Natural sample spaces and the inversion of conditional judgments

Judgments of frequency or probability require formation of an appropriate sample space (i.e., consideration of the set of outcomes that could occur or that could be true). In judgments of the form A given B, the conditioning information, B, delineates the relevant sample space. We propose that when this relevant sample space corresponds to a natural category, appropriate samples are drawn and relatively accurate judgments are made. When the sample space does not correspond to a natural category, a related but inappropriate sample space is substituted and errors occur. Subjects in good sample-space conditions made judgments that had natural categories as the conditioning event (e.g., of 100 randomly selected men, how many prefer brown rather than blue?). Subjects in bad sample-space conditions made judgments that had natural categories as the conditioned event (e.g., of 100 randomly selected people who prefer brown rather than blue, how many are men?). Subjects made complementary judgments that should sum to 100%. As predicted, bad sample-space subjects were much more likely than good sample-space subjects to make errors by deviating from 100%. Data indicated that these errors resulted from subjects' inverting the judgment (e.g., from gender |preference to preference| gender), incorrectly using the natural category as the sample space. Implications are drawn for processes underlying judgments of conditional events and for the understanding of natural kinds in the social realm.

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