A test of two minimax models for predicting the scaling of partitions of stimulus sets
Date
1977
Authors
Lee, Stephen Lee
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Abstract
The organizing of a set of objects by partitioning them into groups is an aspect of many familiar tasks. A distinction is drawn between the sorting version of the partitioning tasks in which the basis for sorting a set of objects into groups is explicitly specified and the classification version of the tasks in which no objective is explicitly specified. In contrast to such traditional problems as concept identification in which the partitioning is prescribed by the experimenter and the subject is required to identify the underlying concept, the subject in either a classification or a sort situation has the freedom to partition a set of objects in any way that he chooses.
The present research is directed towards the ultimate goal of developing a model that would predict the partitions made by subjects when sorting objects on the basis of perceived physical similarity. In sorting on the basis of similarity, subjects presumably attempt to maximize the similarity within groups and the difference between groups. This sorting objective is called the "minimax'' objective. It is argued that, when sorting on similarity, subjects compare possible partitions in terms of the degree to which they meet the mini1nax objective. Two competing models were developed to predict subjects' judgments of the degree to which a given partition of the stimulus objects meet the minimax objective. The proposed models are not models of sorting but models of the judgmental processes that are assumed to be involved in the process of sorting.
The specific purpose of the two dissertation experiments was, first, to test whether subjects can make minimax judgments and, second, to test the two models of the judgmental process. Although both judgmental models could, with the addition of supplementary assumptions, have been tested in a sorting situation, the experiments provided a more direct test of the judgmental assumptions. The relevance of these experiments and models to the problem of sorting is discussed in the dissertation. In each experiment, subjects were required, first, to judge the similarity between all possible pairs of objects and, second, to judge the degree of similarity within and difference between groups for each of a number of selected partitions. Consistency was high among subjects both in their judgments of similarity and in their judgments of minimax. On the basis of the pairwise similarity judgments, predictions of the minimax judgments for partitions were generated from each model and compared with the corresponding minimax judgments actually made by the subjects. The weighted-means model was supported to a degree over the unweighted-means model; the informal verbal reports of subjects tended to confirm this superiority of the weighted model. However, both models were very good predictors of the obtained minimax judgments.