A description-experience gap in statistical intuitions: Of smart babies, risk-savvy chimps, intuitive statisticians, and stupid grown-ups

Do children match described probabilities? The sampling hypothesis applied to repeated risky choice

One way in which children can learn about probabilities of different outcomes before making a decision is from description, for instance, by observing graphical representations of frequency distributions. But how do repeated risky choices develop in early childhood when outcome probabilities are learned from description? Integrating previous findings from children's sampling processes in causal learning and adults' repeated choice behavior, we investigated repeated choices from 201 children aged 3 to 7 years and 100 adults in a child-friendly risky choice task. We expected young children to probability match and predicted that the perceived dependency between choices would shape the underlying choice process. However, the assumed cognitive processes derived from the causal learning and risky choice literature did not generalize to children's or adults' repeated risky choices when outcome probabilities were learned from graphical representations prior to making a decision. Moreover, choice behavior did not differ as a function of the perceived dependency between guesses. Instead, children broadly diversified choices, and switching between options dominated older children's choice behavior. Our results contribute to increasing evidence of childhood as a phase for heightened exploration and highlight the importance of considering the learning format when studying repeated choice across development.

Probabilistic inference and Bayesian-like estimation in animals: Empirical evidence

Animals often make decisions without perfect knowledge of environmental parameters like the quality of an encountered food patch or a potential mate. Theoreticians often assume animals make such decisions using a Bayesian updating process that combines prior information about the frequency distribution of resources in the environment with sample information from an encountered resource; such a process leads to decisions that maximize fitness, given the available information. I examine three aspects of empirical work that shed light on the idea that animals can make such decisions in a Bayesian-like manner. First, many animals are sensitive to variance differences in behavioral options, one metric used to characterize frequency distributions. Second, several species use information about the relative frequency of preferred versus nonpreferred items in different populations to make probabilistic inferences about samples taken from populations in a manner that results in maximizing the likelihood of obtaining a preferred reward. Third, the predictions of Bayesian models often match the behavior of individuals in two main approaches. One approach compares behavior to models that make different assumptions about how individuals estimate the quality of an environmental parameter. The patch exploitation behavior of nine species of birds and mammals has matched the predictions of Bayesian models. The other approach compares the behavior of individuals who learn, through experience, different frequency distributions of resources in their environment. The behavior of three bird species and bumblebees exploiting food patches and fruit flies selecting mates is influenced by their experience learning different frequency distributions of food and mates, respectively, in ways consistent with Bayesian models. These studies lend support to the idea that animals may combine prior and sample information in a Bayesian-like manner to make decisions under uncertainty, but additional work on a greater diversity of species is required to better understand the generality of this ability.

Heuristic strategy of intuitive statistical inferences in 7- to 10-year-old children

Intuitive statistical inferences refer to making inferences about uncertain events based on limited probabilistic information, which is crucial for both human and non-human species' survival and reproduction. Previous research found that 7- and 8-year-old children failed in intuitive statistical inference tasks after heuristic strategies had been controlled. However, few studies systematically explored children's heuristic strategies of intuitive statistical inferences and their potential numerical underpinnings. In the current research, Experiment 1 (N = 81) examined 7- to 10-year-olds' use of different types of heuristic strategies; results revealed that children relied more on focusing on the absolute number strategy. Experiment 2 (N = 99) and Experiment 3 (N = 94) added continuous-format stimuli to examine whether 7- and 8-year-olds could make genuine intuitive statistical inferences instead of heuristics. Results revealed that both 7- and 8-year-olds and 9- and 10-year-olds performed better in intuitive statistical inference tasks with continuous-format stimuli, even after focusing on the absolute number strategy had been controlled. The results across the three experiments preliminarily hinted that the ratio processing system might rely on the approximate number system. Future research could clarify what specific numerical processing mechanism may be used and how it might support children's statistical intuitions.

When intuitive Bayesians need to be good readers: The problem-wording effect on Bayesian reasoning

Are humans intuitive Bayesians? It depends. People seem to be Bayesians when updating probabilities from experience but not when acquiring probabilities from descriptions (i.e., Bayesian textbook problems). Decades of research on textbook problems have focused on how the format of the statistical information (e.g., the natural frequency effect) affects such reasoning. However, it pays much less attention to the wording of these problems. Mathematical problem-solving literature indicates that wording is critical for performance. Wording effects (the wording varied across the problems and manipulations) can also have far-reaching consequences. These may have confounded between-format comparisons and moderated within-format variability in prior research. Therefore, across seven experiments (N = 4909), we investigated the impact of the wording of medical screening problems and statistical formats on Bayesian reasoning in a general adult population. Participants generated more Bayesian answers with natural frequencies than with single-event probabilities, but only with the improved wording. The improved wording of the natural frequencies consistently led to more Bayesian answers than the natural frequencies with standard wording. The improved wording effect occurred mainly due to a more efficient description of the statistical information-cueing required mathematical operations, an unambiguous association of numbers with their reference class and verbal simplification. The wording effect extends the current theoretical explanations of Bayesian reasoning and bears methodological and practical implications. Ultimately, even intuitive Bayesians must be good readers when solving Bayesian textbook problems.

