Prediction problems vary in the extent to which accuracy isrewarded and inaccuracy is penalized—i.e., in their loss func-tions. Here, we focus on a particular feature of loss functionsthat controls how much large errors are penalized relative tohow much precise correctness is rewarded: convexity. Weshow that prediction problems with convex loss functions (i.e.,those in which large errors are particularly harmful) favor sim-pler models that tend to be biased, but exhibit low variability.Conversely, problems with concave loss functions (in whichprecise correctness is particularly rewarded) favor more com-plex models that are less biased, but exhibit higher variabil-ity. We discuss how this relationship between the bias-variancetrade-off and the shape of the loss function may help explainfeatures of human psychology, such as dual-process psychol-ogy and fast versus slow learning strategies, and inform statis-tical inference.

Existing research has emphasized the importance of normality judgments in many aspects of cognition and life (e.g., causal cognition, gradable adjectives, cooperative behavior). Yet little work has explored how people actually come to understand what sorts of things are normal. We argue that people’s normality intuitions reflect a mixture of statistical and evaluative considerations. Specifically, we suggest that people’s intuitions about what is normal can be influenced by representations both of the average and of the ideal. We test this idea in three experiments. Experiment 1a demonstrates that explicit judgments of normality reflect this mixture of statistical and evaluative considerations. Experiments 1b and 2 then show that the hybrid notion that comes out in these explicit judgments can also explain people’s judgments about gradable adjectives. Taken together, these findings have potential implications not only for normality judgments themselves, but also for the many other mental activities that these judgments impact.

People can consciously think about only a few things at a time. But what determines the kind of things that come to mind, among a potentially infinite set of possibilities? Two experiments explored whether the things that come to mind are sampled from a probability distribution that combines what people think is statistically likely and what they think is prescriptively good. Experiment 1 found that when people are asked about the first quantities that come to mind for everyday behaviors and events (e.g., hours of TV that a person could watch in a day), they think of values that are proportional to, and intermediate between, what they think is average and what they think is ideal. Experiment 2 quantitatively manipulated distributions of times people devoted to engaging in a novel hobby (“flubbing”) and the corresponding distributions of goodness of doing this hobby for various amounts of time. The distribution of values that came to mind resembled the mathematical product of the statistical and prescriptive distributions we presented participants, suggesting that something must be both common and good to enter conscious awareness. These results provide insight into the algorithmic process generating people’s conscious thoughts and invite new questions about the adaptive value of thinking about things that are both common and good.

This study demonstrates that changes in mindfulness predict subsequent changes in well-being in a data set including individuals who recently engaged in psychedelic use.