Preference for mixed versus constant delay of reinforcement

Preference for constant and mixed delay of reinforcement was studied using concurrent equal variable-interval schedules. For four pigeons, pecking one key was reinforced following constant delays of 8 sec and mixed delays of 6 or 10 and 2 or 14 sec. Pecking a second key was reinforced following constant delays of 0, 8, 16, and 32 sec. For two additional pigeons, pecking one key was reinforced following delays of 30, 15 or 45, 5 or 55, and 0 or 60 sec. Reinforcements on the other key were delayed 30 sec. It was found that (a) pigeons preferred mixed relative to constant delay of reinforcement, and (b) preference for mixed delay of reinforcement increased as the range of delay interval variability increased.     

Preference between variable-ratio and fixed-ratio schedules: local and extended relations.

Although it has repeatedly been demonstrated that pigeons, as well as other species, will often choose a variable schedule of reinforcement over an equivalent (or even richer) fixed schedule, the exact nature of that controlling relation has yet to be fully assessed. In this study pigeons were given repeated choices between concurrently available fixed-ratio and variable-ratio schedules. The fixed-ratio requirement (30 responses) was constant throughout the experiment, whereas the distribution of individual ratios making up the variable-ratio schedule changed across phases: The smallest and largest of these components were varied gradually, with the mean variable-ratio requirement constant at 60 responses. The birds' choices of the variable-ratio schedule tracked the size of the smallest variable-ratio component. A minimum variable-ratio component at or near 1 produced strong preference for the variable-ratio schedule, whereas increases in the minimum variable-ratio component resulted in reduced preference for the variable-ratio schedule. The birds' behavior was qualitatively consistent with Mazur's (1984) hyperbolic model of delayed reinforcement and could be described as approximate maximizing with respect to reinforcement value.     

Effects on choice of reinforcement delay and conditioned reinforcement

Pigeons chose between fixed-interval schedules of different durations presented in the terminal links of concurrent-chains schedules. The pair of schedules was always in the ratio of 2:1, but the absolute duration of the fixed intervals varied. In one set of conditions, the different terminal-link schedules were associated with different keylight stimuli (cued conditions). In a second set of conditions, the different terminal-link schedules were associated with the same stimulus (uncued conditions). Results from the cued conditions replicated previous findings that preference for the shorter fixed-interval schedule increased with fixed-interval duration. Preferences in the uncued conditions were lower than in the corresponding cued conditions but also increased with fixed-interval length. In addition, the degree of control under the uncued conditions was correlated with the extent to which the schedule during the terminal link was discriminated immediately upon entry into the terminal link. The pattern of results in both conditions was inconsistent with the notion that choice behavior matches relative immediacy of reinforcement. Reanalysis of previous evidence for matching (Chung and Herrnstein, 1967) showed that matching in fact did not occur, as the preferences of their subjects for the shorter of two delays also increased with the absolute size of the delays.     

Duration and rate of reinforcement as determinants of concurrent responding

The duration and frequency of food presentation were varied in concurrent variable-interval variable-interval schedules of reinforcement. In the first experiment, in which pigeons were exposed to a succession of eight different schedules, neither relative duration nor relative frequency of reinforcement had as great an effect on response distribution as they have when they are manipulated separately. These results supported those previously reported by Todorov (1973) and Schneider (1973). In a second experiment, each of seven pigeons was exposed to only one concurrent schedule in which the frequency and/or duration of reinforcement differed on the two keys. Under these conditions, each pigeon's relative rate of response closely matched the relative total access to food that each schedule provided. This result suggests that previous failures to obtain matching may be due to factors such as an insufficient length of exposure to each schedule or to the pigeons' repeated exposure to different concurrent schedules.     

Effects of Interspersing Briefer Mathematics Problems on Assignment Choice in Students with Learning Disabilities

Within- and between-series designs were combined and used to evaluate the effects of interspersing briefer math problems (i.e., one-digit by one-digit multiplication, 1 × 1) with more time-consuming problems (i.e., two-digit by one-digit multiplication, 2 × 1) on time allocation to one of two concurrent computer-delivered mathematics computation assignments in four high school students with specific learning disabilities in mathematics. The computer presented students with a choice of 2 × 1 problems with 1 × 1 problems interspersed every third problem (i.e., experimental assignment) or 2 × 1 problems without interspersal (i.e., control assignment). Visual and statistical analysis showed that students allocated a greater percentage of their time to the interspersal assignments. These results support previous research on the matching law and problem completion rates and suggest that students' preference for assignments can be improved through the interspersal technique. Discussion focuses on future research and applied educational implications for curricula construction and task sequencing.     

