Birnbaum and Quispe-Torreblanca (2018) evaluated a set of six models developed under true-and-error theory against data in which people made choices in repeated gambles. They concluded the three models based on expected utility theory were inadequate accounts of the behavioral data, and argued in favor of the simplest of the remaining three more general models. To reach these conclusions, they used non-Bayesian statistical methods: frequentist point estimation of parameters, bootstrapped confidence intervals of parameters, and null hypothesis significance testing of models. We address the same research goals, based on the same models and the same data, using Bayesian methods. We implement the models as graphical models in JAGS to allow for computational Bayesian analysis. Our results are based on posterior distribution of parameters, posterior predictive checks of descriptive adequacy, and Bayes factors for model comparison. We compare the Bayesian results with those of Birnbaum and Quispe-Torreblanca (2018). We conclude that, while the very general conclusions of the two approaches agree, the Bayesian approach offers better detailed answers, especially for the key question of the evidence the data provide for and against the competing models. Finally, we discuss the conceptual and practical advantages of using Bayesian methods in judgment and decision making research highlighted by this case study.

True and Error Theory (TET) provides a method to separate the variability of behavior into components due to changing true policy and to random error. TET is a testable theory that can serve as a statistical model, allowing one to evaluate substantive theories as nested, special cases. TET is more accurate descriptively and has theoretical advantages over previous approaches. This paper presents a freely available computer program in R that can be used to fit and evaluate both TET and substantive theories that are special cases of it. The program performs Monte Carlo simulations to generate distributions of test statistics and bootstrapping to provide confidence intervals on parameter estimates. Use of the program is illustrated by a reanalysis of previously published data testing whether what appeared to be violations of Expected Utility (EU) theory (Allais paradoxes) by previous methods might actually be consistent with EU theory.

The use of gamification to motivate engagement has greatly increased the number of ways in which people compete. Many of these competitions allow individuals to see how they rank as a competition progresses. Our work aims to provide a better understanding of how individuals feel about different rank outcomes in competitions. We do this by applying the principles of expected utility theory to elicit utility curves for over 3,000 people across three studies using hypothetical competition scenarios. We find consistent support for the following generalizations: 1) individuals are risk-seeking when in second place, 2) they are risk-averse when in second-to-last place, and 3) the utility decrease going from first to second place is greater than their decrease going from second-to-last to last place. Our results suggest individuals are both last-place averse and first-place seeking, with an even stronger inclination towards the latter.

This study provides the first comprehensive analysis of individual perceptions of tail risks. It focuses not only on the probability, as has been studied by Nicholas Barberis and others, but also on anticipation of damage. We examine how those perceptions relate to experts’ estimates and publicly available risk information. Behavioural factors—availability bias, threshold models of choice, worry and trust—are found to have a significant impact on risk perceptions. The probability of tail events is overestimated, which is consistent with probability weighting in prospect theory. Potential damage is underestimated, one reason why individuals do not invest in protective measures.

In a previously published article, I reported some tests of prospect theory's reflection effect over outcomes defined by money and life years gained from treatment. Those results suggested qualified support for the reflection effect over money outcomes and strong support over longevity outcomes. This article reruns those tests while accounting for the intensity of individual risk attitudes, and, overall, show consistency with the reflection effect. However, I argue that these results do not necessarily offer support for the explanatory power of prospect theory. Rather, the results may be driven by evolved responses to circumstances that provoke perceptions of scarcity and abundance. Therefore, from an ecological perspective, behavioral patterns such as those that are consistent with the reflection effect, which, by extension, tend to be considered as erroneous or biased by most behavioral economists because they conflict with the postulates of rational choice theory, may not be unreasonable. Recognizing as such is important when considering how behavioral insights ought to inform public policy design and implementation.

This paper defends revealed preference theory against a pervasive line of criticism, according to which revealed preference methodology relies on appealing to some mental states, in particular an agent’s beliefs, rendering the project incoherent or unmotivated. I argue that all that is established by these arguments is that revealed preference theorists must accept a limited mentalism in their account of the options an agent should be modelled as choosing between. This is consistent both with an essentially behavioural interpretation of preference and with standard revealed preference methodology. And it does not undermine the core motivations of revealed preference theory.

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility theory. I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate.

Whereas many others have scrutinized the Allais paradox from a theoretical angle, we study the paradox from an historical perspective and link our findings to a suggestion as to how decision theory could make use of it today. We emphasize that Allais proposed the paradox as a normative argument, concerned with ‘the rational man’ and not the ‘real man’, to use his words. Moreover, and more subtly, we argue that Allais had an unusual sense of the normative, being concerned not so much with the rationality of choices as with the rationality of the agent as a person. These two claims are buttressed by a detailed investigation – the first of its kind – of the 1952 Paris conference on risk, which set the context for the invention of the paradox, and a detailed reconstruction – also the first of its kind – of Allais’s specific normative argument from his numerous but allusive writings. The paper contrasts these interpretations of what the paradox historically represented, with how it generally came to function within decision theory from the late 1970s onwards: that is, as an empirical refutation of the expected utility hypothesis, and more specifically of the condition of von Neumann–Morgenstern independence that underlies that hypothesis. While not denying that this use of the paradox was fruitful in many ways, we propose another use that turns out also to be compatible with an experimental perspective. Following Allais’s hints on ‘the experimental definition of rationality’, this new use consists in letting the experiment itself speak of the rationality or otherwise of the subjects. In the 1970s, a short sequence of papers inspired by Allais implemented original ways of eliciting the reasons guiding the subjects’ choices, and claimed to be able to draw relevant normative consequences from this information. We end by reviewing this forgotten experimental avenue not simply historically, but with a view to recommending it for possible use by decision theorists today.

In this paper a system for recommending investment channel choices to members of defined contribution retirement funds is proposed. The system is interactive, using a member's answers to a series of questions to derive a utility function. The observed values are interpolated by means of appropriate formulae to produce a smooth utility function over the whole positive range of benefits at retirement. The resulting function, together with stochastic models of the returns on the available channels and of the annuity factor at exit, is then used to recommend an optimum apportionment of the member's investment. The proposed system is applied to the observed values of utility functions of post-retirement income elicited from members of retirement funds. Difficulties in the application are discussed and the results are analysed. The sensitivity of the recommendations to the parameters of the stochastic model is discussed.

This paper addresses the use of expected utility theory for the recommendation of an apportionment between investment channels of a member's interest in a defined contribution retirement fund. Such usage is defended against arguments that have been levelled against expected utility theory and empirical evidence is discussed.