Violations of stochastic transitivity on concurrent chains: Implications for theories of choice.

Pfadt (1991) looked at odd choice patterns in concurrent-chain schedules. These are the two-step schedules you use in preference assessments.

The paper asked: when pick-A-over-B and B-over-C, why do some pigeons later pick C over A? This breaks a rule called stochastic transitivity.

Instead of adding new reward dimensions, the author blamed the procedure itself.

The math showed that small changes in chain links can flip apparent preference.

So the "violation" may be a measurement glitch, not a true mental U-turn.

Hatton et al. (1999) ran hens on simple concurrent ratios and got perfect transitivity. The birds always picked the smaller response requirement. This seems to clash with Pfadt (1991), but the hens never saw the two-step chain structure that can hide reinforcer delays.

Gillberg (1993) kept the one-dimensional view but added schedule interdependence. His contextual matching rule predicts when transitivity will break and when it will hold, building directly on Pfadt (1991).

Pisacreta (1982) supplied the earlier incentive model that A uses. The core idea—value equals reduced delay to food—stays the same; A just shows it can fake intransitivity if the chain links shift.

Houston et al. (1987) warn that low switch rates can make allocation look odd even when preference is stable. Together with A, the message is: check the procedure before you check the organism.

For BCBAs, the paper is a caution flag. If a child picks bubbles over blocks, blocks over trains, but then trains over bubbles, do not rush to say reinforcement is "multidimensional." Look at your chain first. Did the terminal delay change? Did the initial-link schedule shift? Fix the procedure and the circular preference may vanish, saving you from unnecessary program rewrites.