Data from a risky choice experiment are used to estimate a fully parametric stochastic model of risky choice. As is usual with such analyses, Expected Utility Theory is rejected in favour of a form of Rank Dependent Theory. Then an estimate of the risk aversion parameter is deduced for each subject, and this is used to construct a measure of the “closeness to indifference” of each subject in each choice problem. This measure is then used as an explanatory variable in a random effects model of decision time, with other explanatory variables being the complexity of the problem, the financial incentives, and the amount of experience accumulated at the time of performing the task. The most interesting finding is that significantly more effort is allocated to problems in which subjects are close to indifference. This presents us with another reason (in addition to statistical information considerations) why such tasks should play a prominent role in experiments.

Many experiments investigating different decision theories have relied heavily on pairwise choices between lotteries. These are easy to incentivise, but often yield only limited dichotomous information. This paper considers whether respondents’ judgments about their strength of preference (SoP) for one alternative over another can usefully supplement standard choice data. We report extensive evidence that such judgments show sensitivity to variations in question format and parameter values in the directions we should expect, not only within-subject but also between-sample. We illustrate how such judgments can usefully supplement standard pairwise choice data and enrich our understanding of observed behaviour.

This paper examines data from the Norwegian television game show Joker, where contestants make well-specified choices under risk. The game involves very large stakes, randomly drawn contestants, and ample opportunities for learning. Central models of risk choice, including expected utility theory, give a simple prediction of choice under weak conditions, as one decision is always first-order stochastically dominating. We document frequent, systematic and costly violations of dominance. Many contestants appear to have a systematic expectation bias that can be related to Tversky and Kahneman's (Cogn. Psychol. 5(2):207-232, 1973) “availability heuristic”. In addition, contestants seem to make systematic calculation errors that are well captured by the so-called Fechner model.

Experiments frequently use a random incentive system (RIS), where only tasks that are randomly selected at the end of the experiment are for real. The most common type pays every subject one out of her multiple tasks (within-subjects randomization). Recently, another type has become popular, where a subset of subjects is randomly selected, and only these subjects receive one real payment (between-subjects randomization). In earlier tests with simple, static tasks, RISs performed well. The present study investigates RISs in a more complex, dynamic choice experiment. We find that between-subjects randomization reduces risk aversion. While within-subjects randomization delivers unbiased measurements of risk aversion, it does not eliminate carry-over effects from previous tasks. Both types generate an increase in subjects’ error rates. These results suggest that caution is warranted when applying RISs to more complex and dynamic tasks.

In intertemporal and risky choice decisions, parametric utility models are widely used for predicting choice and measuring individuals’ impulsivity and risk aversion. However, parametric utility models cannot describe data deviating from their assumed functional form. We propose a novel method using cubic Bezier splines (CBS) to flexibly model smooth and monotonic utility functions that can be fit to any dataset. CBS shows higher descriptive and predictive accuracy over extant parametric models and can identify common yet novel patterns of behavior that are inconsistent with extant parametric models. Furthermore, CBS provides measures of impulsivity and risk aversion that do not depend on parametric model assumptions.

Choices made in risky scenarios are considered fundamentally noisy because decisions have often been found to be inconsistent when repeated. Past measures of noise may, however, be confounded by the use of randomized contextual factors that are known to influence choice, in particular, the order of trials. In two experiments, we control trial order to test the extent to which inconsistent choice is attributable to changes in experimental context. Both tasks find strong evidence that trial order has no effect on choice consistency, indicating such experimental factors have little influence on behavior compared with internal noise. Choices also showed an increase in consistency across multiple repetitions, suggesting a fall in noise with experience, but this increase was not associated with any improvement in performance, with choices showing no greater adherence to either expected value or expected utility across repetitions. Instead, choices increasingly adhered to simplistic heuristic decision rules, possibly indicating greater reliance on such strategies as the tasks progressed. These results carry implications for a number of decision-making theories, including true-and-error models, rank-based methods, and strategy shift approaches.

Although many models for risky choices between gambles assume that information is somehow integrated, the recently proposed priority heuristic (PH) claims that choices are based on one piece of information only. That is, although the current reason for a choice according to the PH can vary, all other reasons are claimed to be ignored. However, the choices predicted by the PH and other pieces of information are often confounded, thus rendering critical tests of whether decisions are actually based on one reason only, impossible. The current study aims to remedy this problem by manipulating the number of reasons additionally in line with the choice implied by the PH. The results show that participants’ choices and decision times depend heavily on the number of reasons in line with the PH — thus contradicting the notion of non-compensatory, one-reason decision making.

We propose a novel experimental design aimed at investigating whether inducing individuals to use certain choice procedures has an effect on the outcome of their decision. Specifically, by implementing a modification of the mouse-tracing method, we induce subjects to use either alternative-based or characteristic-based search procedures in a between-subject lottery-choice experiment. We find that encouraging subjects to search by characteristic systematically makes them choose riskier options. Consistently with existing literature, our evidence indicates that individuals typically look up information within alternatives. However, when induced to search by characteristic, high prizes receive more attention, leading individuals to switch to non-compensatory heuristics and – consequently – make riskier choices. Our findings are robust to variations in the complexity of the choice problem and individual differences in risk-attitudes, CRT scores, and gender.

