Violations of transitivity: Implications for a theory of contextual choice

Violations of strong stochastic transitivity in concurrent-chains choice were first reported by Navarick and Fantino. In a series of articles, Navarick and Fantino concluded that neither a unidimensional model capable of predicting exact choice probabilities nor a fixed-variable equivalence rule was possible for the concurrent-chains procedure. I show that when choice is modeled contextually (i.e., when preference for a schedule is affected by factors other than the schedule itself, e.g., aspects of the alternative schedule), a unidimensional, exact-choice probability model is possible that both predicts the intransitivities reported by Navarick and Fantino and provides a fixed-variable equivalence rule for the concurrent-chains procedure. The contextual model is an extension of the generalized matching law and violates a key assumption underlying traditional choice models-simple scalability-because of (a) schedule interdependence and (b) bias from procedural contingencies. Therefore, strong stochastic transitivity cannot be expected to hold. Contextual scalability is analyzed to reveal a hierarchy of context effects in choice. Navarick and Fantino's intransitivities can be satisfactorily explained by bias. If attribute sensitivity is context dependent, however, and if there are similarity structures among choice alternatives, the contextual model is shown to be able to predict violations of ordinal preference. Therefore, it may be possible to formulate a deterministic, general psychophysical model of choice as a behavioral alternative to probabilistic, multidimensional choice theories.