What the Solitaire illusion tells us about perception of numerosity

In four experiments we investigated the Solitaire illusion. In this illusion, most observers see as more numerous a set of dots that forms a single central group, compared to dots on the outside of that group. We confirmed and extended the effect to configurations with much higher numerosity than the original and of various colours. Contrary to prediction, separating the two groups, so that they are presented side by side, reduced but did not abolish or reverse the illusion. In this illusion, therefore, neither total size of the region (area), not average distance of the elements has the expected effect. In Experiments 3 and 4 we eliminated the regularity of the pattern, by sampling 50% (Exp 3) or only a 10% (Exp 4) of the elements. These produces quasi-random configurations. For these configurations the bias for the inner groups was still present, and it was only eliminated when the groups were shown as separate. However, the effect never reversed (no bias for the outer group, despite its larger area). We conclude that the Solitaire illusion is evidence of a strong bias in favour of centrally located elements, a bias that can overcome other factors.