On the Classic and Modern Theories of Matching

Abstract

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.Key words: matching theory, matching law, quantitative law of effect, Herrnstein's hyperbola _______________________________________________________________________________ Thirty-five years ago, Richard J. Herrnstein (Herrnstein, 1970) proposed the theory of matching, according to which all behavior can be conceptualized as choice, governed by the matching equation,In this equation the Rs represent response rates or counts, the r s represent reinforcement rates or counts, and the numerical subscripts refer to the two components of a concurrent schedule (Herrnstein, 1961). The equation asserts that organisms allocate their behavior across concurrently available response alternatives in the same proportion that reinforcements are allocated across those alternatives. Herrnstein (1970) turned the purely descriptive matching equation into a theory by applying it to single-alternative schedules. He conceptualized these as two-component concurrent schedules consisting of instrumental responding as one alternative, and background or extraneous responding as the other alternative. For this conceptualization of the single-alternative case, the matching equation can be written R RzR e~r r zr e , where R and r refer to the instrumental response and reinforcement rates or counts, and R e and r e refer to the extraneous response and reinforcement rates or counts. Assuming a constant total amount of behavior to allocate, k, then R + R e 5 k, and the equation can be written R~k r r zr e :

A quantitative analysis of the behavior maintained by delayed reinforcers

“…Differential reinforcement is a variety of selection by consequences (Skinner, 1981), and selectionist models are well-suited to showing how matching can emerge as its product (e.g., McDowell, 2005;McDowell, 2014;McDowell & Popa, 2010). Differential reinforcement presumably engendered the matching of responses per run to the contingencies (Fig.…”

Optimal indolence: a normative microscopic approach to work and leisure

“…This decision has been studied by economists [1][2][3][4][5], behavioural psychologists [6][7][8][9][10][11][12][13][14][15][16], ethologists [17] and neuroscientists [18][19][20][21][22][23][24]. Tasks involving free-operant behaviour are particularly revealing, because subjects can choose what, when and how, minimally encumbered by direct experimenter intervention.…”

Simple Artificial Neural Networks That Match Probability and Exploit and Explore When Confronting a Multiarmed Bandit

“…While modern variations exist [4], the matching law is usually expressed as R = kr=(r + re), where R is response rate, k and re are parameters, and r is reinforcement rate. Intended, to explain response frequency, the matching law also predicts how response strength varies with reinforcement frequency [5].…”