IS MATCHING COMPATIBLE WITH REINFORCEMENT MAXIMIZATION ON CONCURRENT VARIABLE INTERVAL, VARIABLE RATIO?¹

Abstract

Four pigeons on concurrent variable interval, variable ratio approximated the matching relationship with biases toward the variable interval when time spent responding was the measure of behavior and toward the variable ratio when frequency of pecking was the measure of behavior. The local rates of responding were consistently higher on the variable ratio, even when there was overall preference for the variable interval. Matching on concurrent variable interval, variable ratio was shown to be incompatible with maximization of total reinforcement, given the observed local rates of responding and rates of alternation between the schedules. Furthermore, it was shown that the subjects were losing reinforcements at a rate of about 60 per hour by matching rather than maximizing.Key words: concurrent VI VR, matching, maximization, reinforcement, pigeonsIn psychology, biology, and economics it is often assumed that behavioral adaptation entails optimization of some variable or set of variables, such as reinforcement rate, fitness, or wealth (Lea, 1978). In operant psychology one version of this view has motivated theories of concurrent schedule performance. It is, for example, argued that the matching relationship between choice proportions and reinforcement proportions is the result of some process that maximizes reinforcement rate (e.g., Mackintosh, 1974; Shimp, 1975). According to one version of maximization theory, the subject is said to choose between simultaneously available reinforcement schedules so as to produce the greatest reinforcement rate, summing across both schedules (e.g., Rachlin, Green, Kagel, & Battallio, 1976

The copyist model of response emission

“…When fit by Equations 4 and 5, α and β were .91 and − .21, respectively, in terms of relative response rate and .89 and − .03 in terms of relative time allocation. As reflected in these statistics and in a comparison between these simulated performances and actual data from Herrnstein and Heyman (1979, Table 2), the simulation reproduced two empirical effects seen in the target study: (1) The slopes of the relative-response and relative-time data approximated the slope of matching, and (2) response, but not time, data were biased toward the VR.…”

“…In Herrnstein and Heyman's (1979) report on concurrent VR VI schedules, relative response and time allocation approximately track the slope of the matching loci; however, a bias is evident in the unequal distribution of response and time data around the matching line. In particular, when measured in terms of time, they found choice allocation biased toward the VI; however, when measured in terms of responses, the bias was toward the VR-an outcome they attributed to the higher local response rate on their VR schedules.…”

“…Although not central to the purposes of this report, it is an interesting aside to look at the interpretation Herrnstein and Heyman (1979) lent their report and the implications of our simulated outcomes for it. An active topic at the time of that publication was whether matching as outcome could be attributed to matching as process or, alternatively, maximizing as process.…”

Adaptive Behavior and Learning

“…See de Villiers (1977) and de Villiers and Herrnstein (1976) for reviews of matching as a general law of reinforcement. There are several papers deriving matching from various maximizing principles, e.g., Rachlin (1978) and Staddon and Motheral (1978), although these have not gone unchallenged (Herrnstein & Heyman 1979;Heyman, 1979;Staddon & Motheral, 1979). Reviews are Williams (1988) and Staddon & Cerutti (2003).…”

What are we doing when we translate from quantitative models?

“…In the present case, for instance, careful reading of the basic literature reveals that debate is unresolved about whether or when ratio-like schedules contribute to matching (Green, Rachlin, & Hanson, 1983;Herrnstein & Heyman, 1979;MacDonnall, 1988;Savastano & Fantino, 1994;Shimp, 1966;Shurtleff & Silberberg, 1990). Gaps in basic research limit the functional parallels that can be drawn when a laboratoryderived equation is fit to field data.…”