and the Causal Texture of the Environment" (1935), in which they emphasized the fact that the organism in its normal intercourse with its environment must cope with numerous, interdependent, multiformal relations among variables which are partly relevant and partly irrelevant to its purpose, which carry only a limited amount of dependability, and which are organized in a variety of ways. The problem for the organism, therefore, is to know its environment under these complex circumstances. In the effort to do so, the organism brings a variety of processes (generally labeled cognitive), such as perception, learning, and thinking, to bear on the problem of reducing causal ambiguity.

## Application of the lens model

In research applications, individuals are typically asked to make judgments of many cases, typically 30 or more, each involving a different combination of values of the cues. The resulting data are analyzed separately for each individual using a statistical model such as multiple regression analysis. This technique, called judgment analysis, yields measures of cue utilization and the fit of the model to the judgments.
Ideally, a parallel analysis is applied to the criterion based on the same combinations of cue values judged by the person. This results in measures of cue validity and the accuracy of the best fit model for combining the cues to produce a prediction of the criterion.
Once regression models are fit to both the judgment and the criterion, the lens model equation can be used to analyze achievement into several components that are useful for understanding strengths and limitations of judgment processes, and how to improve them.

### An example of the application of the lens model to clinical judgment

Hammond provides an excellent example of Brunswik's lens model applied to clinical psychologists' judgments about their patients (Figure 2). Each case presented to the psychologists included the values of four cues describing a patient. In this study, 10 clinical psychologists judged IQ based on patient responses to four Rorschach test factors ("Cues" X$_1$ ...X$_4$). Each clinician judged 78 patients based on the values of the four cues in their records. The clinicians' judgments of IQ (Y$_s$ in Figure 1) were then compared with patients' scores on a standard IQ test. The actual IQ test score was the objective outcome criterion (Y$_e$ in Figure 1). Each clinician's achievement (r$_a$ in Figure 1) was measured by the correlation between the clinician's judgments of IQ (Y$_s$) and the patients' actual IQ test scores (Y$_e$) for the 78 patients. The resulting median achievement was 0.47 across the 10 clinical psychologists. Correlational statistics and multiple regression analyses were also used to capture the relationships (e.g., correlations) among (1) each cue and clinician's judgments (cue utilization, Figure 1), (2) the cues and the environmental criterion—IQ test score (ecological validity, Figure 1), and (3) the correlations among the cues themselves (inter-cue correlations).

## Development of the lens model

Early in his career, Egon Brunswik was concerned with perceptual constancy, or how people maintain coherence in a changing environment. During this period, Gestalt psychology was a dominant theory of perception. Gestalt psychologists investigated a broad spectrum of perceptual illusions, eventually evolving into an examination of errors in perception.
Some psychologists, including Brunswik and James. J. Gibson rejected the fixation on studying illusions, emphasizing instead the importance of investigating behavior in natural environments, a perspective that identified them as ecological psychologists. Brunswik's interest in understanding the relationship between an organism and its environmental structure can be traced back to his early collaboration with Edward C. Tolman in 1935. Their joint work, "The Organism and the Causal Texture of the Environment," placed a spotlight on environmental texture. They posited that individuals strive to navigate through an environment composed of interconnected and "textured" objects and events.
This viewpoint contrasted with the prevailing trend among psychologists of that era, who were seeking principles of determinism as in the physical sciences, focusing on finding precise mathematical laws governing behavior.
Brunswik conducted rat experiments in Berkeley that showed that rats adhered to a probability-matching rule, reflecting their assessment of the likelihood of obtaining food or other goals. Athanasou and Kaufmann (2015, Table 1) describe the development of the probabilistic concepts during Brunswik's work that finally led to the lens model framework.
Brunswik's colleague, Fritz Heider, was a key figure in the development of the lens model. While Brunswik is often credited with the creation of the lens model, the collaborative efforts between the two researchers are often overlooked. It is misleading to attribute the lens model entirely to Brunswik as the concept of the lens model was initially introduced by Heider. Weiser describes the intellectual context that influenced Brunswik's thinking and traces the evolution of the lens model from Heider's original hand-drawn figure in his private notebooks to Brunswik's final version. He points out that Heider was not concerned with experimentation and quantification which were central to Brunswik's work.
Bernhard Wolf elucidates the inspirations behind the work of Brunswik and Heider in his 1995 book, "Brunswik and ökologische Perspektiven in der Psychologie" (Brunswik and Ecological Perspectives in Psychology). For more detail, see historical papers by Leary and Radler.

