Matching when the number of response alternatives is large

Abstract

Pigeons could choose between five concurrently available response keys, each associated with a different variable-interval schedule of reinforcement. A 2-sec changeover delay was also in effect on each key. In almost all cases, the relative number of responses to a key and the relative time spent at it were nearly equivalent to the relative number of reinforcements it produced. In addition, matching was observed between the relative number of reinforcements at a key and the relative number of changeovers to it.Although Herrnstein's (1970) formulation of the matching principle provides for the general case of several response alternatives, in nearly all studies of matching the number of alternatives has been restricted to two. Typically, the experimental situation is one in which Ss choose between a pair of concurrently available variable-interval (VI) schedules of primary reinforcement. When matching appears under such conditions, it can be expressed by the equationwhere P signifies the number of responses emitted and R the number of reinforcements obtained. The subscripts denote the respective response alternatives and the reinforcement sources associated with them.An exception to this now standard situation was provided by Reynolds (1963), who exposed pigeons to a condition in which three response keys were available. His procedure was a variant of that first introduced by Autor (1969) and now commonly termed a concurrent-chains schedule. In Reynolds's experiment, two-member chain schedules were assigned to each of the three keys. The initial members (or links) of the three chains consisted of identical VI schedules. The keys were also illuminated identically. Whenever an interval elapsed on the VI schedule associated with a particular key, the next response on that key produced either of two effects: (1) The color of the key that had just been pecked was changed and the other two keys were darkened and became inoperative, or (2) all three keys were darkened and made inoperative. This latter effect is known as time-out (TO). The probability that the former effect occurred, i.e., that a keypeck produced a change of key color, was different for each key. When pecking in the first link produced a change in key color for one of the keys, a fixed-ratio (FR) schedule went into effect on that key and remained in effect until the ratio was completed and food delivered. The ratio was the same in all terminal links. Following reinforcement the initial links were reinstated. If responding in the initial links had produced a TO, the animal remairIed in that condition for 30 sec before the initial links resumed.Reynolds alternated sessions in which the three-key choice was available with sessions in which one of the keys was covered and the choice was between the remaining pair. In both cases he found equivalence between the relative rates of responding in the initial links and the relative rates of reinforcement in the terminal links. When three keys were available, he expressed the function relating responses and reinfor...

Effects of the Discriminability of Alternatives in Three‐alternative Concurrent‐schedule Performance

“…This is the question posed in the present research. Previous research has shown that if performance on VI schedules with more than two alternatives is analyzed pairwise, Equation 1 fits well, and there is no effect of the presence, absence, or value of any third alternative on the preference or sensitivity between the other two (Davison & Hunter, 1976;H. Miller & Loveland, 1974;Pliskoff & Brown, 1976).…”

Foraging Strategies and Their Social Significance

“…The optimization theory would also explain why animals march according to "prey size" (length of access to food) when offered two variable-interval schedules that are otherwise identical (Catania, 1963). Although most of the work on matching has involved only two concurrent schedules, Miller and Loveland (1974) have reported matching in a situation where a pigeon is confronted with a choice of five keys, although it is not clear if Shimp's optimization result holds for this more complex environment. Zach and Falls (1976a) studied revisiting of patches (blocks of wood drilled with holes) by ovenbirds in an aviary experiment.…”

Matching‐based Hedonic Scaling in the Pigeon

“…This preservation of equality between distributions of behavior and reinforcement frequency has been demonstrated more recently in diverse experimental settings. These have involved, for example, (1) a continuous type of behavior-standing in place (Baum and Rachlin, 1969); (2) a topographically disparate response-treadle pressing by pigeons (McSweeney, 1975); (3) a large number of response alternatives (Miller and Loveland, 1974;Pliskoff and Brown, 1976); and (4) a naturally occurring aggregate of pigeons (Baum, 1974a). Matching has also been observed in human subjects (see, e.g., Baum, 1975;Schroeder and Holland, 1969).…”