Effects of reinforcement context on choice

Two experiments investigated the effects of successive reinforcement contexts on choice. In the first, concurrent variable-interval schedules of primary reinforcement operated during the initial links of concurrent chains. The rate of this reinforcement arranged by the concurrent schedules was decreased across conditions: When it was higher than the terminal-link rate, preference for the higher frequency initial-link schedule increased relative to baseline. (During baseline, a standard concurrent-schedule procedure was in effect). When the initial-link reinforcement rate was lower than the terminal-link rate, preference converged toward indifference. In the second experiment, a chain schedule was available on a third key while a concurrent schedule was in effect on the side keys. When the terminal link of the chain schedule was produced, the side keys became inoperative. Availability of the chain schedule did not affect choice between the concurrent schedules. These results show that only when successive reinforcement contexts are produced by choice responding do those successive contexts affect choice in concurrent schedules.     

Choice and conditioned reinforcement.

A potential weakness of one formulation of delay-reduction theory is its failure to include a term for rate of conditioned reinforcement, that is, the rate at which the terminal-link stimuli occur in concurrent-chains schedules. The present studies assessed whether or not rate of conditioned reinforcement has an independent effect upon choice. Pigeons responded on either modified concurrent-chains schedules or on comparable concurrent-tandem schedules. The initial link was shortened on only one of two concurrent-chains schedules and on only one of two corresponding concurrent-tandem schedules. This manipulation increased rate of conditioned reinforcement sharply in the chain but not in the tandem schedule. According to a formulation of delay-reduction theory, when the outcomes chosen (the terminal links) are equal, as in Experiment 1, choice should depend only on rate of primary reinforcement; thus, choice should be equivalent for the tandem and chain schedules despite a large difference in rate of conditioned reinforcement. When the outcomes chosen are unequal, however, as in Experiment 2, choice should depend upon both rate of primary reinforcement and relative signaled delay reduction; thus, larger preferences should occur in the chain than in the tandem schedules. These predictions were confirmed, suggesting that increasing the rate of conditioned reinforcement on concurrent-chains schedules may have no independent effect on choice.     

Choice between fixed-interval schedules: Graded versus step-like choice functions

Pigeons chose between two fixed-interval schedules of food reinforcement. A single peck on one of two lighted keys started the fixed-interval schedule correlated with that key. The schedule had to be completed before the next choice opportunity. The durations of the fixed intervals were varied over conditions from 15 s to 40 s. To maximize the rate of reinforcement, the pigeons had to choose exclusively the shorter of the two schedules. Nevertheless, choice was not all-or-none. Instead, relative choice, and the rates of producing the fixed intervals, varied in a graded fashion with the disparity between the two schedules. Choice ratios under this procedure (single response to choose) were highly sensitive to the ratios of the fixed-interval schedules.     

DO CONDITIONAL REINFORCERS COUNT?

Six pigeons were trained on a procedure in which seven components arranged different food-delivery ratios on concurrent variable-interval schedules each session. The components were unsignaled, lasted for 10 food deliveries, and occurred in random order with a 60-s blackout between components. The schedules were arranged using a switching-key procedure in which two responses on a center key changed the schedules and associated stimuli on two side keys. In Experiment 1, over five conditions, an increasing proportion of food deliveries accompanied by a magazine light was replaced with the presentation of the magazine light only. Local analyses of preference showed preference pulses toward the alternative that had just produced either a food-plus-magazine-light or magazine-light-only presentation, but pulses after food deliveries were always greater than those after magazine lights. Increasing proportions of magazine lights did not change the size of preference pulses after food or magazine-light presentations. Experiment 2 investigated the effects of correlations between food ratios and magazine-light ratios: In Condition 6, magazine-light ratios in components were inversely correlated (-1.0) with food ratios, and in Condition 7, magazine-light ratios were uncorrelated with food ratios. In Conditions 8 and 9, pecks also produced occasional 2.5-s flashes of a green keylight. In Condition 8, food and magazine-light ratios were correlated 1.0 whereas food and green-key ratios were correlated -1.0. In Condition 9, food and green-key ratios were correlated 1.0 whereas food and magazine-light ratios were correlated -1.0. Preference pulses toward alternatives after magazine lights and green keys depended on the correlation between these event ratios and the food ratios: If the ratios were correlated +1.0, positive preference pulses resulted; if the correlation was -1.0, preference pulses were negative. These results suggest that the Law of Effect has more to do with events signaling consequences than with strengthening responses.     

