The discrimination of magnitude: A review and theoretical analysis

Abstract

In a discrimination based on magnitude, the same stimulus is presented at two different magnitudes and an outcome, such as food, is signalled by one magnitude but not the other. The review presented in the first part of the article shows that, in general, such a discrimination is acquired more readily when the outcome is signalled by the larger rather than the smaller of the two magnitudes. This asymmetry is observed with magnitudes based on sound, odour, temporal duration, quantity, and physical length. The second part of the article, explores the implications of this pattern of results for the theory of discrimination learning presented by Pearce (1994). The asymmetry found with discriminations based on magnitude contradicts predictions derived from the original version of the theory, but it can be explained by a modified version. The asymmetry also has important implications for understanding how animals represent magnitudes.

Pavlovian summation: Data and theory.

“…Here, I consider Pearce’s (1987) model, the best-known configural model, and its extension by Inman and Pearce (2018). The extended model adds a parameter y , ranging between 0 and 1, that introduces a potential asymmetry in generalization such that generalization from X to Y is not necessarily equal to generalization from Y to X .…”

“…Additionally, knowledge of the modality effect can be strengthened by covering more species and experimental paradigms. For Possible Values of g av in Inman and Pearce's (2018) Model, as a Function of c, the Fraction of Common Elements Shared by A and B, and y, a Parameter of the Model's Similarity Function example, within-modality data in rabbits come from just three experiments (white squares in Figure 3), and all pigeon data from just two studies (Figure 6b). Lack of data also prevents robust conclusions about differences between summation in humans and in other species.…”

The importance of trials.

“…This asymmetry is explained in associative terms by assuming that X competes more strongly with A for conditioning (mutual overshadowing between A and X limits how much is learned about each) than for control of responding (any generalization decrement produced by X would be comparatively weak; Brandon et al, 2000; Wagner & Brandon, 2001). An alternative, configural, explanation of the asymmetry is that presentation of A will retrieve the configural memory of AX less effectively than presentation of AX can retrieve the memory of A (Inman & Pearce, 2018). The impact of this asymmetry is also evident when comparing simple discriminations between A and AX: Animals are quicker to master a discrimination in which AX is always reinforced and A is never reinforced (AX+ vs. A−) than the reverse discrimination (A+ vs. AX−; Holland, 1991; Reberg & Leclerc, 1977; Sainsbury & Jenkins, 1967).…”

Wolves and Dogs May Rely on Non-numerical Cues in Quantity Discrimination Tasks When Given the Choice

“…In most studies in which two groups of animals are trained to select different options depending on their magnitude (be it quantity, odor intensity, auditory intensity, etc. ), the group trained to choose the higher magnitude seems to have an easier time acquiring the skill ( Zielinski and Jakubowska, 1977 ; Pelz et al, 1997 ; Watanabe, 1998 ; Vonk and Beran, 2012 ; see Inman and Pearce, 2018 for a review).…”