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

Four experimental studies are reported using a total of 712 participants to investigate the basis of a recently reported numerosity illusion called "weak-outnumber-strong" (WOS). In the weak-outnumber-strong illusion, when equal numbers of white and gray dots (e.g., 50 of each) are intermixed against a darker gray background, the gray dots seem much more numerous than the white. Two principles seem to be supported by these new results: 1) Subsets of mixtures are generally underestimated; thus, in mixtures of red and green dots, both sets are underestimated (using a matching task) just as the white dots are in the weak-outnumber-strong illusion, but 2) the gray dots seem to be filled in as if partially occluded by the brighter white dots. This second principle is supported by manipulations of depth perception both by pictorial cues (partial occlusion) and by binocular cues (stereopsis), such that the illusion is abolished when the gray dots are depicted as closer than the white dots, but remains strong when they are depicted as lying behind the white dots. Finally, an online investigation of a prior false-floor hypothesis concerning the effect suggests that manipulations of relative contrast may affect the segmentation process, which produces the visual bias known as subset underestimation.