This article describes a study of transitivity of preference and of transparent dominance with 220 participants who judged each choice problem 4 times. It shows how a true-and-error model with 2 error terms per choice problem can be applied to replicated data, to ask if violations of dominance or of transitivity are ‘real’ rather than due to random response errors. These models allow one to estimate the incidence of systematic violations and of error rates. The new data showed about 3% violations of transitivity, corrected for error. This incidence might be statistically significant, but a skeptic might dismiss it as too small to build a theory upon. Tests of dominance found violations with overall rates from 4% to 18%. As in previous research, violations of transparent dominance appeared almost exclusively among people who systematically prefer ‘safe’ gambles (with low ranges of outcomes) over ‘riskier’ gambles with higher expected values when the ‘safe’ gamble was dominated by the higher-ranged gamble. For those participants and choice problems, rates of violation were 28%–45%, corrected for error. It was theorized that these violations of dominance may be due to a subgroup of risk-averse participants using a strategy in this experiment to find ‘safe’ alternatives, without comparing outcomes between gambles.

The Markov True and Error (MARTER) model (Birnbaum & Wan, 2020) has three components: a risky decision making model with one or more parameters, a Markov model that describes stochastic variation of parameters over time, and a true and error (TE) model that describes probabilistic relations between true preferences and overt responses. In this study, we simulated data according to 57 generating models that either did or did not satisfy the assumptions of the True and Error fitting model, that either did or did not satisfy the error independence assumptions, that either did or did not satisfy transitivity, and that had various patterns of error rates. A key assumption in the TE fitting model is that a person’s true preferences do not change in the short time within a session; that is, preference reversals between two responses by the same person to two presentations of the same choice problem in the same brief session are due to random error. In a set of 48 simulations, data generating models either satisfied this assumption or they implemented a systematic violation, in which true preferences could change within sessions. We used the true and error (TE) fitting model to analyze the simulated data, and we found that it did a good job of distinguishing transitive from intransitive models and in estimating parameters not only when the generating model satisfied the model assumptions, but also when model assumptions were violated in this way. When the generating model violated the assumptions, statistical tests of the TE fitting models correctly detected the violations. Even when the data contained violations of the TE model, the parameter estimates representing probabilities of true preference patterns were surprisingly accurate, except for error rates, which were inflated by model violations. In a second set of simulations, the generating model either had error rates that were or were not independent of true preferences and transitivity either was or was not satisfied. It was found again that the TE analysis was able to detect the violations of the fitting model, and the analysis correctly identified whether the data had been generated by a transitive or intransitive process; however, in this case, estimated incidence of a preference pattern was reduced if that preference pattern had a higher error rate. Overall, the violations could be detected and did not affect the ability of the TE analysis to discriminate between transitive and intransitive processes.

This paper describes a theory of the variability of risky choice that describes empirical properties of choice data, including sequential effects and systematic violations of response independence. The Markov True and Error (MARTER) model represents the formation and fluctuation of true preferences produced by stochastic variation of parameters over time, which produces changing true preference patterns. This model includes a probabilistic association between true preferences and overt responses due to random error. Computer programs have been developed to simulate data according to this model, to fit data to the TE model, and to test and analyze violations of iid (independent and identical distributions) that are predicted by the model. Data simulated from MARTER models show properties that are characteristic of real data, including violations of iid similar to those observed in previous empirical research. This paper also illustrates how methods based on analysis of binary response proportions do not and in many cases cannot correctly diagnose what model was used to generate the data. The MARTER model is extremely general and neutral with respect to models of risky decision making. For example, the transitive transfer of attention exchange (TAX) model and intransitive Lexicographic Semiorder (LS) models can both be represented as special cases of MARTER, and they can be tested against each other, even when binary choice proportions cannot discriminate which model was used to simulate the data. Software to simulate data according to this model, and to fit data to this model, to test this model, and to compare special case theories are included or linked to this article.

It is important to understand the impact of individual differences in decision making from childhood to adulthood. This cohort-based study extends our knowledge by comparing decision making of children across the age range of 8 to 17 years and their parents. Based on prior research and theory focusing on different types of framing effects, we uncover several key differences across ages, including levels of risk taking and sensitivity to expected value differences between risky and riskless choices. Furthermore, we find that measures such as Numeracy and Surgency help explain both age-related and individual differences on our tasks, especially for decisions involving risk. We discuss the role of diverse task measures in understanding how individual difference factors affect different aspects of decision making, including the ability and effort to process numerical information and the ability to suppress affective reactions to stimulus labels.