## Brunswik's original lens model

Since Brunswik developed the lens model to examine visual perception it has been generalized to other kinds of judgments by Kenneth R. Hammond and others. As a result, some of Brunswik's original terms have fallen into disuse.
The "Initial focal variable" refers to a property of the object that is to be judged or perceived, e.g., size, weight, or distance from the observer. This is usually now called the distal variable, criterion, gold standard, or Y$_e$. In Figure 3, "Vicarious mediation" refers to the variables that describe the object (proximal variables, cues, sensory cues, items of information) such as color, clarity, retinal image. They must mediate vicariously between the object and the person because, in Brunswik's view, direct perception is not possible. The object gives rise to the cues by some process ("Process detail") but there are other unknown variables that affect the cues ("Stray causes). The "Terminal focal variable" is the inference (perception, judgment, Y$_s$) made by a person. The cues are combined into a judgment by some process ("Process detail"), but other unknown variables affect the judgment as well ("Stray effects"). The "Functional arc" represents achievement or accuracy, that is, the degree of match between the actual property of the object and the judgment of that property. Accuracy is the goal of the observer. "Feedback" typically refers to knowledge of results, often called "outcome feedback." However, in Brunswik's words: "A semicircular arrow is appended to the terminal focus to indicate that lens patterns do not stand in isolation but are apt to reflect back upon the person in a future state in what is now sometimes called a 'feedback loop..." (Brunswik, 1952, p. 20). This suggests that Brunswik had something more in mind when he added the feedback arrow, perhaps related to his interest in cybernetics (Brunswik, 1956, p. 141).
Brunswik described the concepts of stray causes and stray effects as follows:
   Impossibility of foolproof distal achievement. "Functional validity." Quasi-rationality .- In line with the inherent probability character of object-cue and of means-end relationships, gross organismic coming-to-terms with the environment can thus never become foolproof, especially so far as the more vital remote distal variables are concerned. It is in this sense that, as William James has phrased it, perception is "of probable things." In the terminology of Reichenbach's probabilistic empiricism, behavior and the inferences implicit in it must retain a certain "wager-" or "posit"-character. Perceptual and behavioral functioning is spoiled much in the manner in which stray rays ... are apt to interfere with perfect focusing. Imperfections of achievement may in part be ascribable to the "lens" itself, that is, to the organism as an imperfect machine. More essentially, however, they arise by virtue of the intrinsic undependability of the intra-environmental object-cue and means-end relationships that must be utilized by the organism .... (p. 23)
The terms "stray causes: and "stray effects" were replaced with the "zones of ambiguity" by Hammond et al.

## Fundamental concepts embodied in the lens model

The lens model is a framework for understanding judgment and designing studies of judgment. It is not really a theory, but it embodies theoretical concepts of Egon Brunswik's Probabilistic functionalism.

### Symmetry

The lens model embodies the central concepts of symmetry between the environmental system and cognitive system. There are imperfect relations between the cues and both the judgment and the object being judged, and cue validities on the environment side correspond with cue utilizations on the cognitive side.

