On applying the matching law to between-subject data

Rate matching, probability matching, and optimization in concurrent ratio schedules

Much research has documented rate matching in concurrent variable-interval schedules, but comparatively little research has examined performance in concurrent variable-ratio schedules, except in discrete-trials procedures that sometimes produce probability matching. One should expect that the two types of schedule would result in different performances, because ratio schedules cannot improve with time the way interval schedules do; ratio schedules lack the temporal dynamics of interval schedules. The present experiment exposed rats to concurrent variable-ratio schedules. Seven unsignaled components were presented in random order within each daily session, with probability ratios ranging from 1:8 to 8:1. Three conditions were studied that varied the overall probability of food while leaving probability ratios the same. Choice appeared to conform to probability matching, because sensitivities in the rate-matching relation were close to 0.5, whereas sensitivities to probability ratio were close to 1.0. The sensitivities alone, however, could not confirm probability matching, because undermatching to rate occurs often. Analyses at smaller time scales supported the interpretation of probability matching. In particular, control by food deliveries was highly local in concurrent variable-ratio schedules, in contrast with concurrent variable-interval schedules, in which control is extended. Activity continued to switch between alternatives throughout components, contradicting optimal sampling theory.

Matching Behaviours and Rewards

Matching describes how behaviour is related to rewards. The matching law holds when the ratio of an individual's behaviours equals the ratio of the rewards obtained. From its origins in the study of pigeons working for food in the laboratory, the law has been applied to a range of species, both in the laboratory and outside it (e.g., human sporting decisions). Probability matching occurs when the probability of a behaviour equals the probability of being rewarded. Input matching predicts the distribution of individuals across habitats. We evaluate the rationality of the matching law and probability matching, expose the logic of matching in real-world cases, review how recent neuroscience findings relate to matching, and suggest future research directions.