The expected likelihood of transitivity for a probabilistic chooser

May [18] developed an algebraic choice model of pairwise preference comparison in which subjects respond precisely to ordinal information on attributes of comparison. This study considers a probabilistic choice model variation of May's model, in which subjects respond with various degrees of precision in comparison to May's model. This precision can be viewed as an indirect measure of the subject's level of perception of the attributes of comparison. The purpose of the study is to examine the expected likelihood with which subjects will have transitive responses, as the degree of precision is varied. Closed form representations are obtained for the expected likelihood of transitivity for three alternatives for each different level of precision. Results indicate that a relatively small change in this precision can lead to substantial changes in the expected likelihood of transitivity.

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