A Selective Sampling Account of Forming Numerosity Representations

Two leading models of numerosity judgments describe numerical representations as Gaussian distributions on a mental number line. The linear model posits that both numerosity and variability increase linearly with number, while the logarithmic model assumes logarithmic scaling with constant variability. In this study, we use the selective sampling account, which proposes that information is gathered selectively based on goals and available resources, to explore the cognitive processes underlying variations in variability and scaling. In intermingled displays of blue and yellow dots (B/Y task), participants relied on incomplete representations of dots positioned near the center, where spatial resolution is highest, leading to increasing variability with set size. In contrast, spatially separated displays (L/R task) facilitated more comprehensive sampling, resulting in approximately constant variability across set sizes. Behavioral patterns and modeling analyses suggest that linear and logarithmic scaling capture sensitivity differences shaped by the display format and spatial resolution demands. Eye-tracking data further support our account, emphasizing the role of selective attention in forming numerical representations and providing a unified framework for understanding variability and scaling across tasks.