Implicit and Explicit Subadditivity

STUDY 1: IMPLICIT AND EXPLICIT SUBADDITIVITY

Study 1 uses two problems that have the same formal structure. Let A1, A2, and B denote three mutually exclusive and exhaustive hypotheses, and let A be an implicit disjunction of A1 and A2. In each problem, different groups of participants evaluated the implicit disjunction P(A, B), the explicit disjunction P(A1 ∨ A2, B), the component, P(A1, A2 ∨ B), and the component P(A2, A1 ∨ B).

A total of 178 Stanford students participated in the study to fulfill course requirements. They were divided into four groups of roughly equal size. Every group evaluated both problems, each in a different condition. The first problem concerns the outcome of the next presidential election in the United States. Participants in the implicit group evaluated “the probability that the winner of the next presidential election will not be a Democrat.” Participants in the explicit group evaluated the probability that “the winner of the next presidential election will be a Republican or an Independent rather than a Democrat.” Participants in the two remaining groups evaluated either “the probability that the winner of the next presidential election will be a Republican rather than a Democrat or an Independent” or “the probability that the winner of the next presidential election will be an Independent rather than a Democrat or a Republican.”

The second problem concerns the outcome of a criminal trial. All participants read the following scenario:

Susan L. has accused her boss, Frank G., of unwelcome sexual advances and the promise of promotion in exchange for sexual favors. Frank G. denies any wrongdoing. The case has been brought before a jury consisting of seven men and five women. There were no eyewitnesses, but Susan’s boyfriend has testified that she told him about the incidents in question. The jury is now deliberating.

Participants in the implicit group evaluated “the probability that this trial will not result in a guilty verdict.” Participants in the explicit group evaluated “the probability of either a not guilty verdict or a hung jury rather than a guilty verdict.” Participants in the two remaining groups evaluated either “the probability of a not guilty verdict rather than a guilty verdict or a hung jury” or “the probability of a hung jury rather than a not guilty verdict or a guilty verdict.”

Table 26.1 presents median probability judgments for each of the two problems. Although support theory does not require strict inequalities for implicit and explicit subadditivity, the statistical tests reported in this article test the strict version of these inequalities against the null hypothesis of equality. In particular, we used the Mann–Whitney statistic to test the hypothesis that the judged probability of the implicit disjunction, P(A, B), is strictly smaller than the judged probability of the explicit disjunction, P(A1 ∨ A2, B). This analysis provides some evidence for implicit subadditivity in Problem 2(p *< .*05, one-sided) but not in Problem 1. We used the same statistic to test the hypothesis that the judged probability of the explicit disjunction, P(A1 ∨ A2, B), is strictly smaller than the sum of the judged probabilities of the single components, P(A1, A2 ∨ B) + P(A2, A1 ∨ B). Because the latter were assessed by different groups of participants, we generated 100 “synthetic” distributions of such sums by pairing at random participants from the two groups. The median of the Mann–Whitney statistics across these distributions was significant in both Problem 1 (median p *< .*05) and Problem 2 (median p *< .*0001). Thus, strict explicit subadditivity was confirmed for both problems, and strict implicit subadditivity was observed in the trial problem but not in the election problem. The latter observation is not too surprising because here the implicit disjunction, non-Democrat, is naturally unpacked into the explicit disjunction, Republican or Independent.