When the weaker conquer: A contrast-dependent illusion of visual numerosity

Humans and many nonhuman species have the capacity to perceive the approximate numerosity of a large set of elements. In the visual domain, various factors have been found to affect perceived numerosity, including, as studied here, the effect of luminance contrast. We report a new numerosity illusion in which low-contrast elements appear to be more numerous than high-contrast ones when intermixed in the same display, an effect we have called "the weak conquer the strong." The illusion occurred for both positive and negative contrast disks of the same sign; for example, white disks appeared less numerous than light gray disks when presented on a dark gray field (all positive contrasts). The illusion grew in size as the contrast difference between the two sets of disks became smaller but did not hold for disks with opposite signs, such as white and dark gray disks on a light gray field. The illusion was also eliminated when the disks were segregated spatially, in which case the high-contrast (white) disks and low-contrast (gray) disks appeared equally numerous. The illusion is due to the loss of some high-contrast elements; e.g., the perceived numerosity of the white disks was decreased whereas that of gray ones was preserved as shown by matching to isolated sets of white or gray disks. We speculate that failure in segregation coupled with error in contrast normalization may account for the numerosity illusion.