Determinants of Linear Judgment: A Meta-Analysis of Lens Model Studies

Abstract

The mathematical representation of Brunswik's lens model has been used extensively to study human judgment and provides a unique opportunity to conduct a meta-analysis of studies that covers roughly five decades. Specifically, we analyze statistics of the "lens model equation" (Tucker, 1964) associated with 259 different task environments obtained from 78 papers. In short, we find -on average -fairly high levels of judgmental achievement and note that people can achieve similar levels of cognitive performance in both noisy and predictable environments. Although overall performance varies little between laboratory and field studies, both differ in terms of components of performance and types of environments (numbers of cues and redundancy). An analysis of learning studies reveals that the most effective form of feedback is information about the task. We also analyze empirically when bootstrapping is more likely to occur. We conclude by indicating shortcomings of the kinds of studies conducted to date, limitations in the lens model methodology, and possibilities for future research.Keywords: judgment, lens model, linear models, learning, bootstrapping Determinants of linear judgment 3 Since the 1960s, many psychologists have used the framework of Brunswik's (1952) lens model to study processes where humans make predictions of specific criteria (see, e.g., Brehmer & Joyce, 1988;Cooksey, 1996;Hastie & Kameda, 2005). For example, a person might make a judgment (i.e., prediction) about another person's intelligence, about the likelihood of rain, whether a job candidate will be successful, and so on. In all these cases, the simple beauty of Brunswik's model lies in recognizing that both the person's judgment and the actual criterion predicted can be thought of as two separate functions of cues that are available in the environment. Thus, the accuracy of human judgment depends on the extent to which the function that describes it matches its environmental counterpart.But how good or accurate are people at making judgments and on what does this depend? These are important questions that have generated considerable controversy in the psychological literature (Cohen, 1981;Gigerenzer, 1996;Kahneman & Tversky, 1996). Whereas it is unlikely that these questions can be answered satisfactorily by any particular approach, an advantage of research conducted within the Brunswikian tradition is the use of a common methodology for formalizing the lens model. Thus, not only can researchers within this tradition communicate results within a common framework, it is possible to aggregate results quantitatively across many studies and make statements that reflect the accumulation of results. This is the purpose of the current paper in which we present a meta-analysis of studies conducted using the lens model over a period of five decades.The paper is organized as follows. We first describe the mathematical formulation of the lens model. Second, we specify how we identified and included particular studies Determinants of linear ju...

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