Toward a contemporary quantitative model of punishment.

A direct-suppression, or subtractive, model of punishment has been supported as the qualitatively and quantitatively superior matching law-based punishment model (Critchfield, Paletz, MacAleese, & Newland, 2003; de Villiers, 1980; Farley, 1980). However, this conclusion was made without testing the model against its predecessors, including the original (Herrnstein, 1961) and generalized (Baum, 1974) matching laws, which have different numbers of parameters. To rectify this issue, we reanalyzed a set of data collected by Critchfield et al. (2003) using information theoretic model selection criteria. We found that the most advanced version of the direct-suppression model (Critchfield et al., 2003) does not convincingly outperform the generalized matching law, an account that does not include punishment rates in its prediction of behavior allocation. We hypothesize that this failure to outperform the generalized matching law is due to significant theoretical shortcomings in model development. To address these shortcomings, we present a list of requirements that all punishment models should satisfy. The requirements include formal statements of flexibility, efficiency, and adherence to theory. We compare all past punishment models to the items on this list through algebraic arguments and model selection criteria. None of the models presented in the literature thus far meets all of the requirements.