The expected likelihood of transitivity of preference

May's model of pairwise preference determination is used to assess the expected likelihood that a subject's pairwise preference comparisons on three alternatives will be transitive. A closed form representation for this expected likelihood is obtained for each situation considered. When the subject is assumed to act precisely according to rankings on attributes with May's model, the computed expected likelihoods the relatively large. When the subject becomes a probabilistic chooser, as defined in a specific manner, expected likelihoods of transitivity decrease significantly from corresponding values with May's model. For a probabilistic Chooser, there is a significant likelihood that the subject might yield transitive pairwise preferences substantially different than the results suggested by May's model.This research was supported by a grant from the General University Research Program and through a fellowship from the Center for Advanced Study, both of the University of Delaware. Very helpful input from John H. Antil, Meryl P. Gardner, and James M. Munch is also acknowledged.     

Human nonverbal counting estimated by response production and verbal report

In three experiments, people were shown sequential displays and were prevented from verbal counting by being required to perform other cognitive tasks. In Experiment 1, the subjects were shown three 1.target (target5 = 8, 16, or 32) sequences of colored geometric shapes. On occasional question trials, the subjects were asked to estimate the target number after the final item in the sequence. On other test trials, items continued to appear beyond the target, and the subjects estimated the target manually by tapping a space bar. In Experiments 2 and 3, a matching-to-sample procedure required the subjects to estimate the same sequence of items (target = 8, 11, 14, 17, or 20) both verbally and manually. The results indicated that (1) manual and verbal estimates closely approximated target size in Experiments 1 and 2, (2) coefficients of variation were constant across target size, and (3) correlations between manual and verbal estimates were positive in Experiments 2 and 3. Requiring the subjects to perform a counting task during presentation of items led to underestimation of number in Experiment 3. nt]mis|This research was funded by a research grant from the Natural Sciences and Engineering Research Council of Canada to W.A.R. and by the Ontario Graduate Scholarship in Science and Technology and the Ontario Graduate Scholarship to M.J.B.     

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