The Δ–∑ hypothesis: How contrast and reinforcement rate combine to generate suboptimal choice

Abstract

When given a choice between two alternatives, each offering food after the same delay with different but signaled probabilities, pigeons often prefer the low probability alternative. This preference is surprising because pigeons fail to maximize the rate of food intake; they exhibit a suboptimal preference. We advance a new explanation, the Δ-P hypothesis, in which the difference in probability of reinforcement within terminal links (Δ) and the overall reinforcement probability rate of each alternative ( P ) are the key variables responsible for such suboptimal preference. We tested the Δ-P hypothesis in two experiments. In Experiment 1, we manipulated the Δs while maintaining constant all other parameters of the task, in particular the P s. We predicted a preference for the alternative with the larger Δ. In Experiment 2, we examined the effect of the overall reinforcement probabilities, the P s, while maintaining constant all other parameters of the task, in particular the Δs. We predicted a preference for the larger P . The results of both experiments support the Δ-P hypothesis.

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

“…To test this prediction, we pitted a Δ = .5 option, constructed with different pairs of probability values, against a Δ = 0 option, constructed with the same probability of .5 in both terminal links. In Experiment 1, we replicated the results from previous research (González et al, 2020), finding a preference for Δ = .5 relative to Δ = 0 when the former was constructed with the pair .75/.25. A preference for Δ = .5 was also obtained with the new pair 1/.5.…”

“…Results from two experiments showed that animals were sensitive to both higher-order variables (González et al, 2020). In Experiment 1, the Δs varied across conditions while the Σs remained equal.…”

“…We have previously advanced an account of suboptimal choice with a simple quantitative hypothesis (González et al, 2020). According to the Delta-Sigma hypothesis, the value of an alternative, V, increases directly with two higher-order variables associated with that alternative, the difference between the reinforcement probabilities in the terminal links of the alternative (Delta, Δ), and the overall probability of reinforcement obtained by choosing the alternative (Sigma, P ).…”

The functional equivalence of two variants of the suboptimal choice task: choice proportion and response latency as measures of value

“…The newly proposed Delta-Sigma hypothesis (González et al 2020), on the other hand, suggests that the contrast, defined as the difference between the two reinforcement probabilities associated with each terminal link within an alternative (Delta, ∆), and the overall reinforcement probability of each alternative (Sigma, ∑) are the main determinants of choice. In the standard task (see Fig.…”

“…For instance, the temporal dynamics of value accumulation by two stimuli (S 1 ± , and S 2 ± ) presented sequentially may be lessened compared to the single-stimulus situation (S ± ). On the other hand, the ∆-∑ hypothesis (González et al 2020) was conceived for the two-option variation and assumed that the single-option version was equivalent under certain conditions. Applying the ∆-∑ hypothesis to the optimal alternative in the original procedure is not straightforward because, with only one terminal link stimulus, we cannot compute ∆.…”