Choice: A local analysis

Analyses of free-operant choice usually employ one of two general procedures: the simple concurrent procedure (i.e., a concurrent variable-interval variable-interval schedule) or the concurrent-chains procedure (i.e., concurrently available initial links, each leading to an exclusively available terminal link). Theories about choice usually focus on only one of the two procedures. For example, maximization theories, which assert that behavior is distributed between two alternatives in such a way that overall rate of reinforcement is maximized, have been applied only to the simple concurrent procedure. In the present paper, a form of the pairing hypothesis (according to which pairings between one stimulus and another affect the value of the first, and pairings between responses and reinforcers affect the value of the former) is developed in a way that allows it to make qualitative predictions with regard to choice in a variety of simple concurrent and concurrent-chains procedures. The predictions include matching on concurrent variable-interval variable-interval schedules, preference reversal in the self-control paradigm, and preference for tandem over chained terminal links.     

Choice for aperiodic versus periodic ratio schedules: A comparison of concurrent and concurrent-chain procedures

Choice between mixed-ratio schedules, consisting of equiprobable ratios of 1 and 99 responses per reinforcement, and fixed-ratio schedules of food reinforcement was assessed by two commonly used procedures: concurrent schedules and concurrent-chains schedules. Rats were trained under concurrent fixed-ratio mixed-ratio schedules, in which both ratio schedules were simultaneously available, and under a concurrent-chains schedule, in which access to one of the mutually exclusive ratio schedules comprising the terminal links was contingent on a single “choice” response. The distribution of responses between the two ratio schedules was taken as the choice proportion under the concurrent procedure, and the distribution of “choice” responses was taken as the choice proportion under the concurrent-chains procedure. Seven of eight rats displayed systematic choice; of those, each displayed nearly exclusive choice for fixed-ratio 35 to the mixed-ratio schedule under the concurrent procedure, but each displayed nearly exclusive choice for the mixed-ratio schedule to fixed-ratio 35 under the concurrent-chains procedure. Thus, preference for a fixed or a mixed schedule of reinforcement depended on the procedure used to assess preference.     

Effects of unsignaled delay of reinforcement on preference and resistance to change

In Phase 1, pigeons were trained on a concurrent chain in which a 3-s unsignaled delay of reinforcement was imposed on responding in a terminal link in some conditions. Preference for that terminal link was always reduced in comparison with conditions in which there was no delay, substantially so for 3 of the 4 pigeons. In Phase 2, pigeons responded in a two-component multiple schedule. The scheduled rates of reinforcement were equal, but a 3-s unsignaled delay was imposed in one component. Resistance of responding to prefeeding and extinction was reduced in the delay component for the same 3 subjects for which the data had shown strong effects of delay on preference. Systematic observation revealed differences in response topography. In the delay component, subjects oriented more closely to the key and responses were less forceful compared with the no-delay component. Our results give further evidence that preference and resistance to change covary within subjects. However, they challenge the premise that the critical determiners of preference (i.e., terminal-link value) and resistance to change (behavioral mass) may be quantified purely in terms of stimulus—reinforcer relations.     

Preference for signaled versus unsignaled reinforcement delay in concurrent-chain schedules

A concurrent-chain schedule was employed to examine pigeons' preferences for signaled versus unsignaled delay of reinforcement in which the delay durations ranged from zero to ten seconds. In general, pigeons preferred signaled delay over unsignaled delay especially when a variable-interval 30-second schedule operated in each initial link; when a variable-interval 90-second schedule operated in each initial link, these preferences tended toward indifference or were attenuated. In addition, prior training seemed to exert partial control over behavior. Responding in the terminal link was higher under signaled delay than unsignaled delay in a majority of the cases. Moreover, response rates under signaled delay remained fairly constant whereas responding under unsignaled delay was initially high, but decreased systematically with delay durations as short as 2.5 seconds. These results are consistent with a number of other studies demonstrating the significant role of a signal for impending positive stimuli.