Sensitivity to molar feedback functions: A test of molar optimality theory.

Abstract

Molar optimality models assume that any reward schedule can be described by a molar feedback function, which is the relation between average response rates and average reinforcement rates enforced by that particular schedule. This molar feedback function is considered, by optimality models, to be a sufficient description of the schedule for the prediction of steady-state molar performance. In this article we challenge the fundamental assumption of all molar optimality modelsthat animals are directly sensitive to this molar feedback function. We found that animals were sensitive to the schedule conditions in effect, especially at the molecular level of postfood time, but they were not directly sensitive to the slopes of any ofthe molar feedback functions that we manipulated. Our data do not simply represent a failure to maximize a particular utility function so that this form of the function requires alteration. Rather, they demonstrate that animals may not be sensitive to the molar rates of responding and reinforcement described by the molar feedback functions. Our animals were sensitive to the schedules at a molecular level, and it is to this molecular level that we should direct our attention.Operant behavior can be explained in terms of its antecedents (causal accounts) or its consequences (functional accounts). The best developed functional accounts are in terms of optimality theory. Consequences can be measured moment by moment (molecular accounts) or as averages (molar accounts). Molar optimality accounts measure consequences in terms of the molar feedback function (MFF: Baum, 1973;Kagel, Battalio, Green, & Rachlin, 1980;Rachlin & Burkhard, 1978;Staddon, 1979;Timberlake, 1980), that is, the relation between average response rates and average reinforcement rates enforced by a particular schedule. It is possible to derive MFFs for all common reinforcement schedules. For example, the MFF for ratio schedules is a straight line through the origin, because reinforcement rate is directly proportional to response rate. The MFF for variable-interval schedules is a positively accelerated function with an asymptote at the scheduled maximum reinforcement rate, because reinforcement rate is directly related to response rate, but with diminishing returns.Molar optimality theories relate the differences in molar performance engendered by different schedules to the properties of the MFFs associated with them. For example, Staddon's ( 1979) minimum-distance model and Rachlin and Burkhard's (1 978) value-maximizing model both incorporate the MFF as a constraint to the objective function to be maximized or minimized. Any success of optimality theories in explaining performance These experiments were supported in part by a grant from the National Science Foundation to J. E. R. Staddon.The differences between different schedules implies that animals are in some way sensitive to MFF properties such as slope (cf. Staddon, 1982). As the slope of the MFF is changed, the slope of the corresponding response function should also chan...

The copyist model of response emission

“…In some of these schedules, the rate of reinforcement was positively correlated with response rate (Cole, 1999;McDowell & Wixted, 1986;Reed et al, 2003;Reed et al, 2000); in others, there was an inverse relation between these variables (Ettinger, Reid, & Staddon, 1987;Jacobs & Hackenberg, 2000;Reed & Schachtman, 1991;Tanno & Sakagami, 2008;Vaughan, 1987;Vaughan & Miller, 1984); and in still others, reinforcer rate was largely independent of response rate (Dawson & Dickinson, 1990;Kuch & Platt, 1976;Tanno & Sakagami, 2008). With few exceptions (Dawson & Dickinson, 1990), these studies fail to show control of rates by molar variables.…”

“…For example, negativefeedback schedules, where reinforcement rates decrease as response rates increase, affect rate emission in humans (Jacobs & Hackenberg, 2000), but not in rats (Ettinger et al, 1987;Reed & Schachtman, 1991;Tanno & Sakagami, 2008). In this circumstance, the predictive adequacy of the copyist model is necessarily impaired (it cannot predict species differences in outcome).…”

The role of response-reinforcer correlation in signaled reinforcement effects

“…This schedule was arranged so that, as response rates increased beyond a certain level, reinforcement frequency decreased. Animals, although sensitive to this contingency (Ettinger, Reid, & Staddon, 1987;Reed & Schachtman, 1989;Vaughan, 1982), demonstrate extremely inefficient patterns of responding (Vaughan & Miller, 1984), which result in a very poor response-reinforcer correlation. If potentiation is likely when the response-reinforcer correlation is low, then such an effect should be observed on a schedule with a component in which responses can produce reinforcement omission.…”

Instrumental responding by rats on free-operant schedules with components that schedule response-dependent reinforcer omission: Implications for optimization theories

“…Staddon and Hinson (1983) criticized the failure of Mazur (1981) to find optimal performance in a choice situation on these grounds. Given that optimization theories assume sensitivity of the subject to the molar-feedback function (Ettinger et al, 1987), if the subjects were not sensitive to the contingency in operation, then the appropriate instrumental performance (i.e., optimal levels of responding) could not be expected to develop.…”

“…Recently, however, several researchers have attempted to assess the success of optimization theories in accounting for responding in novel free-operant situations (Ettinger, Reid, & Staddon, 1987;Mazur, 1981;Thomas, 1981;Tiemy, Smith, & Gannon, 1987;Vaughan & Miller, 1984). The studies by Vaughan and Miller (1984; see also Vaughan, 1982) and Thomas (1981Thomas ( , 1983 differed from the others in that they employed schedules that contained a component that organized a negative contingency between responding and reinforcement.…”