The capacity of fine vision of individual object is limited by the "bottleneck" of attention and working memory. Still, at every moment we see large collections of objects. What exactly happens to individual representations when the observer attempts to distribute attention between multiple objects? One view is that a fixed number of objects are represented with good fidelity while others are represented with poor fidelity. Another theory is that attention is evenly distributed among all objects but fidelity decreases as set size grows. This debate is one in the core of a theory of summary representation of multiple objects (Alvarez, 2011; Myczek & Simons, 2008). Here we directly tested how the capacity and fidelity change with set size. Participants were briefly shown sets of 1, 2, 4, or 8 circles of various sizes. Then, one of the circles increased or decreased in size by 2- 20% (change step 2%). The change was synchronized with a global background flash masking the local transient caused by the circle change. Observers had to respond whether they had seen an increment or decrement in any of the circles (2AFC). These manipulations rely on an assumption that one needs attention to the stimulus to spot a change (Rensink et al., 1997). Psychometric functions were fit using normal cumulative density functions. We found that the set size affects the probability of correct response at which the function reaches a plateau: the larger was a set size, the lower was such probability. The standard deviations of the functions typically associated with fidelity were relatively similar across set sizes within each observer. We conclude, therefore, that, when observers perceive multiple objects during a short time, they focus attention on a limited sample of items represented with the same fidelity, rather than evenly distribute it among all the objects.
It has been shown that multiple objects can be efficiently represented as ensemble summary statistics, such as the average. Recently, Kanaya et al. (2018) demonstrated the amplification effect in the perception of average. Their participants judged the mean size or temporal frequency of ensembles, and they tended to exaggerate their estimates, especially larger set sizes. Kanaya et al. explained it by non-exhaustive sampling mechanism favoring ~sqrt(N) most salient items, which are either largest or most frequently ones. But how do the rest of elements contribute to ensemble perception? In our study, we used orientation averaging (which does not have any inevitably salient values) and manipulated the salience of individual items via size. Participants had to adjust the average orientation of 4, 8, or 16 triangles. We measured systematic biases, like Kanaya et al. (2018), and SD of errors that are known to correlate with the physical ensemble range. In Experiment 1, most clockwise elements could be bigger, counterclockwise, middle, or all elements were same-size. We found strong clockwise and counterclockwise biases in the corresponding conditions. The biases increased with set size replicating Kanaya et al. (2018). But we found no SD difference between the conditions suggesting that all items were somehow taken into account. In Experiment 2, we compared distributions with same ranges (full-sets) but salient elements being middle or extreme (most clockwise and counterclockwise). We used distribution with only middle elements or only extremes as controls (half-sets). We found that SD in the full-sets were greater than in the middle half-sets and smaller than in the extreme half-sets suggesting that all items were taken into account. We also found that SD in the extreme full-sets were greater than in the middle full-sets in large set size. We conclude that both exhaustive and amplification types of sampling work in averaging.