Butler and Pogrebna (2018) devised triples of three-branch gambles theorized to violate transitivity of preference according to a most probable winner model. According to this model, a person chooses the option that has the higher probability to yield a better outcome than the other alternative. They tested 11 triples with 100 participants and found cases that appeared to violate weak stochastic transitivity and the triangle inequality. But tests of weak stochastic transitivity and the triangle inequality do not provide a proper method to compare transitive and intransitive models that allow mixtures of preference patterns and random errors. Those older methods can yield false conclusions regarding transitivity, for example, if different participants have different true preferences or if different choice problems have different rates of error. This paper reanalyzes their data using a true and error (TE) model, which does not require these unrealistic assumptions, and which provides estimates of the incidence of transitive and intransitive behavior in a mixture. Reanalysis indicated that 3 of the 11 triples showed convincing evidence of violations of transitivity in the opposite direction of the predictions of the most probable winner model. Further, these and other triples showed other significant violations of the most probable winner model. Despite some violations of the true and error model, the data of Butler and Pogrebna appear to contradict not only transitive utility models but they also refute the most probable winner model as a descriptive theory of choice behavior.

While previous research has found that children make more risky decisions than their parents, little is known about the developmental trajectory for the ability to make advantageous decisions. In a sample of children, 5-11 years old, we administered a new risky decision making task in which the relative expected value (EV) of the risky and riskless choice options was varied over trials. Younger children (age 5-7) showed significantly less responsiveness to EV differences than their parents on both trials involving risky gains and trials involving risky losses. For older children (age 8-11) this deficit was smaller overall but was greater on loss trials than on gain trials. Children of both ages made more risky choices than adults when risky choices were disadvantageous. We further analyzed these results in terms of children's ability to utilize probability and outcome information, and discussed them in terms of developing brain structures vital for decision making under uncertainty.

We study individual decision making in a lottery-choice task performed by three different populations: gamblers under psychological treatment (“addicts”), gamblers’ spouses (“victims”), and people who are neither gamblers or gamblers’ spouses (“normals”). We find that addicts are willing to take less risk than normals, but the difference is smaller as a gambler’s time under treatment increases. The large majority of victims report themselves unwilling to take any risk at all. However, addicts in the first year of treatment react more than other addicts to the different values of the risk-return parameter.

We investigated how frequency and amount of punishment affect the decision making of Iranian subjects. In our first experiment, performing a computer-based Persian version of the Iowa Gambling Task (IGT), our subjects scored remarkably lower than their Western counterparts. Moreover, our subjects chose more frequently and more rapidly from decks that had less frequent but larger amounts of punishments in comparison to decks that had more frequent punishments with smaller amounts. In our second experiment, subjects did not differentiate between decks with the same frequency of punishment but with different punishment amounts. However, among decks with the same amount but different frequency of punishment, a significant preference was apparent towards decks with less frequency of punishment. Our results differ from previous studies, indicating a different strategy in risky decision making among healthy adult Iranian subjects, as they show low attention to the amount of punishment and are more concerned with the frequency of punishment.

There are many ways to measure how people manage risk when they make decisions. A standard approach is to measure risk propensity using self-report questionnaires. An alternative approach is to use decision-making tasks that involve risk and uncertainty, and apply cognitive models of task behavior to infer parameters that measure people’s risk propensity. We report the results of a within-participants experiment that used three questionnaires and four decision-making tasks. The questionnaires are the Risk Propensity Scale, the Risk Taking Index, and the Domain Specific Risk Taking Scale. The decision-making tasks are the Balloon Analogue Risk Task, the preferential choice gambling task, the optimal stopping problem, and the bandit problem. We analyze the relationships between the risk measures and cognitive parameters using Bayesian inferences about the patterns of correlation, and using a novel cognitive latent variable modeling approach. The results show that people’s risk propensity is generally consistent within different conditions for each of the decision-making tasks. There is, however, little evidence that the way people manage risk generalizes across the tasks, or that it corresponds to the questionnaire measures.

The body of literature on the relationship between risk aversion and wealth is extensive. However, little attention has been given to examining how future realizations of wealth might affect (current) risk decisions. Using paired lottery choice experiments and exposing subjects experimentally to imagined future wealth frames, I find that individuals are more risk-seeking if they are asked to imagine that they will be wealthy in the future. Yet I find that individuals are not significantly more risk-averse if they are asked to imagine that they will be poor in the future. I discuss theoretical and policy implications of these findings, including why savings rates are so low in the United States.

In risky decision making, whether decision makers follow an expectation rule as hypothesised by mainstream theories is a compelling question. To tackle this question and enrich our knowledge of the underlying mechanism of risky decision making, we developed a series of new experimental paradigms that directly examined the computation processes to systematically investigate the process of risky decision making and explore the boundary condition of expectation rule over the course of a decade. In this article, we introduce these methods and review behavioural, eye-tracking, event-related potential, and functional magnetic resonance imaging studies that employed these methods. Results of these studies consistently showed that decision makers in the single-application condition did not perform the weighting and summing process assumed by the expectation rule. Moreover, decision makers were inclined to adopt a non-compensatory strategy, such as a heuristic one, in risky decision making. Furthermore, results indicated that the expectation rule was only applicable for conditions that involved decisions applied to numerous events (multiple applications) or to people (everyone). The findings indicated that using an index based on expected value to prescribe human risk preferences appears to be an artificial or false index of risk preference, and emphasised a new methodological direction for risky decision-making research.