Violations of transitive preference: A comparison of compensatory and noncompensatory accounts

Violations of transitive preference can be accounted for by both the noncompensatory lexicographic semiorder heuristic and the compensatory additive difference model. However, the two have not been directly compared. Here, we fully develop a simplified additive difference (SAD) model, which includes a graphical analysis of precisely which parameter values are consistent with adherence to, or violation of, transitive preference, as specified by weak stochastic transitivity (WST) and triangle inequalities (TI). The model is compatible with compensatory, within-dimension evaluation. We also develop a stochastic difference threshold model that also predicts intransitive preferences and encompasses a stochastic lexicographic semiorder model. We apply frequentist methods to compare the goodness of fit of both of these models to Tversky’s (1969) data and four replications and Bayes factor methods to determine the strength of evidence for each model. We find that the two methods of analysis converge and that, for two thirds of the participants for whom predictions can be made, one of these models predicting violations of WST has a good and the best fit and has strong Bayesian support relative to an encompassing model. Furthermore, for about 20% of all participants, the SAD model (consistent with violations of WST or TI) is significantly better-fitting and has stronger Bayesian support than the stochastic difference threshold model. Finally, Bayes factor analysis finds strong evidence against transitive models for most participants for whom the SAD model consistent with violation of WST or TI is strongly supported.