Subadditivity in Frequency Judgment

STUDY 3: SIMILAR VERSUS DISSIMILAR COMPONENTS

Although support theory has been conceived as a model of probability judgment, it can be readily applied to assessments of percentage or relative frequency (Tversky & Koehler, 1994). Moreover, judgments of absolute frequency can serve as support for certain hypotheses. For example, the probability that it will snow in Chicago next November may be based on an estimate of the frequency of snowy and nonsnowy Novembers in the previous decade. It is instructive, therefore, to test whether assessed frequency satisfies implicit and explicit subadditivity. One might expect that judgments of absolute frequency are less vulnerable to these biases because the additivity of frequency is simpler and more intuitive than the additivity of probability.

The study of frequency judgment also provides an opportunity for testing another potential source of explicit subadditivity, namely a regressive bias towards the midpoint of the scale (e.g., .5), reflecting either response bias or random error (see, e.g., Erev, Wallsten, & Budescu, 1994). This account implies explicit subadditivity when the two components are below the midpoint and explicit superadditivity when the two components are above the midpoint. Because the probability scale is bounded by one, the above prediction cannot be tested using judgments of probability or relative frequency, but it can be readily tested in judgments of absolute frequency.

The participants, 152 Stanford students, were asked to estimate the number of fellow undergraduates majoring in particular fields. Participants were given the following instructions:

Consider all Stanford students who have declared one major. We would like you to estimate the number of students majoring in particular fields. Obviously, you are not expected to know the exact figures. We are interested in your impressions regarding the popularity of different majors.

For your information, 120 students major in History. Using this number as a standard of comparison, please give your best estimates of the following. The three most accurate respondents will receive a prize of $20.

Twenty-four majors were divided into three sets of 8. From each set of 8 majors, we constructed four pairs of similar majors (e.g., Mathematics and Computer Science), and four pairs of dissimilar majors (e.g., Mathematics and Italian). Participants were randomly divided into three groups. The participants in each group evaluated each of the 8 individual majors from one set, the four similar pairs of majors from another set, and the four dissimilar pairs from a third set. Thus, each participant encountered each major exactly once. The excerpt ends with the study design; its results are not included.