Implied occlusion and subset underestimation explain the weak-outnumber-strong numerosity illusion

When equal numbers of white and gray dots are scattered against a dark gray background without overlapping, the number of white dots appears, subjectively, to be fewer than the number of gray dots (Lei & Reeves, 2018, 2022). This has been dubbed the weak-outnumber-strong numerosity illusion. Whereas previous reports of this illusion have argued that it is due to the gray dots creating a false pedestal in computing the total contrast of the white dots (thus lowering their perceived number), we report here evidence that two other principles seem to determine the effect. Four experiments will be reported. In Experiment 1, we show that subset estimation (as for the white dots) occurs equally for most subsets of different-color dots, but not for gray dots, suggesting that it is the gray dots that are primarily the cause of the illusion. In Experiments 2 and 3, we used partial occlusion or stereopsis to separate the white and gray dots into two depth planes. In both cases, the illusion is eliminated when the gray dots are in front, suggesting that it may be caused as a result of perceiving the dimmer gray dots as “filled in” behind the white dots. In Experiment 4, we re-evaluated the false floor illusion by varying the contrast of the gray dots. Our results suggest a U-shaped function, consistent with the idea that the subset underestimation of white is reduced when the gray dots are sufficiently dim, and is applied more equally to the gray dots as they are made much brighter, resulting in less relative difference at low and high gray levels. The weak-outnumber-strong illusion is visually compelling, but appears to be due to both an issue with underestimating subsets and with implied occlusion of the dimmer dots.