A Selective Sampling Account for Forming Numerosity Representations

Two leading models of numerosity judgments address scaling problems by describing numerical representations as Gaussian distributions on a mental line. The linear account posits that numerosity representations and their variability increase linearly with number, while the log account assumes they increase logarithmically with constant variability. Here, we use the selective sampling account—which posits that information is sampled selectively from the display based on goals and available resources—to elucidate the cognitive processes underlying the different assumptions made for variability and scale. When participants were asked to discriminate between intermingled displays of blue and yellow dots, they appeared to rely on incomplete representations composed of the larger dots and those in the central area. In contrast, when the arrays were spatially separated on screen, their judgments were based on more comprehensive representations. Consequently, the proportion of sampled dots explains the source of increasing versus constant variability with set size. Additionally, we found that the representation scale may reflect sensitivity to the visual display based on spatial resolution demands, with high sensitivity corresponding to a linear scale and low sensitivity corresponding to a logarithmic scale. Lastly, manipulating the perceptual properties prioritized by the model during sampling—namely, visual size and spatial position—resulted in substantial effects on behavior. We conclude that selective sampling offers a unified and detailed explanation for variations in behavior across common numerosity discrimination tasks, while providing insights into the distribution of attention, as confirmed by eye tracking.