Ratio versus difference comparators in choice.

Pigeons pecked two keys for food. The team changed the amount of food and the delay to food across keys. They asked: do birds pick the key with the bigger ratio or the bigger difference? Ratio rule: compare 4 pellets / 2 s versus 2 pellets / 8 s. Difference rule: compare 4 − 2 pellets and 2 − 8 s. They ran many short sessions and counted pecks.

The ratio rule won. When the ratio of amount to delay favored one key, pigeons chose that key almost every time. The simple difference in pellets or seconds could not predict the birds' picks. Ratio math explained the data; difference math did not.

Durand (1982) built a dual-sensitivity model that already stretched the matching law. Rojahn et al. (1994) go deeper by swapping the whole decision engine—ratio beats difference.

Cullinan et al. (2001) later added signals to delays. They showed that signaling can bend choice, but the bend still follows ratio rules. The two studies fit: ratio first, signals tweak it.

Oliveira et al. (2014) used concurrent chains to draw smooth discount curves. Their curves rest on the same ratio logic the target paper validates. Together they give you two ways—simple schedules or chained links—to test ratio choice in any lab.

When you set up concurrent schedules for a client, think ratios, not raw differences. A 3:1 payoff rate will pull behavior even if the extra seconds look small on paper. Check your VR-VI or FR-VI setups with quick ratio math before session starts.