How do we determine how much of something is present? A large body of research has investigated the mechanisms and consequences of number estimation, yet surprisingly little work has investigated area estimation. Indeed, area is often treated as a pesky confound in the study of number. Here, we describe the additive-area heuristic, a means of rapidly estimating visual area that results in substantial distortions of perceived area in many contexts, visible even in simple demonstrations. We show that when we controlled for additive area, observers were unable to discriminate on the basis of true area, per se, and that these results could not be explained by other spatial dimensions. These findings reflect a powerful perceptual illusion in their own right but also have implications for other work, namely, that which relies on area controls to support claims about number estimation. We discuss several areas of research potentially affected by these findings.

When evaluating information, we cannot always rely on what has been presented as truth: Different sources might disagree with each other, and sometimes there may be no underlying truth. Accordingly, we must use other cues to evaluate information—perhaps the most salient of which is consensus. But what counts as consensus? Do we attend only to surface-level indications of consensus, or do we also probe deeper and consider why sources agree? Four experiments demonstrated that individuals evaluate consensus only superficially: Participants were equally confident in conclusions drawn from a true consensus (derived from independent primary sources) and a false consensus (derived from only one primary source). This phenomenon was robust, occurring even immediately after participants explicitly stated that a true consensus was more believable than a false consensus. This illusion of consensus reveals a powerful means by which misinformation may spread.

How do we represent extent in our spatial world? Recent work has shown that even the simplest spatial judgments estimates of 2D area present challenges to our visual system. Indeed, area judgments are best accounted for by`additive area' (the sum of objects' dimensions) rather than`true area' (i.e., a pixel count). But is`additive area' itself the right explanation or might other models better explain the results? Here, we oer three direct and novel demonstrations that`additive area' explains area judgments. First, using stimuli that are simultaneously equated for number and all other confounding dimensions, we show that area judgments are nevertheless explained by`additive area'. Next, we show how`scaling' models of area fail to explain even basic illusions of area. By contrasting squares with diamonds (i.e., the same squares, but rotated), we show a robust tendency to perceive the diamonds as having more area an eect that no other model of area perception would predict. These results not only conrm the fundamental role of`additive area' in judgments of spatial extent, but they highlight the importance of accounting for this dimension in studies of other features (e.g., density, number) in visual perception.

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Representing spatial information is one of our most foundational abilities. Yet in the present work we find that even the simplest possible spatial tasks reveal surprising, systematic misrepresentations of space-such as biases wherein objects are perceived and remembered as being nearer to the centers of their surrounding quadrants. We employed both a placement task (in which observers see two differently sized shapes, one of which has a dot in it, and then must place a second dot in the other shape so that their relative locations are equated) and a matching task (in which observers see two dots, each inside a separate shape, and must simply report whether their relative locations are matched). Some of the resulting biases were shape specific. For example, when dots appeared in a triangle during the placement task, the dots placed by observers were biased away from certain parts of the symmetry axes. But other systematic biases were not shape specific, and seemed instead to reflect differences in the grain of resolution for different regions of space. For example, with both a circle and even a shapeless configuration (with only a central landmark) in the matching task, observers were better at discriminating angular differences (when a dot changed positions around the circle, as opposed to inward/outward changes) in cardinal versus oblique sectors. These data reveal a powerful angular spatial bias, and highlight how the resolution of spatial representation differs for different regions and dimensions of space itself.