### Achievement and Functional validity

As described above, the arc connecting the judgment and the criterion represents achievement, or accuracy of judgment. Brunswik called this "functional validity." (p. 23):
   "Achievement," in the sense of the probability for an initial focal event (say, a measured stimulus ) to be followed by its terminal counterpart (say, the correct perceptual estimate), may, then, be defined as "functional validity" and measured by a correlation coefficient.
(Although Brunswik embraced the correlation coefficient, there is nothing about the lens model that requires correlations. Correlations have some weaknesses and other measures may be more appropriate in certain contexts.)
The lens model's domain is achieving accuracy in a complex and uncertain world. Factors that limit achievement include: cues that are probabilistic indicators of the criterion, complex entanglement among cues and the criterion, missing cues, suboptimal use of cues by the person and inconsistent use of cues. These factors have been quantified by the lens model equation and have been extensively studied.

### Uncertainty/probabilism

Uncertainty is fundamental to Brunswik's theory. In Brunswik's original model (Figure 3) "stray causes" and "stray effects" represent uncertainty on both sides of the model. The "Zones of ambiguity" (Figure 1) also include uncertainty.
In the environment, the cues are only probabilistically related to the criterion. Hence, perfect judgment is impossible. The relation between the cues and the judgment is also probabilistic because people are not perfectly consistent when making judgments.

### Vicarious mediation and vicarious functioning

For most tasks, including clinical inference, there is no single cue that perfectly predicts the criterion (Y$_e$). Instead, prediction is mediated by multiple cues (X$_i$), each with some predictive validity of the criterion ("ecological validity"). Moreover, the cues are often substitutable, so that equivalent levels of predictive validity often are possible using different ways of combining cues. For example, in clinical inference, different clinicians could have equivalent levels of achievement using different (substitutable) cue combinations. Nevertheless, as Brunswik pointed out, the highest predictive validity ("probabilistic stabilization, achievement") is typically achieved by consistently using the cues with the highest ecological validity ("family hierarchy of cues"). This was observed in the clinical inference case described above: "Certain clinicians were found to be using invalid cues, others neglected the valid ones" (p. 261).
The lens model represents Brunswik's key concepts of vicarious mediation and vicarious functioning. The left side of the lens model represents vicarious mediation—the structure of the task environment that allows various potentially substitutable ways of combining the cues to predict the criterion. The right side of the lens represents vicarious functioning—the different ways that people combine the cues when making judgments.

#### Representative design

The existence of cue intercorrelations is central to Brunswik's concept of Representative design. Some judgment and decision-making studies neglect to represent the environment in which a judgment takes place. The lens model approach emphasizes the importance of environmental representation in research.

#### Idiographic study

Another basic tenet of Brunswik's theory is the importance of an idiographic approach – separate analyses of each person before aggregating the results. This contrasts with the nomothetic approach that combines the responses of the participants in a study, thus averaging out individual differences. The lens model represents one or more judgments made by a single individual.

#### Quasi-rationality

Brunswik argued that judgment is not wholly rational but involves elements of both perception and thinking, that is, it is "quasi-rational." Quasi-rational thought involves elements of both intuition and analysis. This is not indirectly represented in the lens model because it is embedded in "Process detail" and "Stray effects" on the right side of Figure 3.

## Applications and extensions

A major application of the lens model has been in the study of multiple cue probability learning. The lens model has been applied to studies studying human judgment in many other domains including business, education, medicine, social psychology, forecasting, meteorology, evaluation research, and cybersecurity. See Karelaia and Hogarth (2008) and Kaufmann and Athanasou (2009) for reviews of lens model applications.

### Single, double, triple, and N-system cases

Hammond and his colleagues extended Brunswik's classical double-system lens model, to include single-system (one judge at a time), double system (two judges), triple-system (two judges and a criterion), and N-system (N-judges, with or without a criterion) cases (see Cooksey, Chapter 2). These cases describe research designs as well as practical applications of the lens model. They have been used to study aesthetic and value judgments, interpersonal learning, cognitive conflict, and social values. For more information on these designs, see judgment analysis and the lens model equation.