Scaling preferences using probabilistic choice models: is there a ratio-scale representation of subjective liking?

In two online experiments, we tested whether preference judgments can be used to derive a valid ratio-scale representation of subjective liking across different stimulus sets. Therefore, participants were asked to indicate their preferences for all possible pairwise comparisons of 20 paintings (Experiment 1) and 20 faces (Experiment 2). Probabilistic choice models were fit to the resulting preference probabilities (requiring different degrees of stochastic transitivity), demonstrating that a ratio-scale representation of the liking of both paintings and faces can be derived consistently from the preference judgments. While the preference judgments of paintings were consistent with the highly restrictive Bradley–Terry–Luce model (Bradley and Terry, Biometrika 39:324–345, 1952; Luce, 1959), the liking of faces could be represented on a ratio scale only when accounting for face gender as an additional aspect in an elimination-by-aspects model. These ratio-scaled liking scores were then related to direct evaluative ratings of the same stimuli on a 21-point Likert scale, given both before and after the pairwise comparisons. It was found in both studies that evaluative ratings can be described accurately as a logarithmic function of the indirectly derived liking scores for both types of stimuli. The results indicate that participants are able (a) to consistently judge preferences across two heterogeneous stimulus sets, and (b) to validly report their liking in direct evaluative ratings, although the numeric labels derived from direct evaluative ratings cannot be interpreted at face value for ratio-scaled liking scores.