The Crowd Size Illusion
Gabriel Waterhouse, Sami R. Yousif · Journal of Vision · 2025
After several relaxing days on the beach, you step up to the podium to give your talk. Looking out on the audience, you find that some, but not all, of the seats are occupied. The crowd looks empty. But what if your impression is an illusion? What if the number you perceive is influenced not just by the number of filled seats, but the number of empty ones? We tested this putative “crowd size illusion” by having participants compare and estimate the numbers of dots in displays with and without visible grids: Some displays contained random arrangements of dots, whereas others contained dots arranged within “cells” in a grid (like people, in seats). When only about 15-30% of the “seats” were occupied, people tended to find the display with the grid to have fewer dots (consistent with the intuition described above). In a second experiment, we replicated this finding in a direct estimation task. But does the presence of a grid always result in underestimation? Imagine the same scenario as before, except the audience is full to the brim. In that case, might you perceive more people? In a third experiment, we found that when occupancy of the grids was high, those displays were perceived as more numerous. This effect is continuous: Observers underestimated the number of dots when more “seats” were empty and overestimated when more “seats” were full. Both illusions are powerful enough that they are readily appreciated in simple demonstrations. Furthermore, the fact that the direction of the illusion depends on the percentage of occupied cells indicates that this illusion cannot be explained by confounds with continuous spatial properties. In this way, the crowd size illusion is more than a curiosity: It points to a number system that represents number in a part-whole format.