Testing the Δ-∑ hypothesis in the suboptimal choice task: Same delta with different probabilities of reinforcement

In a concurrent-chain procedure, pigeons choose between 2 initial-link stimuli; one is followed by terminal link stimuli that signal reliably whether food will be delivered after a delay; the other is followed by terminal link stimuli that do not signal whether food will be delivered after the delay. Pigeons prefer the former alternative even when it yields a lower overall probability of food. Recently, we proposed the Delta-Sigma (∆-∑) hypothesis to explain the effect: Preference depends on the difference (∆) between the reinforcement probabilities associated with the terminal link stimuli, and the overall probability of reinforcement (∑) associated with the alternative. The hypothesis predicts that, for constant ∑, animals should prefer alternatives with greater ∆ values regardless of the specific probabilities of reinforcement that determine ∆. In 2 experiments, we tested this prediction by comparing a ∆ = .5 against a ∆ = 0 alternative, with the former obtained with different pairs of reinforcement probabilities across conditions. The results supported the hypothesis when the 2 probabilities defining ∆ were significantly greater than 0, but not when one of them was close to 0. The results challenge our theoretical accounts of suboptimal choice and the variables considered to determine pigeons' preference.