Preference for fixed-interval schedules: an alternative model.

Jensen et al. (1973) built a new math model for pigeon choice. Pigeons pecked in a two-key setup. First, birds chose which key to enter. Then they waited for food on fixed-interval schedules. The team tracked every peck and seed.

The model used three simple parts: how long each final wait lasted, how often food arrived overall, and how many times the bird entered each side.

The new formula explained 94% of the birds’ choices. It solved old puzzles that older equations could not. Terminal-link time mattered more than just food rate.

Davison (1969) and Alba et al. (1972) showed pigeons follow the matching law in similar two-key chains. The 1973 model keeps their core idea but adds cleaner math.

Later studies tweaked the same theme. Sarber et al. (1983) swapped raw rates for square-root rates and got a tighter fit. Hinson (1988) wrapped the delay idea inside a hyperbolic decay curve.

Lloyd (2002) seems to clash: when final delays kept a 10-s gap, preference still faded as waits grew longer. The 1973 model missed that absolute time also hurts. The gap is real, so check delay length, not just the difference.

If you run token boards, chained schedules, or DRO timers, think beyond simple rate. Count how long the client waits in each final link, how often reinforcers arrive overall, and how many entries each side gets. Shorter absolute waits keep preference strong, even when the gap between sides stays the same. Try trimming the longest terminal delay first.