Violations of transitivity: Implications for a theory of contextual choice.
Context within chained schedules, not hidden reward traits, can make client choices look circular.
01Research in Context
What this study did
Gillberg (1993) wrote a theory paper. It asks why animals sometimes break the rule of transitivity. Transitivity means if A is picked over B, and B over C, then A should beat C. The paper says the setting, not extra dimensions of reward, causes the breaks. It adds a context term to the generalized matching law.
What they found
The model shows that linked schedules can make choices look circular. When the first link feeds into the second, the best option can flip. The math keeps the single reward scale but lets context bend the curve.
How this fits with other research
Pfadt (1991) set the stage. That paper also blamed the procedure, not new reward traits. Gillberg (1993) keeps the idea and gives it a clear equation.
Hatton et al. (1999) seems to clash. Hens picked in a straight line across different work loads. The birds stayed transitive while Gillberg (1993) says breaks should happen. The gap is in the method: hens saw simple response costs, not the chained set-ups that create context flips.
Pisacreta (1982) gave the math bones. The earlier model handled chained schedules but stayed silent on loops. Gillberg (1993) keeps the bones and adds the context muscle.
Why it matters
When you run a concurrent-chain preference assessment, watch the links. If the first choice only opens the gate to the second, transitivity can fail without extra reward traits. Build in context checks—swap the order, retest, and see if the loop holds. If it breaks, adjust the chain, not the reinforcer.
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02At a glance
03Original abstract
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.
Journal of the experimental analysis of behavior, 1993 · doi:10.1901/jeab.1993.60-185