Matching, Undermatching, and Overmatching in Studies of Choice

Abstract

Almost all of 103 sets of data from 23 different studies of choice conformed closely to the equation: log (B1/B2) = a log (r1/r2) + log b, where B, and B2 are either numbers of responses or times spent at Alternatives 1 and 2, r, and r2 are the rates of reinforcement obtained from Alternatives 1 and 2, and a and b are empirical constants. Although the matching relation requires the slope a to equal 1.0, the best-fitting values of a frequently deviated from this. For B1 and B2 measured as numbers of responses, a tended to fall short of 1.0 (undermatching). For B1 and B2 measured as times, a fell to both sides of 1.0, with the largest mode at about 1.O. Those experiments that produced values of a for both responses and time revealed only a rough correspondence between the two values; a was often noticeably larger for time. Statistical techniques for assessing significance of a deviation of a from 1.0 suggested that values of a between .90 and 1.11 can be considered good approximations to matching. Of the two experimenters who contributed the most data, one generally found undermatching, while the other generally found matching. The difference in results probably arises from differences in procedure. The procedural variations that lead to undermatching appear to be those that produce (a) asymmetrical pausing that favors the poorer alternative; (b) systematic temporal variation in preference that favors the poorer alternative; and (c) patterns of responding that involve changing over between alternatives or brief bouts at the alternatives.Key words: matching relation, undermatching, overmatching, choice, conc VIVIIn experiments with concurrent variableinterval schedules, when the ratio of responding or time spent at two alternatives (Bl/B2) is graphed in logarithmic coordinates as a function of the ratio of reinforcement (r1/r2) obtained from the two alternatives, the data points usually conform to a straight line: B1 = a log r + log b(1) log a log Exponentiating both sides of this equation produces a power function of the type familiar in psychophysics (Stevens, 1957(Stevens, , 1975:

Timing in Choice Experiments.

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The Matching Law: A Tutorial for Practitioners

“…Baum, 1979 A review of matching law studies with specific attention to sensitivity to reinforcement parameters.…”

Association of liking and reinforcing value with children's physical activity

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