The Understanding/Acceptance Principle and Spearman’s Positive Manifold

THE UNDERSTANDING/ACCEPTANCE PRINCIPLE AND SPEARMAN’S POSITIVE MANIFOLD

The understanding/acceptance principle simply formalizes the judgment of most theorists that we should resist the conclusion that individuals with more computational power are systematically computing the non normative response. Such an outcome would be an absolute first in a psychometric field that is 100 years and thousands of studies old (Brody, 1997; Carroll, 1993, 1997; Lubinski & Humphreys, 1997; Neisser et al., 1996; Sternberg & Kaufman, 1998). It would mean that Spearman’s (1904, 1927) positive manifold for cognitive tasks – virtually unchallenged for 100 years – had finally broken down.

In fact, it is probably helpful to articulate the understanding/acceptance principle somewhat more formally in terms of positive manifold – the fact that different measures of cognitive ability almost always correlate with each other (see Carroll, 1993, 1997). The individual differences version of the understanding/acceptance principle puts positive manifold to use in areas of cognitive psychology in which the nature of the appropriate normative model to apply is in dispute. The point is that scoring a vocabulary item on a cognitive ability test and scoring a probabilistic reasoning response on a task from the heuristics and biases literature are not the same. The correct response in the former task has a canonical interpretation agreed on by all investigators; whereas the normative appropriateness of responses on tasks from the latter domain has been the subject of extremely contentious dispute (Cohen, 1981, 1982, 1986; Cosmides & Tooby, 1996; Einhorn & Hogarth, 1981; Gigerenzer, 1991a, 1993, 1996; Kahneman & Tversky, 1996; Koehler, 1996; Stein, 1996). Positive manifold between the two classes of tasks would only be expected if the normative model being used for directional scoring of the tasks in the latter domain is correct. Positive correlations with developmental maturity (e.g., Byrnes & Overton, 1986; Klahr, Fay, & Dunbar, 1993; Markovits & Vachon, 1989; Moshman & Franks, 1986) would seem to have the same implication.

Likewise, given that positive manifold is the norm among cognitive tasks, a negative correlation (or, to a lesser extent, the lack of a correlation) between a probabilistic reasoning task and more standard cognitive ability measures might be taken as a signal that the wrong normative model is being applied to the former task or that there are alternative models that are equally appropriate. The latter point is relevant because the pattern of results in our studies has not always displayed positive manifold. Although, as previously mentioned, for a wide variety of tasks in the heuristics and biases literature we have found positive correlations (belief bias in syllogistic reasoning, covariation detection, causal base-rate use, selection task performance, assessing the likelihood ratio, sunk cost effects, outcome bias, if/only thinking, searching for unconfounded variables), in some cases we have found no correlations (overconfidence effect and false consensus effect). Some tasks have also produced negative correlations.