Magnitude comparison revisited: An alternative approach to binary choice under uncertainty

Abstract

Two generations of psychologists have been interested in understanding binary choice under uncertainty. In the 1970s and 1980s, researchers assumed that people rely on a two-stage magnitude comparison process to make these decisions (Banks, 1977; Moyer & Dumais, 1978). More recently, the focus has shifted to approaches that rely on probabilistic cues and simple heuristics (Gigerenzer & Goldstein, Psychological Review 103, 650-669, 1996). Here, we test competing predictions derived from these two very different approaches and conclude that the magnitude comparison process plays a central role in this task. In support of this conclusion, we present an experiment in which participants were timed as they decided which of two vehicles was more expensive. Pairs composed of one luxury vehicle (e.g., BMW 323i) and one nonluxury vehicle (e.g., Toyota 4Runner) were critical because the magnitude comparison approach correctly predicted that reaction times would decrease with subjective distance, whereas the heuristics approach incorrectly predicted that there would be no relation.

The role of subjective linear orders in probabilistic inferences

“…Thus, TTB could also predict a distance effect for pairs of recognized objects. In contrast, Brown and Tan (2011) argued that in their study TTB did not predict the observed distance effect, because the pairs that they used could have been answered by considering the same highly valid cue, thus implying no decision-time differences.…”

“…As an alternative, Brown and Tan (2011) recently proposed that participants may engage in magnitude comparisons that are based on subjectively built orders of the objects involved. They tested a set of 16 cars (asking for the more expensive one in each pair) and found that participants' decision times were better explained by assuming magnitude comparisons based on subjective linear orders than by assuming the use of specific heuristics, as predicted by the toolbox approach.…”

“…We will then describe tests of these predictions in a reanalysis of a published experiment (Hilbig & Pohl, 2009, Exp. 3) and in a new experiment. Brown and Tan (2011) suggested that decision makers rely on magnitude comparisons based on the subjective linear order of objects-thus avoiding the need to switch tools from trial to trial. Prior research had shown that in comparative tasks in which well-learned objects are ordered along a criterion, people possess or build subjective linear orders and subsequently base their decisions on this mental representation (see, e.g., Banks, 1977;Moyer & Bayer, 1976;Moyer & Dumais, 1978;Parkman, 1971).…”

Magnitude comparison extended: How lack of knowledge informs comparative judgments under uncertainty.

“…Despite the overlap between this new line of research and the symbolic comparison literature from the 1970s and 1980s, both proponents and critics of fast-and-frugal inference heuristics have neglected this earlier research and have come to conceptualize the judgment process (and the underlying processing architecture) in a fundamentally different way (Brown & Tan, 2011). We next describe the different process models for choice situations involving one recognized and one unrecognized object.…”

“…SDEs have been documented in a wide variety of knowledge domains, which include (a) comparisons on concrete dimensions such as the sizes of animals (e.g., Moyer, 1973) and other everyday objects (Paivio, 1975); (b) comparisons on abstract dimensions such as the magnitudes of numbers (e.g., Dehaene, Dupoux, & Mehler, 1990;Moyer & Landauer, 1967), time, quality, temperature terms (Holyoak & Walker, 1976), and the semantic goodness of words (A. Friedman, 1978); and (c) comparisons that involve some degree of uncertainty with respect to the position of target items along the criterion dimension, such as the military power of countries (Kerst & Howard, 1977) and the price of cars (Brown & Tan, 2011).…”