The Future of Decisions From Experience: Connecting Real-World Decision Problems to Cognitive Processes

In many important real-world decision domains, such as finance, the environment, and health, behavior is strongly influenced by experience. Renewed interest in studying this influence led to important advancements in the understanding of these decisions from experience (DfE) in the last 20 years. Building on this literature, we suggest ways the standard experimental design should be extended to better approach important real-world DfE. These extensions include, for example, introducing more complex choice situations, delaying feedback, and including social interactions. When acting upon experiences in these richer and more complicated environments, extensive cognitive processes go into making a decision. Therefore, we argue for integrating cognitive processes more explicitly into experimental research in DfE. These cognitive processes include attention to and perception of numeric and nonnumeric experiences, the influence of episodic and semantic memory, and the mental models involved in learning processes. Understanding these basic cognitive processes can advance the modeling, understanding and prediction of DfE in the laboratory and in the real world. We highlight the potential of experimental research in DfE for theory integration across the behavioral, decision, and cognitive sciences. Furthermore, this research could lead to new methodology that better informs decision-making and policy interventions.

Calculated Feelings: How Children Use Probability to Infer Emotions

Developing the ability to accurately infer others' emotions is crucial for children's cognitive development. Here, we offer a new theoretical perspective on how children develop this ability. We first review recent work showing that with age, children increasingly use probability to infer emotions. We discuss how these findings do not fit with prominent accounts of how children understand emotions, namely the script account and the theory of mind account. We then outline a theory of how probability allows children to infer others' emotions. Specifically, we suggest that probability provides children with information about how much weight to put on alternative outcomes, allowing them to infer emotions by comparing outcomes to counterfactual alternatives.

Different types of uncertainty in multisensory perceptual decision making

Efficient decision-making requires accounting for sources of uncertainty (noise, or variability). Many studies have shown how the nervous system is able to account for perceptual uncertainty (noise, variability) that arises from limitations in its own abilities to encode perceptual stimuli. However, many other sources of uncertainty exist, reflecting for example variability in the behaviour of other agents or physical processes. Here we review previous studies on decision making under uncertainty as a function of the different types of uncertainty that the nervous system encounters, showing that noise that is intrinsic to the perceptual system can often be accounted for near-optimally (i.e. not statistically different from optimally), whereas accounting for other types of uncertainty can be much more challenging. As an example, we present a study in which participants made decisions about multisensory stimuli with both intrinsic (perceptual) and extrinsic (environmental) uncertainty and show that the nervous system accounts for these differently when making decisions: they account for internal uncertainty but under-account for external. Human perceptual systems may be well equipped to account for intrinsic (perceptual) uncertainty because, in principle, they have access to this. Accounting for external uncertainty is more challenging because this uncertainty must be learned. This article is part of the theme issue 'Decision and control processes in multisensory perception'.

Giraffes make decisions based on statistical information

The ability to make inferences based on statistical information has so far been tested only in animals having large brains in relation to their body size, like primates and parrots. Here we tested if giraffes (Giraffa camelopardalis), despite having a smaller relative brain size, can rely on relative frequencies to predict sampling outcomes. We presented them with two transparent containers filled with different quantities of highly-liked food and less-preferred food. The experimenter covertly drew one piece of food from each container, and let the giraffe choose between the two options. In the first task, we varied the quantity and relative frequency of highly-liked and less-preferred food pieces. In the second task, we inserted a physical barrier in both containers, so giraffes only had to take into account the upper part of the container when predicting the outcome. In both tasks giraffes successfully selected the container more likely to provide the highly-liked food, integrating physical information to correctly predict sampling information. By ruling out alternative explanations based on simpler quantity heuristics and learning processes, we showed that giraffes can make decisions based on statistical inferences.

