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While the human visual system is sensitive to numerosity, the mechanisms that allow perception to extract and represent the number of objects in a scene remains unknown. Prominent theoretical approaches posit that numerosity perception emerges from passive experience with visual scenes throughout development, and that unsupervised deep neural network models mirror all characteristic behavioral features observed in participants. Here, we derive and test a novel prediction: if the visual number sense emerges from exposure to real-world scenes, then the closer a stimulus aligns with the natural statistics of the real world, the better number perception should be. But - in contrast to this prediction - we observe no such advantage (and sometimes even a notable impairment) in number perception for natural scenes compared to artificial dot displays in college-aged adults. These findings are not accounted for by the difficulty in object identification, visual clutter, the parsability of objects from the rest of the scene, or increased occlusion. This pattern of results represents a fundamental challenge to recent models of numerosity perception based in experiential learning of statistical regularities, and instead suggests that the visual number sense is attuned to abstract number of objects, independent of their underlying correlation with non-numeric features. We discuss our results in the context of recent proposals that suggest that object complexity and entropy may play a role in number perception.

Beliefs about how effective a cause will be at achieving possible outcomes are critical inputs into a range of decisions, from how to treat an illness to which products to purchase. We identify scope-the number of distinct outcomes a cause is known to achieve-as an important input into judgments of efficacy. We compare causes that lead to worse outcomes (i.e., banes) to those leading to improvements (i.e., boons). People believe that banes with broader scope (i.e., those that lead to more possible outcomes) are more effective and lead to stronger outcomes. In contrast, people believe that boons with narrower scope (i.e., those that lead to fewer possible outcomes) are more effective and lead to stronger outcomes. We document this pattern across four experiments, finding support for differences in mental models for boons and banes.

This paper proposes an original account of decision anomalies and a computational alternative to existing dynamic models of multi-attribute choice. To date, most models attempting to account for the "Big Three" decision anomalies (similarity, attraction, and compromise effects) are variants of evidence accumulation models, or rational Bayesian analysis. This paper provides an existence proof of a new approach in the form of a multi-agent system based on the principles of voting geometry. Assuming there are a number of neural systems (agents) within an individual's brain, the Big Three decision anomalies can arise as a natural consequence of aggregating preferences across these agents. We operationalize these principles in VAMP, (Voting Agent Model of Preferences), and compare its performance to existing computational models as well as to empirical data. This provides a fundamentally different lens for understanding decision anomalies in multi-attribute choice.

In this issue of Cognition , Thompson and her colleagues challenge the results from a paper we published several years ago (Alter, Oppenheimer, Epley, & Eyre, 2007). That paper demonstrated that metacognitive difficulty or disfluency can trigger more analytical thinking as measured by accuracy on several reasoning tasks. In their experiments, Thompson et al. find evidence that people process information more deeply—but not necessarily more accurately—when they experience disfluency. These results are consistent with our original theorizing, but the authors misinterpret it as counter-evidence because they suggest that accuracy (and even confidence) is a measure of deeper processing rather than a contingent outcome of such processing. We further suggest that Thompson et al. err when they discriminate between “perceptual fluency” and “answer fluency,” the former of which is an element of the latter. Thompson et al. advance research by adding reaction time as a measure of deeper cognitive processing, but we caution against misinterpreting the meaning of accuracy.

Previous research has shown that disfluency – the subjective experience of difficulty associated with cognitive operations – leads to deeper processing. Two studies explore the extent to which this deeper processing engendered by disfluency interventions can lead to improved memory performance. Study 1 found that information in hard-to-read fonts was better remembered than easier to read information in a controlled laboratory setting. Study 2 extended this finding to high school classrooms. The results suggest that superficial changes to learning materials could yield significant improvements in educational outcomes.

The ‘fast and frugal’ approach to reasoning (Gigerenzer, G., & Todd, P. M. (1999). Simple heuristics that make us smart. New York: Oxford University Press) claims that individuals use non-compensatory strategies in judgment – the idea that only one cue is taken into account in reasoning. The simplest and most important of these heuristics postulates that judgment sometimes relies solely on recognition. However, the studies that have investigated usage of the recognition heuristic have confounded recognition with other cues that could also lead to similar judgments. This paper tests whether mere recognition is actually driving the findings in support of the recognition heuristic. Two studies provide evidence that judgments do not conform to the recognition heuristic when these confounds are accounted for. Implications for the study of simple heuristics are discussed.

In this issue of Cognition, Thompson and her colleagues challenge the results from a paper we published several years ago (Alter, Oppenheimer, Epley,Eyre, 2007). That paper demonstrated that metacognitive difficulty or disfluency can trigger more analytical thinking as measured by accuracy on several reasoning tasks. In their experiments, Thompson et al. find evidence that people process information more deeply-but not necessarily more accurately-when they experience disfluency. These results are consistent with our original theorizing, but the authors misinterpret it as counter-evidence because they suggest that accuracy (and even confidence) is a measure of deeper processing rather than a contingent outcome of such processing. We further suggest that Thompson et al. err when they discriminate between "perceptual fluency" and "answer fluency," the former of which is an element of the latter. Thompson et al. advance research by adding reaction time as a measure of deeper cognitive processing, but we caution against misinterpreting the meaning of accuracy.

Previous research has shown that disfluency--the subjective experience of difficulty associated with cognitive operations - leads to deeper processing. Two studies explore the extent to which this deeper processing engendered by disfluency interventions can lead to improved memory performance. Study 1 found that information in hard-to-read fonts was better remembered than easier to read information in a controlled laboratory setting. Study 2 extended this finding to high school classrooms. The results suggest that superficial changes to learning materials could yield significant improvements in educational outcomes.

Research has shown that judgments tend to assimilate to irrelevant "anchors." We extend anchoring effects to show that anchors can even operate across modalities by, apparently, priming a general sense of magnitude that is not moored to any unit or scale. An initial study showed that participants drawing long "anchor" lines made higher numerical estimates of target lengths than did those drawing shorter lines. We then replicated this finding, showing that a similar pattern was obtained even when the target estimates were not in the dimension of length. A third study showed that an anchor's length relative to its context, and not its absolute length, is the key to predicting the anchor's impact on judgments. A final study demonstrated that magnitude priming (priming a sense of largeness or smallness) is a plausible mechanism underlying the reported effects. We conclude that the boundary conditions of anchoring effects may be much looser than previously thought, with anchors operating across modalities and dimensions to bias judgment.