Explicit Subadditivity

Table 26.3. Median Frequency Estimates and the Actual Number of Students in Each Major (Study 3)

The table data are not included in this excerpt.

Explicit subadditivity implies that the estimated number of students in a given pair of majors is less than or equal to the sum of the estimates of the individual majors. If this phenomenon is driven, at least in part, by participants’ tendency to repack the individual components, then we should expect greater subadditivity for similar than for dissimilar pairs because it is easier and more natural to pack related majors (e.g., Mathematics and Computer Science) than unrelated majors (e.g., Mathematics and Italian). Finally, if participants estimate the total number of students who major in one of two fields by anchoring on the larger major and making an insufficient upward adjustment, then we expect the judgments to be more sensitive to the larger than to the smaller component of each pair.

Table 26.3 presents median estimates for each of the 24 majors, along with the official numbers. The correlation between the estimated and correct values is .93, and the average absolute deviation of prediction is 24, indicating that our respondents had a reasonably good idea of the relative popularity of the various majors at their university.

Tables 26.4 and 26.5 present, separately for similar and dissimilar pairs, the median frequency estimates for the pairs, denoted FAB, the median sums of frequency estimates of the individual majors, computed within the data of each participant and denoted FA + FB, and the ratio of these values. The results provide strong evidence for subadditivity: The estimate of the pair is less than the sum of the individual estimates in 23 of 24 cases, and the mean value of FAB/(FA + FB) across all pairs is only .69. This effect cannot be explained by a regression towards a central value (e.g., 120, which was given as a standard of comparison) because subadditivity is very much in evidence for both large and small pairs of majors. Recall that a symmetric error model predicts subadditivity for pairs of small majors and superadditivity for pairs of large majors, contrary to the data in Tables 26.4 and 26.5.

Table 26.4. Median Frequency Estimates for Each Similar Pair (FAB), Median Sum of Estimated Components (FA + FB) and Their Ratio (Study 3). Only the caption is included here.

Table 26.5. Median Frequency Estimates for Each Dissimilar Pair (FAB), Median Sum of Estimated Components (FA + FB), and Their Ratio (Study 3). Only the caption is included here.

In accord with repacking, the similar pairs tend to be more subadditive than the dissimilar pairs: The values of FAB/(FA + FB) are generally lower in Table 26.4 than in Table 26.5 (p < .05 by a one-sided Mann–Whitney test). However, the presence of strict explicit subadditivity in both cases suggests an anchoring and adjustment process.

To test this account, we compared, separately for similar and dissimilar pairs, the median estimate of each pair, FAB, with the higher of the two medians of estimates for individual majors forming the pair, denoted FH. For similar pairs, the mean value of FH was 108, whereas the mean value of F AB was 113 (t = .22, ns). For dissimilar pairs, the mean value of FH was 111, whereas the mean value of F AB was 124 (t = .56, ns). Thus, the estimates for the pairs (overall mean = 119) are much closer to the higher of the two majors (overall mean = 109) than to the sum of the individual estimates (overall mean = 165). These data are consistent with the notion that participants estimated the pairs by focusing on the larger component.