Instruction effects on randomness in sequence generation

Randomness is a fundamental property of human behavior. It occurs both in the form of intrinsic random variability, say when repetitions of a task yield slightly different behavioral outcomes, or in the form of explicit randomness, say when a person tries to avoid being predicted in a game of rock, paper and scissors. Randomness has frequently been studied using random sequence generation tasks (RSG). A key finding has been that humans are poor at deliberately producing random behavior. At the same time, it has been shown that people might be better randomizers if randomness is only an implicit (rather than an explicit) requirement of the task. We therefore hypothesized that randomization performance might vary with the exact instructions with which randomness is elicited. To test this, we acquired data from a large online sample (n = 388), where every participant made 1,000 binary choices based on one of the following instructions: choose either randomly, freely, irregularly, according to an imaginary coin toss or perform a perceptual guessing task. Our results show significant differences in randomness between the conditions as quantified by conditional entropy and estimated Markov order. The randomization scores were highest in the conditions where people were asked to be irregular or mentally simulate a random event (coin toss) thus yielding recommendations for future studies on randomization behavior.

Experiencing statistical information improves children's and adults' inferences

How good are people's statistical intuitions? Recent research has highlighted that sequential experience of statistical information improves adults' statistical intuitions relative to situations where this information is described. Yet little is known about whether this is also the case for children's statistical intuitions. In a study with 100 children (8-11 years old) and 100 adults (19-35 years old), we found that sequentially experiencing statistical information improved both adults' and children's inferences in two paradigmatic reasoning problems: conjunction and Bayesian reasoning problems. Moreover, adults' statistical competencies when they learned statistical information through description were surpassed by children's inferences when they learned through experience. We conclude that experience of statistical information plays a key role in shaping children's reasoning under uncertainty-a conclusion that has important implications for education policy.

Young children’s use of probabilistic reliability and base-rates in decision-making

Children are skilled reasoners who readily use causal, reliability, and base-rate (i.e., prior probability) information in their decisions. Though these abilities are typically studied in isolation, children often must consider multiple pieces of information to make an informed decision. Four experiments (N = 320) explored the development of children’s ability to use reliability and base-rate information when making decisions about draw outcomes. Experiment 1 examined the age at which children can first compare and choose between probabilistically reliable machines. Three- and 4-year-old children saw machines that were probabilistically reliable at obtaining objects while sampling from uniform distributions (i.e., all target or non-target objects). Although 4-year-old children correctly used reliability in their decisions, 3-year-olds did not. In Experiment 2a, 4- to 6-year-olds were presented with the same probabilistically reliable machines, although they sampled from a mixture of target and non-target items. Here, children tended to choose the machine with the better proportion of targets, regardless of reliability. This was replicated in Experiment 2b. In Experiment 3, children were presented with one perfectly reliable machine and one probabilistically unreliable machine. Here, children continued to mostly choose the machine with the better proportion of targets. These results raise questions about base-rate overuse early in development and highlight the need for additional work on children’s ability to use multiple pieces of information in decision-making.

Viruses, Vaccines, and COVID-19: Explaining and Improving Risky Decision-making

Risky decision-making lies at the center of the COVID-19 pandemic and will determine future viral outbreaks. Therefore, a critical evaluation of major explanations of such decision-making is of acute practical importance. We review the underlying mechanisms and predictions offered by expectancy-value and dual-process theories. We then highlight how fuzzy-trace theory builds on these approaches and provides further insight into how knowledge, emotions, values, and metacognitive inhibition influence risky decision-making through its unique mental representational architecture (i.e., parallel verbatim and gist representations of information). We discuss how social values relate to decision-making according to fuzzy-trace theory, including how categorical gist representations cue core values. Although gist often supports health-promoting behaviors such as vaccination, social distancing, and mask-wearing, why this is not always the case as with status-quo gist is explained, and suggestions are offered for how to overcome the "battle for the gist" as it plays out in social media.

Experts use base rates in real-world sequential decisions

Human behavior is often assumed to be irrational, full of errors, and affected by cognitive biases. One of these biases is base-rate neglect, which happens when the base rates of a specific category are not considered when making decisions. We argue here that while naïve subjects demonstrate base-rate neglect in laboratory conditions, experts tested in the real world do use base rates. Our explanation is that lab studies use single questions, whereas, in the real world, most decisions are sequential in nature, leading to a more realistic test of base-rate use. One decision that lends itself to testing base-rate use in real life occurs in beach volleyball-specifically, deciding to whom to serve to win the game. Analyzing the sequential choices in expert athletes in more than 1,300 games revealed that they were sensitive to base rates and adapted their decision strategies to the performance of the opponent. Our data describes a threshold at which players change their strategy and use base rates. We conclude that the debate over whether decision makers use base rates should be shifted to real-world tests, and the focus should be on when and how base rates are used.