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 primary data were peck-by-peck sequential records of four pigeons responding on several different concurrent variable-interval schedules. According to the hypothesis that the subject chooses the alternative with the highest probability of reinforcement at the moment, response-by-response performance in concurrent schedules should show sequential dependencies. However, such dependencies were not found, and it was possible to describe molecular-level performance with simple Markov chain models. The Markov model description implies that the momentary changeover probabilities were proportional to the overall relative reinforcement frequencies, and that changeover probabilities did not change as a function of previous responding. A second finding was that although a changeover-delay procedure was omitted, relative response frequencies closely approximated relative reinforcement frequencies.

Research findings on addiction are contradictory. According to biographical records and widely used diagnostic manuals, addicts use drugs compulsively, meaning that drug use is out of control and independent of its aversive consequences. This account is supported by studies that show significant heritabilities for alcoholism and other addictions and by laboratory experiments in which repeated administration of addictive drugs caused changes in neural substrates associated with reward. Epidemiological and experimental data, however, show that the consequences of drug consumption can significantly modify drug intake in addicts. The disease model can account for the compulsive features of addiction, but not occasions in which price and punishment reduced drug consumption in addicts. Conversely, learning models of addiction can account for the influence of price and punishment, but not compulsive drug taking. The occasion for this target article is that recent developments in behavioral choice theory resolve the apparent contradictions in the addiction literature. The basic argument includes the following four statements: First, repeated consumption of an addictive drug decreases its future value and the future value of competing activities. Second, the frequency of an activity is a function of its relative (not absolute) value. This implies that an activity that reduces the values of competing behaviors can increase in frequency even if its own value also declines. Third, a recent experiment (Heyman & Tanz 1995) shows that the effective reinforcement contingencies are relative to a frame of reference, and this frame of reference can change so as to favor optimal or suboptimal choice. Fourth, if the frame of reference is local, reinforcement contingencies will favor excessive drug use, but if the frame of reference is global, the reinforcement contingencies will favor controlled drug use. The transition from a global to a local frame of reference explains relapse and other compulsive features of addiction.

Individuals who smoke cigarettes regularly but do not become dependent on them provide a unique opportunity for studying the factors that inhibit drug dependence. Previous research on this population, sometimes referred to as 'cigarette chippers', showed that they did not differ from regular smokers in terms of smoking topography (e.g. puff number and duration) and circulating nicotine levels, but that they did show more self-control according to answers on a questionnaire. We evaluated the generality of this finding using a behavioral choice procedure. The participants were undergraduate students (n=71), who were regular smokers, chippers, or nonsmokers. In the choice procedure, one option was a smaller but sooner amount of money, and the other option was a larger but delayed amount of money. Under these conditions, preference for the sooner smaller amount implies that the later larger monetary amounts were discounted. It is widely assumed that the rate of discounting provides an operational definition of impulsivity. In one version of the procedure, the money was hypothetical. In a second version, each choice had a chance of producing an actual monetary outcome. When there was an actual monetary outcome, regular smokers were more likely to choose the sooner but smaller monetary option than chippers and nonsmokers. For all participants, the rate of discounting decreased as the magnitude of the monetary outcomes increased, and for smokers and chippers the differences in discount rates in the two versions of the delayed outcome procedure were the same. These findings are consistent with the view that chippers are less impulsive than smokers. Quantitative aspects of these findings led to the hypothesis that discount rates decrease as a negative power function of the monetary value of the options. This result establishes an analogy between delay discounting experiments and psychophysical experiments. Results from two earlier studies support the analogy.