In 3 recent blogs (1, 2, 3) I've been discussing the Lens Model which was proposed by the psychologist Egon Brunswik (1903-1955) as a way to simultaneously understand how an organism relates to world and how we might go about researching and designing experiments to understand that relationship.

The Lens Model has been used and applied in various domains of psychology (perception, decision making, social judgment, etc...) since Brunswik first proposed it. The person most responsible for promoting the lens model after Brunswik's death in 1955 was professor Kenneth R. Hammond (1917 - 2015) so to explore the lens model in more detail I tracked down Kenneth's most highly cited book, Human Judgment and Social Policy: Irreducible Uncertainty, Inevitable Error, Unavoidable Injustice (1996), which includes a discussion of Brunswik's contributions, the lens model, and many other topics. In 1997 this book won the Outstanding Research Publication Award from the American Educational Research Association. It deserves the recognition and I highly recommend it to anyone with an interest in judgment and decision making. Hammond was almost 80 when he wrote the book and offers many insights into the philosophical and scientific basis of judgment and policy. He wrote 2 more books after this one.

In today's blog I want to focus more narrowly on Kenneth's discussion of the Lens Model and how information from cues is organized. I'll begin by displaying Ken's version of the Lens Model which appeared on page 168 of his book:

There are four things I want you to notice regarding Kenneth's version of the lens model:

1. Kenneth prefers to use the term "indicators" rather than "cues". In this version of the lens model the organism's judgment about some intangible aspect of world is mediated by Multiple Fallible Indicators.
2. The degree of validity between an indicator (e.g., obesity) and some intangible state of the world (e.g., diabetes) is depicted by the thickness of the line connecting them.
3. The degree to which an indicator (e.g. obesity) is utilized in making a judgment about the world (e.g., person has diabetes) can also be depicted by thickness of the line connecting them. The ecological validity of an indicator may not be matched by a corresponding degree of utilization of that indicator in making a judgment (i.e., line thickness may change as it passes through the lens).
4. There is an arc that runs from "Judgment" to the "Intangible State" that is being judged. This functional arc is a measure of the "Accuracy of Judgment". Brunswik labelled the functional arc with the word "Achievement" but Hammond had a particular theoretical axe to grind in this book (correspondence vs coherence theories of truth) and preferred the phrase "Accuracy of Judgment" to stress the importance of correspondence over rational coherence in accounting for "Achievement".

To more fully understand the lens model we need to understand how the information from multiple fallible indicators is combined to yield a judgment. Here is Ken explaining how this happens:

One feature of the lens model is its explicit representation of the cues used in the judgment process. Although such diagrams are useful, they do not show one of the most important aspects of the judgment process - the organizing principles, the cognitive mechanism by which the information from multiple fallible indicators is organized into a judgment. One such principle is simply "add the information". Thus, if the task is selecting a mate, and, on a scale from 1 to 10 cue No. 1 (wealth) is a 5, cue No. 2 (physique) is a 7, and cue No. 3 (chastity) is a 2, the organism simply adds these cue values and reaches a judgment of 14 (where the maximum score is 30). Another principles involves averaging the cue values; another principle requires weighting each cue according to its importance before averaging them. An interesting and highly important discovery, first introduced to judgment and decision making researchers by R.M. Dawes and B. Corrigan, is that organizing principles of this type will be extremely robust in irreducibly uncertain environments. That is, if (1) the environmental task or situation is not perfectly predictable (uncertain), (2) there are several fallible cues, and (3) the cues are redundant (even slightly), then (4) these organizing principles (it doesn't matter which one) will provide the subject with a close approximation to the correct inference about the intangible state of the environment, no matter which organizing principle may actually exist therein - that is, even if the organism organizes the information incorrectly relative to the task conditions!

I cannot overemphasize the importance of the robustness of what the professionals call the linear model. "Robustness" means that this method of organizing information into a judgment is powerful indeed. Any organism that possesses a robust cognitive organizing principle has a very valuable asset in the natural world, or in any information system involving multiple fallible indicators and irreducible uncertainty. Its value is twofold:

1. It allows one to be right for the wrong reason - that is, one can make correct inferences even if the principles used to organize the information is not the correct one (one may exhibit correspondence competence without correct knowledge of the environmental system and without coherence competence).

2. One does not have to learn what the correct principle is in order to make almost correct, useful inferences. This conclusion suggest that learning was not an important cognitive activity in the early days of Homo sapiens. Whether early Homo sapiens learned this robust organizing principle or were endowed with it - that is, their biological make up included it from the very beginning - I cannot say, of course, nor can anyone else. I can say, however, that any organism possessing such a robust principle would have - and I will insist, did have - an evolutionary advantage over any organism that relied on a more analytical - and thus less robust and more fragile - organizing principle.

Because we can arrive at accurate judgments about the world with a lens model that uses one of these simple organizing principles, Ken Hammond, and Egon Brunsik before him, argued that alot of our thinking is "quasirational". It occupies a middle ground between pure intuition and a fully-coherent rational explanation. Hammond argues that this quasirational thinking is what people are referring to when they use the term "common sense". Where many have argued that entrepreneurship and investing are matters of either intuition (system 1) or sophisticated rational models (system 2), Hammond and Brunswik are arguing that many entrepreneurial and investment judgments, because they operate in an environment of extreme uncertainty, occupy a quasirational middle ground which a lens model attempts to capture. Common sense is used to organize information from multiple fallible indicators into a judgment that is often accurate.

A final comment to make on the lens model is to point out that it was developed during an historical period of time when multiple correlation and multiple regression statistical techniques were being pioneered and introduced into academic research. Gerd Gigerenzer has argued (link to PDF article) that statistical tools often get turned into psychological theories (i.e., tools to theories heuristic) so that one might view the lens model as the type of psychological model you get when you generalize the importance of multiple correlation and multiple linear regression techniques and ideas. Multiple correlation and multiple linear regression are often used to create and evaluate lens models. While the lens model can sometimes be usefully equated with multiple linear regression, part of Brunsik's inspiration for the lens model was how our senses combine information from multiple fallible cues to arrive at accurate perceptual judgments. Further development of the lens model might take inspiration from nature (i.e., how vision, hearing, touch, smell, and taste combine multiple fallible cues to yield accurate judgments) to find additional organizing principles.