The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory-2-stage dynamic signal detection (2DSD) theory-that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account for choice and decision time. To estimate confidence, we assume that evidence continues to accumulate after the choice. Judges then interrupt the process to categorize the accumulated evidence into a confidence rating. The model explains all known interrelationships between the 3 indices of performance. Furthermore, the model also accounts for the distributions of each variable in both a perceptual and general knowledge task. The dynamic nature of the model also reveals the moderating effects of time pressure on the accuracy of choice and confidence. Finally, the model specifies the optimal solution for giving the fastest choice and confidence rating for a given level of choice and confidence accuracy. Judges are found to act in a manner consistent with the optimal solution when making confidence judgments.

Risky prospects come in different forms. Sometimes options are presented with convenient descriptions summarizing outcomes and their respective likelihoods. People can thus make decisions from description. In other cases people must call on their encounters with such prospects, making decisions from experience. Recent studies report a systematic and large description-experience gap. One key determinant of this gap is people's tendency to rely on small samples resulting in substantial sampling error. Here we examine whether this gap exists even when people draw on large samples. Although smaller, the gap persists. We use the choices of the present and previous studies to test a large set of candidate strategies that model decisions from experience, including 12 heuristics, two associative-learning models and the two-stage model of cumulative prospect theory. This model analysis suggests-as one explanation for the remaining description-experience gap in large samples-that people treat probabilities differently in both types of decisions.

This article models the cognitive processes underlying learning and sequential choice in a risk-taking task for the purposes of understanding how they occur in this moderately complex environment and how behavior in it relates to self-reported real-world risk taking. The best stochastic model assumes that participants incorrectly treat outcome probabilities as stationary, update probabilities in a Bayesian fashion, evaluate choice policies prior to rather than during responding, and maintain constant response sensitivity. The model parameter associated with subjective value of gains correlates well with external risk taking. Both the overall approach, which can be expanded as the basic paradigm is varied, and the specific results provide direction for theories of risky choice and for understanding risk taking as a public health problem.

a b s t r a c tIn many decisions we cannot consult explicit statistics telling us about the risks involved in our actions. In lieu of such data, we can arrive at an understanding of our dicey options by sampling from them. The size of the samples that we take determines, ceteris paribus, how good our choices will be. Studies of decisions from experience have observed that people tend to rely on relatively small samples from payoff distributions, and small samples are at times rendered even smaller because of recency. We suggest one contributing and previously unnoticed reason for reliance on frugal search: Small samples amplify the difference between the expected earnings associated with the payoff distributions, thus making the options more distinct and choice easier. We describe the magnitude of this amplification effect, and the potential costs that it exacts, and we empirically test four of its implications.

A sequential risk-taking paradigm used to identify real-world risk takers invokes both learning and decision processes. This article expands the paradigm to a larger class of tasks with different stochastic environments and different learning requirements. Generalizing a Bayesian sequential risk-taking model to the larger set of tasks clarifies the roles of learning and decision making during sequential risky choice. Results show that respondents adapt their learning processes and associated mental representations of the task to the stochastic environment. Furthermore, their Bayesian learning processes are shown to interfere with the paradigm's identification of risky drug use, whereas the decision-making process facilitates its diagnosticity. Theoretical implications of the results in terms of both understanding risk-taking behavior and improving risk-taking assessment methods are discussed.Keywords: risk taking, learning, Bayesian, individual differences, cognitive psychometrics Learning and decision making are conceptually linked. Typically only after decision makers (DMs) make a decision do they observe or experience the precise outcome of that decision. For example, only after commuters select a traffic route do they determine its effectiveness, and only after athletes use a steroid do they learn about the precise properties it has on their body. These observations better inform DMs about the precise properties of their choice options and shape their next decision among the same or similar options. Despite this natural association between decision and learning processes, most decision-making theories fail to incorporate or explicate a learning component (e.g., Busemeyer & Townsend, 1993;González-Vallejo, 2002;Kahneman & Tversky, 1979). Yet, how DMs learn from experience has proven an important process in understanding risk-taking behavior. It can, for example, create an aversion toward risky alternatives in the gain domain and an attraction toward risky alternatives in the loss domain-a pattern typically attributed to how DMs evaluate outcomes (Denrell, 2007;March, 1996). The learning process can even produce the opposite pattern (Erev & Barron, 2005;Hertwig, Barron, Weber, & Erev, 2004;Weber, Shafir, & Blais, 2004).Applying theories of decision making to the Balloon Analogue Risk Task (BART; Lejuez et al., 2002) or to the Iowa Gambling Task (Bechara, Damasio, Damasio, & Anderson, 1994) also exposes the necessity of learning. Clinicians use these laboratorybased gambling tasks to study and identify people with specific clinical or neurological deficits. Cognitive models of these tasks reveal that decision and learning processes are necessary to account for choices made by both clinical and normal populations (Busemeyer & Stout, 2002;Wallsten, Pleskac, & Lejuez, 2005). Besides describing behavior during the tasks, the models also show how the populations differ on the underlying cognitive dimensions captured within the models. For example, during the BART, Wallsten et al. (2005) found that people who take un...

The distinction between risk and uncertainty is deeply entrenched in psychologists ' and economists' thinking. Knight (1921), to whom it is frequently attributed, however, went beyond this dichotomy. Within the domain of risk, he set apart a priori and statistical probabilities, a distinction that maps onto that between decisions from description and experience, respectively. We argue this distinction is important because risky choices based on a priori (described) and statistical (experienced) probabilities can substantially diverge. To understand why, we examine various possible contributing factors to the description-experience gap. We find that payoff variability and memory limitations play only a small role in the emergence of the gap. In contrast, the presence of rare events and their representation as either natural frequencies in decisions from experience or single-event probabilities in decisions from description appear relevant for the gap.

Sequential risk-taking tasks, especially the Balloon Analogue Risk Task (BART), have proven powerful and useful methods in studying and identifying real-world risk takers. A natural index in these tasks is the average number of risks the participant takes in a trial (e.g., pumps on the balloons), but this is difficult to estimate because some trials terminate early because of the consequences of those risks (e.g., when the desired number of balloon pumps exceeds the explosion point). The standard corrective strategy is to use an adjusted score that ignores such event-terminated trials. Although previous data supports the utility of this adjusted score, the authors show formally that it is biased. Therefore, the authors developed an automatic response procedure, in which respondents state at the beginning of each trial how many risks they wish to take and then observe the sequence of events unfold. A study comparing this new automatic and the original manual BART shows that the automatic procedure yields unbiased statistics whereas maintaining the BART's predictive validity of substance use. The authors also found that providing respondents with the expected-value-maximizing strategy and complete trial-by-trial feedback increased the number of risks they were willing to take during the BART. The authors interpret these results in terms of the potential utility of the automatic version including shorter administration time, unbiased behavioral measures, and minimizing motor involvement, which is important in neuroscientific investigations or with clinical populations with motor limitations.

This article models the cognitive processes underlying learning and sequential choice in a risk-taking task for the purposes of understanding how they occur in this moderately complex environment and how behavior in it relates to self-reported real-world risk taking. The best stochastic model assumes that participants incorrectly treat outcome probabilities as stationary, update probabilities in a Bayesian fashion, evaluate choice policies prior to rather than during responding, and maintain constant response sensitivity. The model parameter associated with subjective value of gains correlates well with external risk taking. Both the overall approach, which can be expanded as the basic paradigm is varied, and the specific results provide direction for theories of risky choice and for understanding risk taking as a public health problem.