Molecular Maximizing Characterizes Choice on Vaughan's (1981) Procedure

Abstract

Pigeons keypecked on a two-key procedure in which their choice ratios during one time period determined the reinforcement rates assigned to each key during the next period (Vaughan, 1981). During each of four phases, which differed in the reinforcement rates they provided for different choice ratios, the duration of these periods was four minutes, duplicating one condition from Vaughan's study. During the other four phases, these periods lasted six seconds. When these periods were long, the results were similar to Vaughan's and appeared compatible with melioration theory. But when these periods were short, the data were consistent with molecular maximizing (see Silberberg & Ziriax, 1982) and were incompatible with melioration, molar maximizing, and matching. In a simulation, swa birds following a molecular-maximizing algorithm responded on the short-and long-period conditions of this experiment. When the time periods lasted four minutes, the results were similar to Vaughan's and to the results of the four-minute conditions of this study; when the time periods lasted six seconds, the choice data were similar to the data from real subjects for the six-second conditions. Thus, a molecular-maximizing response rule generated choice data comparable to those from the short-and long-period conditions of this experiment. These data show that, among extant accounts, choice on the Vaughan procedure is most compatible with molecular maximizing.Key words: maximizing, matching, melioration, choice, key peck, pigeons When animals are given choices between two concurrently available variable-interval (VI) schedules, the proportion of their responses or time allocations on these schedules typically approximates the proportion of reinforcements these schedules deliver (e.g., see de Villiers, 1977 (1) (2) where P and T refer to responses and time allocated to a schedule, R refers to reinforcement frequency, and the subscripts 1 and 2 distinguish between the two VI schedules.

The copyist model of response emission

“…In the present simulation, the choice allocation rules used in the prior simulation were used on the procedures of Vaughan (1981) and Silberberg and Ziriax (1985), who also used Vaughan's (1981) design in a melioration assay. All conditions within each report were simulated save conditions 4 and 5 from Silberberg and Ziriax.…”

“…7 presents simulated relative VI-b response rates as a function of their relative VI-b reinforcement rates obtained using the Vaughan (1981) and Silberberg and Ziriax (1985) procedures. The bottom panel presents the simulated relative VI-b response rate as a function of the actual relative VI-b response rates obtained in these two studies.…”

“…Toward this end, we modified the Peele et al account to enable it to make its IRT selection not from a memory composed solely of reinforced IRTs, but from an average of sequential IRTs in which the weight assigned to each IRT composing the mean diminishes exponentially as a function of its backward distance from reinforcement. Simulated Relative Reinforcement Rate to VI b Vaughan (1981) Silberberg & Ziriax (1985) 0.00 (1) the simulated relative VI-b reinforcement rate (top panel) and (2) the obtained relative VI-b response rate from the target publications (Silberberg & Ziriax, 1985, The copyist model this change creates, along with other minor modifications in the original Peele et al (1984) account, had felicitous effects. As is shown in Fig.…”

“…When this was done, the performances approximated major features of the Herrnstein (1961), Stubbs and Pliskoff (1969), Baum (1974), Herrnstein and Heyman (1979), Herrnstein and Loveland (1975), Vaughan (1981), and Silberberg and Ziriax (1985) studies that were targeted for simulation. This model, and no other, provides a comprehensive account of both matching and local response rate in choice procedures.…”

Quasi‐dynamic Choice Models: Melioration and Ratio in Variance

“…Neither approach easily explains all the data, but ratio invariance seems to provide a better picture of pigeons' response to probabilistic choice procedures. Ratio invariance is also more adaptive (less susceptible to "traps") and closer to the original expression of the law of effect than pure hill-climbing processes such as momentary maximizing and melioration, although such processes may come in to play on more complex procedures that provide opportunities for temporal discrimination.Key words: Bush-Mosteller, melioration, momentary maximizing, molecular maximizing, ratio invariance, source independence, matchingThe initial stimulus for this paper was Stephen Lea's request to the reviewers of a manuscript by Will Vaughan that they prepare commentaries suitable for independent publication along with Vaughan's paper, which is itself a critical commentary on an earlier paper by Silberberg and Ziriax (1985). The most important aspect of this controversy is about the adequacy of different models for free-operant choice, which is the major focus of this paper.…”