Many people exhibit inconsistent preferences when they make choices based on descriptive summaries as compared to choices based on prior experiences. Theoretically, factors that promote more deliberative and skilled decision making (e.g., statistical numeracy) should also tend to promote more consistent choices and preferences regardless of information presentation formats. To test this hypothesis, in two studies I investigated individual differences in information search strategies (e.g., the amount and direction of information search) while estimating the degree to which numeracy predicted risky choice consistency across (a) decisions-from-description and (b) the decisions-from-samples. Results from Study 1 revealed that numeracy was generally associated with more extensive sampling and greater choice consistency across paradigms. Instead of reflecting differences in logical maximizing strategies (e.g., calculating expected values), analyses indicated that highly-numerate participants largely generated consistent choices by relying on heuristic-type processes (e.g., alternated between options less and exploring options with higher outcome variability more). In Study 2, the relationship between numeracy and choice consistency was eliminated when all participants were forced to make choices after experiencing the same fixed amount of sampling (i.e., provided the same amount of information). Taken together, the results of both studies converge with and extend previous findings (e.g., Skilled Decision Theory), indicating that numerate participants may generally exhibit more consistent preferences and choices via deliberatative heuristic search during decision making.

Similar to research on risky choice, the traditional analysis of intertemporal choice takes the view that an individual behaves so as to maximize the discounted sum of all future utilities. The well-known Allais paradox contradicts the fundamental postulates of maximizing the expected value or utility of a risky option. We describe a violation of the law of diminishing marginal utility as well as an intertemporal version of the Allais paradox.

Although the priority heuristic (PH) is conceived as a cognitive-process model, some of its critical process assumptions remain to be tested. The PH makes very strong ordinal and quantitative assumptions about the strictly sequential, non-compensatory use of three cues in choices between lotteries: (1) the difference between worst outcomes, (2) the difference in worst-case probabilities, and (3) the best outcome that can be obtained. These aspects were manipulated orthogonally in the present experiment. No support was found for the PH. Although the main effect of the primary worst-outcome manipulation was significant, it came along with other effects that the PH excludes. A strong effect of the secondary manipulation of worst-outcome probabilities was not confined to small differences in worst-outcomes; it was actually stronger for large worst-outcome differences. Overall winning probabilities that the PH ignores exerted a systematic influence. The overall rate of choices correctly predicted by the PH was close to chance, although high inter-judge agreement reflected systematic responding. These findings raise fundamental questions about the theoretical status of heuristics as fixed modules.

Runs of gains and losses are particularly salient to decision makers because of their perceived departure from randomness, as well as their immediate impact on the financial status of the decision makers. Past research has focused on decision making biases that relate to faulty conceptions of chance and luck, such as the gambler’s fallacy and the hot hand effect. Participants in the current study bet on the outcomes of a long sequence of simulated coin tosses. Risk preferences were found to change as a function of run valence (i.e., losses vs. gains), run length, and financial status. Individuals were found to differ in the effect of all of these factors, in their responses to runs of gains and losses in sequential risky choice.

We introduce the Berlin Numeracy Test, a new psychometrically sound instrument that quickly assesses statistical numeracy and risk literacy. We present 21 studies (n=5336) showing robust psychometric discriminability across 15 countries (e.g., Germany, Pakistan, Japan, USA) and diverse samples (e.g., medical professionals, general populations, Mechanical Turk web panels). Analyses demonstrate desirable patterns of convergent validity (e.g., numeracy, general cognitive abilities), discriminant validity (e.g., personality, motivation), and criterion validity (e.g., numerical and non-numerical questions about risk). The Berlin Numeracy Test was found to be the strongest predictor of comprehension of everyday risks (e.g., evaluating claims about products and treatments; interpreting forecasts), doubling the predictive power of other numeracy instruments and accounting for unique variance beyond other cognitive tests (e.g., cognitive reflection, working memory, intelligence). The Berlin Numeracy Test typically takes about three minutes to complete and is available in multiple languages and formats, including a computer adaptive test that automatically scores and reports data to researchers (http://www.riskliteracy.org). The online forum also provides interactive content for public outreach and education, and offers a recommendation system for test format selection. Discussion centers on construct validity of numeracy for risk literacy, underlying cognitive mechanisms, and applications in adaptive decision support.

Earlier frameworks have indicated that older adults tend to experience decline intheir deliberative decisional capacity, while their affective abilities tend toremain intact (Peters, Hess, Västfjäll, & Auman, 2007). Thepresent study applied this framework to the study of risky decision-makingacross the lifespan. Two versions of the Columbia Card Task (CCT) were used totrigger either affective decision-making (i.e., the “warm” CCT) ordeliberative decision-making (i.e., the “cold” CCT) in a sample of158 individuals across the lifespan. Overall there were no age differences inrisk seeking. However, there was a significant interaction between age andcondition, such that older adults were relatively more risk seeking in the coldcondition only. In terms of everyday decision-making, context matters and riskpropensity may shift within older adults depending upon the context.

