How Illusory Is the Solitaire Illusion? Assessing the Degree of Misperception of Numerosity in Adult Humans

Abstract

The Solitaire illusion occurs when the spatial arrangement of items influences the subjective estimation of their quantity. Unlike other illusory phenomena frequently reported in humans and often also in non-human animals, evidence of the Solitaire illusion in species other than humans remains weak. However, before concluding that this perceptual bias affects quantity judgments differently in human and non-human animals, further investigations on the strength of the Solitaire illusion is required. To date, no study has assessed the exact misperception of numerosity generated by the Solitaire arrangement, and the possibility exists that the numerical effects generated by the illusion are too subtle to be detected by non-human animals. The present study investigated the strength of this illusion in adult humans. In a relative numerosity task, participants were required to select which array contained more blue items in the presence of two arrays made of identical blue and yellow items. Participants perceived the Solitaire illusion as predicted, overestimating the Solitaire array with centrally clustered blue items as more numerous than the Solitaire array with blue items on the perimeter. Their performance in the presence of the Solitaire array was similar to that observed in control trials with numerical ratios larger than 0.67, suggesting that the illusory array produces a substantial overestimation of the number of blue items in one array relative to the other. This aspect was more directly investigated in a numerosity identification task in which participants were required to estimate the number of blue items when single arrays were presented one at a time. In the presence of the Solitaire array, participants slightly overestimated the number of items when they were centrally located while they underestimated the number of items when those items were located on the perimeter. Items located on the perimeter were perceived to be 76% as numerous as centrally located items. The magnitude of misperception of numerosity reported here may represent a useful tool to help to understand whether non-human animals have different perceptual mechanisms or, instead, do not display adequate numerical abilities to spot the illusory difference generated in the Solitaire array.

Do Domestic Dogs (Canis lupus familiaris) Perceive Numerosity Illusions?

“…One possible reason for dogs' lack of susceptibility is that the level of the estimation error generated by the illusion falls slightly above dogs' quantity discrimination ratio threshold. Agrillo and colleagues [15] showed that, in humans, the illusion creates a perceived quantitative difference close to a ratio of 0.76. Data from the first experiment of the current study seem to indicate that dogs' discriminative ratio threshold falls somewhere between 0.75-which dogs cannot discriminate-and 0.67; it is, therefore, possible that dogs' quantity discrimination ability is not sufficiently sensitive to detect the difference generated by the spatial arrangement.…”

“…At the group level, dogs proved able to spontaneously discriminate between two food quantities with a ratio of 0.67 (8 vs. 12 food pieces), but not between quantities with a ratio of 0.75 (9 vs. 12). In humans, the Solitaire illusion creates a perceived quantitative difference close to the ratio of 0.76 [15]. In view of this, at least some dogs might display sufficient quantitative abilities to be tested in the presence of the Solitaire illusion, which we assessed in Experiments 2 and 3.…”

“…Rhesus monkeys do not perceive the illusion either [13], while data from capuchin monkeys are mixed, with two studies showing a slight illusory effect only at the population level [13,14]. However, larger inter-individual variability has been observed in the studies of capuchin monkeys compared with the human literature [15,16], suggesting a weaker perception of this illusion. A recent study using alternative (linear) versions of the Solitaire illusion ( Figure 1B) led to the same conclusions in both rhesus and capuchin monkeys [17].…”

“…In the current study, we investigated whether dogs are susceptible to the Solitaire illusion. As a recent study showed that items located on the periphery are perceived as 76% more numerous compared with centrally located items by humans [15], in the first experiment, we assessed dogs' quantitative skills in the ratios of 0.67 (8 vs. 12 food pieces) and 0.75 (9 vs. 12). Although previous studies revealed that the quantity discrimination abilities of untrained dogs fall in a lower range, such experiments were performed with smaller numerosities than the ones typically used in the Solitaire illusion.…”

Exploring the Jastrow Illusion in Humans (Homo sapiens), Rhesus Monkeys (Macaca mulatta), and Capuchin Monkeys (Sapajus apella)

“…Despite the perceptual similarities in illusory experiences across species that we noted earlier, some human illusions are not universally experienced by other species. Dogs, for example, do not readily perceive the Ponzo illusion (Byosiere, Feng, Rutter, et al., 2017; Byosiere et al., 2018), and nonhuman primates do not consistently show the Solitaire illusion reported in humans (Agrillo, Parrish, & Beran, 2014a, 2016; Parrish, Agrillo, Perdue, & Beran, 2016). So, the lack of susceptibility by other species to the Jastrow illusion would offer new insights into the nature of that experience for our species, and what may underlie susceptibility to such misperceptions.…”