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.

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.

We investigated whether older adults are more likely than younger adults to violate a foundational property of rational decision making, the axiom of transitive preference. Our experiment consisted of two groups, older (ages 60-75; 21 participants) and younger (ages 18-30; 20 participants) adults. We used Bayesian model selection to investigate whether individuals were better described via (transitive) weak order-based decision strategies or (possibly intransitive) lexicographic semiorder decision strategies. We found weak evidence for the hypothesis that older adults violate transitivity at a higher rate than younger adults. At the same time, a hierarchical Bayesian analysis suggests that, in this study, the distribution of decision strategies across individuals is similar for both older and younger adults.