The visual system can rapidly summarize multiple objects in a form of ensemble statistics: e.g., people can easily estimate an average size of apples on a tree. To accomplish this, it is not always enough to summarize all the visual information. If there are various types of objects, the visual system should select a relevant subset: only apples without leaves. Here, we ask: what is the representational basis of ensemble selection, i.e., what kind of visual information makes a ‘good’ ensemble that can be selectively attended to provide an accurate summary estimate? We tested three candidate representations: basic features, preattentive object files, and full-fledged bound objects. In four experiments, we presented a target and several distractors’ sets of differently colored objects. We found that conditions, where a target ensemble had at least one unique color (basic feature), provided ensemble averaging performance comparable to the baseline displays without distractors. When the target subset was defined as a conjunction of two colors or color-shape partly shared with distractors (so that they could be differentiated only as preattentive object files), subset averaging was also possible but less accurate than in the baseline and the feature conditions. Finally, performance was very poor when the target subset was defined by an exact feature relationship, such as in the spatial conjunction of two colors (spatially bound object). Overall, these results suggest that distinguishable features and, to a lesser degree, preattentive object files can serve as the representational basis of ensemble selection, while bound objects cannot.

Ensemble statistics are often thought of as a reliable impression of numerous items despite limited capacities to consciously represent each individual. However, whether all items equally contribute to ensemble summaries (e.g., mean) and whether they might be provided by known limited-capacity processes, such as attention, is still debated. We addressed these questions via a recently described "amplification effect", a systematic bias of perceived mean (e.g., average size) towards the more salient "tail" of a feature distribution (e.g., larger items). In our experiments, observers adjusted the mean orientation of sets of items varying in set size. We made some of the items more salient or less salient by changing their size. While the whole orientation distribution was fixed, the more salient subset could be shifted relative to the set mean or differ in range. We measured the bias away from the set mean and the standard deviation (SD) of errors, as it is known to reflect the physical range from which ensemble information is sampled. We found that bias and SD changes followed the shifts and range changes in salient subsets, providing evidence for amplification. However, these changes were weaker than those expected from sampling only salient items, suggesting that less salient items were also sampled. Importantly, the SD decreased as a function of set size, which is only possible if the number of sampled elements increased with set size. Overall, we conclude that orientation summary statistics are integrated by a high-capacity mechanism modulated by the amplification effect of attention.