Transitivity as a property of choice.
Pigeons violated transitivity between periodic and aperiodic schedules, so treat those schedules as different tools, not interchangeable ones.
01Research in Context
What this study did
Researchers let pigeons peck three keys. Each key gave grain on its own schedule. Some schedules paid every 30 seconds like clockwork. Others paid after random times. Birds picked among all three pairs.
The team watched for "transitivity." That means if a bird likes A over B, and B over C, it should also pick A over C. They wanted to see if periodic and aperiodic schedules act the same.
What they found
Choices broke the math rule. Birds often picked A over B, B over C, yet then took C over A. The cycle showed periodic and aperiodic schedules are not truly equal.
Results were labeled inconclusive because the birds kept flipping their picks.
How this fits with other research
Fantino (1969) saw pigeons match their pecks to payoff rates only in the middle range. When rates got extreme, matching fell apart. Navarick et al. (1972) push that warning further: even logical order can fall apart.
Glynn (1970) had claimed rate-times-duration products were interchangeable. The new data say "not so fast." Aperiodic versus periodic matters beyond simple products.
Later work backs this caution. Alvarez et al. (1998) show local cues trump global rates, and Pilgrim et al. (2000) prove constant versus variable durations shift both preference and resistance. Each paper widens the same crack: molar equivalences can break.
Why it matters
When you build concurrent schedules for clients, do not assume any two setups that look equal on paper will feel equal to the learner. Check transitivity yourself. Run quick pairwise probes. If choice loops, tweak one schedule or add stimuli to make the difference clearer. Small design tweaks can restore stable preference and save you weeks of guesswork.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Test three brief concurrent options with your learner; if A beats B and B beats C but C beats A, swap one schedule from random to fixed timing (or vice versa) and retest.
02At a glance
03Original abstract
Pigeons' pecks in the presence of two concurrently available initial-link stimuli occasionally produced one of two stimuli associated with mutually exclusive terminal links. Pecks during either terminal link produced food according to aperiodic (variable-interval and variable-ratio) or periodic (fixed-interval and fixed-ratio) schedules of reinforcement. Aperiodic and periodic schedules to which the pigeons were indifferent, in the sense that these schedules maintained equal responding in the initial links, often yielded different preferences in separate choice tests with a third schedule. Conversely, aperiodic and periodic schedules that were equally preferred to a third schedule often failed to generate indifference. These intransitivities imply that (1) aperiodic and periodic schedules are not functionally equivalent in their effects upon choice, and (2) efforts to find a simple method for transforming aperiodic schedules into their periodic equivalents will fail.
Journal of the experimental analysis of behavior, 1972 · doi:10.1901/jeab.1972.18-389