Individual differences in cognitive abilities and skills can predict normatively superior and logically consistent judgments and decisions. The current experiment investigates the processes that mediate individual differences in risky choices. We assessed working memory span, numeracy, and cognitive impulsivity and conducted a protocol analysis to trace variations in conscious deliberative processes. People higher in cognitive abilities made more choices consistent with expected values; however, expected-value choices rarely resulted from expected-value calculations. Instead, the cognitive ability and choice relationship was mediated by the number of simple considerations made during decision making — e.g., transforming probabilities and considering the relative size of gains. Results imply that, even in simple lotteries, superior risky decisions associated with cognitive abilities and controlled cognition can reflect metacognitive dynamics and elaborative heuristic search processes, rather than normative calculations. Modes of cognitive control (e.g., dual process dynamics) and implications for process models of risky decision-making (e.g., priority heuristic) are discussed.

Revealed preference is the dominant approach for inferring preferences, but it is limited in that it relies solely on discrete choice data. When a person chooses one alternative over another, we cannot infer the strength of their preference or predict how likely they will be to make the same choice again. However, the choice process also produces response times (RTs), which are continuous and easily observable. It has been shown that RTs often decrease with strength-of-preference. This is a basic property of sequential sampling models such as the drift diffusion model. What remains unclear is whether this relationship is sufficiently strong, relative to the other factors that affect RTs, to allow us to reliably infer strength-of-preference across individuals. Using several experiments, we show that even when every subject chooses the same alternative, we can still rank them based on their RTs and predict their behavior on other choice problems. We can also use RTs to predict whether a subject will repeat or reverse their decision when presented with the same choice problem a second time. Finally, as a proof-of-concept, we demonstrate that it is also possible to recover individual preference parameters from RTs alone. These results demonstrate that it is indeed possible to use RTs to infer preferences.

The present study investigated skilled and adaptive strategy selection in risky decision making. We proposed that people with high objective numeracy, a strong predictor of general decision making skill, would have a broad repertoire of choice strategies andadaptively select these strategies depending on the importance of the decision. Thus more objectively numerate people would maximize their effort (e.g., invest more time) in important, high-payoff decisions and switch to a simple, fast heuristic strategy in trivial decisions. Subjective numeracy would, by contrast, be more closely related to interest in problem solving for its own sake and would not yield such an effect of importance. Participants made twelve high-payoff choices and twelve low-payoff choices in binary two-outcome gambles framed as gains. We measured objective and subjective numeracy using standard measures. Results showed that people with high subjective numeracy generally maximized the expected value (EV) in all decisions. In contrast, participants with high objective numeracy maximized EV only when choice problems were meaningful (i.e., they could result in high payoffs). When choice problems were trivial (i.e., choosing the normatively better option would not result in a large payoff), more objectively numerate participants made choices consistent with faster, more frugal heuristic strategies.

This study examined framing effects in decisions concerning public health. Tversky and Kahneman’s famous Asian Disease Problem served as experimental paradigm. Subjects chose between a sure and a risky option either presented as gains (saving lives) or as losses (dying). The amount of risk varied in terms of different probabilities. The number of affected people was either small (low need) or large (high need). Additionally, the decisions were linked to three different types of diseases (unusual infection, AIDS, leukemia). We also implemented two different time constraints during which the subjects had to give a response. Finally, we tested a within-subject design. The data analysis assuming a linear mixed effects model revealed significant effects of framing, probabilities, and need. Furthermore, the type of disease and time constraints were moderating the framing effect. Across the different diseases, framing effects were amplified when decision time was short.

The principle of loss aversion is thought to explain a wide range of anomalousphenomena involving tradeoffs between losses and gains. In this article, I showthat the anomalies loss aversion was introduced to explain - the risky betpremium, the endowment effect, and the status-quo bias - are characterized notonly by a loss/gain tradeoff, but by a tradeoff between the status-quo andchange; and, that a propensity towards the status-quo in the latter tradeoff issufficient to explain these phenomena. Moreover, I show that two basicpsychological principles - (1) that motives drive behavior; and (2) thatpreferences tend to be fuzzy and ill-defined - imply the existence of a robustand fundamental propensity of this sort. Thus, a loss aversion principle isrendered superfluous to an account of the phenomena it was introduced toexplain.

Mathematical and computational decision models are powerful tools for studyingchoice behavior, and hundreds of distinct decision models have been proposedover the long interdisciplinary history of decision making research. Theexistence of so many models has led to theoretical fragmentation and redundancy,obscuring key insights into choice behavior, and preventing consensus about theessential properties of preferential choice. We provide a synthesis of formalmodels of risky, multiattribute, and intertemporal choice, three importantdomains in decision making. We identify recurring insights discovered byscholars of different generations and different disciplines across these threedomains, and use these insights to classify over 150 existing models asinvolving various combinations of eight key mathematical and computationalproperties. These properties capture the main avenues of theoretical developmentin decision making research and can be used to understand the similarities anddifferences between decision models, aiding both theoretical analyses andempirical tests.