Testable conditions for triads of paired comparison choices

Forty-two choice models, each representing stimuli by one-dimensional probability distributions, are obtained by relaxing the assumptions of Thurstone's Case V Law of Comparative Judgment. The models which imply or fail to imply each of nine testable probabilistic conditions are determined. Stochastic transitivity is vulnerable in most of these models. The results suggest discarding weak stochastic transitivity, and in its place using the conjunction of weak stochastic transitivity and the triangular condition. However, unless it is possible to predict which stimuli will produce violations of the conditions, none of the conditions can be rejected on the basis of too frequent intransitive triads of choices.I am grateful to the referees, and to J. H. Griesmer and C. H. Coombs for a number of helpful criticisms and comments. J. H. Griesmer suggested a proof of Theorem 9, and a referee suggested a more direct proof of Theorem 5. A proof of Theorem 5 and the result concerning a maximally intransitive judge were given in 18].