The midweight method to measure attitudes towards risk and ambiguity

This paper introduces a parameter-free method for measuring the weighting functions of prospect theory and rank-dependent utility. These weighting functions capture risk attitudes, subjective beliefs, and ambiguity attitudes. Our method, called the midweight method, is based on a convenient way to obtain midpoints in the weighting function scale. It can be used both for risk (known probabilities) and for uncertainty (unknown probabilities). The resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity, i.e., the difference between uncertainty and risk. Compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity, our method is more efficient and can accommodate violations of expected utility under risk. An experiment demonstrates the tractability of our method, yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods, as predicted by Ellsberg

Stake effects on ambiguity attitudes for gains and losses

We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small- probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk (known probabilities) and uncertainty (unknown probabilities). For risk we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased uncertainty aversion for large-probability gains and for small-probability losses

Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field

We test whether probability weighting affects household portfolio choice in a representative survey. On average, people display inverse-S shaped probability weighting, overweighting low probability events. As theory predicts, probability weighting is positively associated with portfolio underdiversification and significant Sharpe ratio losses. Analyzing respondents’ individual stock holdings, we find higher probability weighting is associated with owning lottery-type stocks and positively-skewed equity portfolios. People with higher probability weighting are less likely to own mutual funds and more likely to either avoid equities or hold individual stocks. We are the first to empirically link individuals’ elicited probability weighting and real-world decisions under risk

Experience and rationality under risk: re-examining the impact of sampling experience

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Are Black Swans Really Ignored?

This paper investigates the often-discussed over – and under – weighting of rare and extreme events – so called “black swans” – in decisions from experience (DFE). We first resolve the problem of lack of control over experienced probabilities by adjusting the common sampling paradigm of DFE. Our experimental design also controls for utility and uncertainty of experienced probabilities (ambiguity). This enables us to exactly identify the deviations from Expected Utility due to over – or under – weighting of probabilities under risk. Our results confirm the well-known gap between DFE and traditional decisions from description (DFD) but do not provide evidence for underweighting of small probabilities in DFE. We found that experience leads to less pronounced overweighting of small probabilities, and less pronounced underweighting of large probabilities. Thus, our findings suggest a clear de-biasing effect of sampling experience: it attenuates – rather than reverses – the commonly found inverse S-shaped probability weighting in DFD

Utility Independence of Multiattribute Utility Theory is Equivalent to Standard Sequence Invariance of Conjoint Measurement

Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain

Socioeconomic Differences in Ambiguity Attitudes, Partial Ambiguity and A-insensitivity: Evidence from Real-World Decision Making under Uncertainty

Using a nonlinear mixed logit model, this study investigates commuter choice behaviour in the presence of uncertain travel time. Within the proposed source-dependent extended expected utility framework, the uncertainty-risk gap is captured in the source function and the attitude towards ambiguity is measured over the full subjective probability distribution. Based on one revealed preference dataset, we structurally estimated observed heterogeneity in ambiguity attitudes in terms of socioeconomic covariates and unobserved between-subject heterogeneity in taste preferences, while controlling for risk attitude and allowing for the trade-off between attributes. In addition to revealed age and gender differences in ambiguity preferences, other important findings include partial ambiguity seeking in this type of loss domain and the existence of likelihood insensitivity under uncertainty (i.e., a-insensitivity). This systematic investigation of decision making under uncertainty in real-market settings would offer behaviourally realistic inputs into the evaluation of social effects and design of effective policies

Using Preferred Outcome Distributions to Estimate Value and Probability Weighting Functions in Decisions under Risk

In this paper we propose the use of preferred outcome distributions as a new method to elicit individuals’ value and probability weighting functions in decisions under risk. Extant approaches for the elicitation of these two key ingredients of individuals’ risk attitude typically rely on a long, chained sequence of lottery choices. In contrast, preferred outcome distributions can be elicited through an intuitive graphical interface, and, as we show, the information contained in two preferred outcome distributions is sufficient to identify non-parametrically both the value function and the probability weighting function in rank-dependent utility models. To illustrate our method and its advantages, we run an incentive-compatible lab study in which participants use a simple graphical interface – the Distribution Builder (Goldstein et al. 2008) – to construct their preferred outcome distributions, subject to a budget constraint. Results show that estimates of the value function are in line with previous research but that probability weighting biases are diminished, thus favoring our proposed approach based on preferred outcome distributions

Using Preferred Outcome Distributions to estimate Value and Probability Weighting Functions in Decisions under Risk

In this paper we propose the use of preferred outcome distributions as a new method to elicit individuals' value and probability weighting functions in decisions under risk. Extant approaches for the elicitation of these two key ingredients of individuals' risk attitude typically rely on a long, chained sequence of lottery choices. In contrast, preferred outcome distributions can be elicited through an intuitive graphical interface, and, as we show, the information contained in two preferred outcome distributions is sufficient to identify non-parametrically both the value function and the probability weighting function in rank-dependent utility models. To illustrate our method and its advantages, we run an incentive-compatible lab study in which participants use a simple graphical interface - the Distribution Builder (Goldstein et al. 2008) - to construct their preferred outcome distributions, subject to a budget constraint. Results show that estimates of the value function are in line with previous research but that probability weighting biases are diminished, thus favoring our proposed approach based on preferred outcome distributions

Measuring risk and time preferences in an integrated framework

We investigate time discounting under risk. To this end, we modify a popular multiple price list (MPL) design to elicit time discounting. Structural estimations of model parameters yield several new insights. For one, we find present bias to persist under risk, contrary to some previous evidence from the psychology literature. We further confirm the robustness of inverse-S shaped probability weighting. This is important inasmuch as random choice predicts the opposite shape in our setup. We also show that correcting for probability weighting under risk impacts the assessment of discount rates. Those are systematically underestimated under the commonly used, more restrictive, expected utility. (C) 2019 Elsevier Inc. All rights reserved