Random ambiguity

Investigation of the Stochastic Choice under Risk using Experimental Data

Stochastic orderings in random utility models

This paper contributes to our understanding of individual decision making by testing the proposal that differential weighting of 2 (or more) goals can be an important factor leading to stochastic (probabilistic) choice. The tested models follow from the endogenous maximum entropy program (eMEP) paradigm (Swait & Marley, 2013), which proposes that stochastic choice is (partially or entirely) a consequence of balancing multiple goals. That framework leads to an interpretation of the scale factor in classic random utility models (such as the multinomial logit [MNL]) as an endogenous property of a decision maker—an interpretation that is in stark contrast to the standard interpretation of the scale as due to heterogeneity or other “noise.” The new perspective is supported by data from a task that manipulates (by a prime) an individual’s propensity to be either consistent or to seek variety, suggesting that balanced pursuit of exploitation and exploration goals is a reasonable interpretation of stochastic choice.

Allais, Ellsberg, and Preferences for Hedging

Two of the most well-known regularities of preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behavior of an agent who can display both tendencies at the same time. We introduce a novel notion of preference for hedging that applies to both objective lotteries and uncertain acts, and captures both aversion to ambiguity and attraction towards certainty in objective lotteries. We show that this axiom, together with other standard axioms, is equivalent to two representations that generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both representations the agent evaluates ambiguity using multiple priors, but does not use Expected Utility to evaluate objective lotteries. In the rst representation, lotteries are evaluated by distorting probabilities as in the Rank Dependent Utility model, but using the worst from a set of such distortions. In the second, equivalent, representation the agent treats objective lotteries as ‘ambiguous objects,’ and uses a set of priors to evaluate them. We show that a preference for hedging is not sucient to guarantee an Ellsberg-like behavior if the agent violates Expected

The mHealth applications (mHealth apps) are shown as a promising and scalable solution for addressing various healthcare challenges and improving overall health outcomes. This study employs additive utility theory and random utility and discrete choice modeling to investigate the role of health literacy and the key constructs proposed in the Health Belief Model (HBM), namely perceived benefits, perceived barriers, perceived susceptibility, perceived severity, and self-efficacy, in influencing mHealth apps preferences. This study was conducted using a sample of 353 participants in Malaysia who are aged above 21 years old and have an income. Results show that Health Services Apps (English) is the most preferred by respondents, with education level as the strongest predictor of choice. Besides, English is the most preferred language in each category of mHealth apps as compared to the other languages. The results provide useful insights for policymakers and app developers to develop appropriate strategies for the integration of mHealth apps with existing healthcare systems. At the theoretical level, this study tries to expand the dimensions of additive utility theory on research of mHealth apps preferences and further enriches the application areas of HBM.

Random utility models with binary tree decomposable rank orders satisfy Tversky's elimination-by-aspects model

We develop a revealed preference test for the Choquet expected utility model with ambiguity aversion, which does not rely on specific functional form assumptions on the utility index. It is computationally efficient if the number of states is not too large, even for a large number of observations. This is a nice feature compared to other existing revealed preference tests for decision models with ambiguity. We illustrate the usefulness of our results by implementing our test on two experimental datasets from the literature, and we compare the empirical fit of this model to the subjective expected utility model. (JEL C91, D81, D91, G41)

We present a Gaussian Process – Latent Class Choice Model (GP-LCCM) to integrate a non-parametric class of probabilistic machine learning within discrete choice models (DCMs). Gaussian Processes (GPs) are kernel-based algorithms that incorporate expert knowledge by assuming priors over latent functions rather than priors over parameters, which makes them more flexible in addressing nonlinear problems. By integrating a Gaussian Process within a LCCM structure, we aim at improving discrete representations of unobserved heterogeneity. The proposed model would assign individuals probabilistically to behaviorally homogeneous clusters (latent classes) using GPs and simultaneously estimate class-specific choice models by relying on random utility models. Furthermore, we derive and implement an Expectation-Maximization (EM) algorithm to jointly estimate/infer the hyperparameters of the GP kernel function and the class-specific choice parameters by relying on a Laplace approximation and gradient-based numerical optimization methods, respectively. The model is tested on two different mode choice applications and compared against different LCCM benchmarks. Results show that GP-LCCM allows for a more complex and flexible representation of heterogeneity and improves both in-sample fit and out-of-sample predictive power. Moreover, behavioral and economic interpretability is maintained at the class-specific choice model level while local interpretation of the latent classes can still be achieved, although the non-parametric characteristic of GPs lessens the transparency of the model.

Discrete Choice Models with Ambiguity Aversion: Product Line Pricing and Competition

The random utility model is one of the most fundamental models in discrete choice analysis in economics. Although Falmagne (1978) obtained an axiomatization of the random utility model, his characterization requires strong observability of choices, i.e., the frequencies of choices must be observed from all subsets of the set of alternatives. Little is known, however, about the axiomatization when the frequencies on some choice sets are not observable. In fact, the problem of obtaining a tight characterization appears to be out of reach in most cases in view of a related NP-hard problem. We consider the following incomplete dataset. Let X be a finite set of alternatives. Let X* ⊆ X bea set of unobservable alternatives. Let D ⊆ 2X be the set of choice sets. We assume that the choice frequency ρ(D, x) is unobservable (i.e., not defined) if and only if x ∈ X* or D ∉ D. Let M* ≡ {(D,x)|x ∈ D ∈ 2X and [x ∈ X* or D ∉ D]} be the set of all pairs (D,x) such that ρ(D, x) is not observable. To state our theorem, for any ρ and (D, x) ∈ M ≡ {(D, x) ∈ D × X | x ∈ D}, define a Block-Marschak polynomial by K(ρ, D, x) = ΣE:E⊇D(−1)|E\D|ρ(E,x).

After 40 years of deriving metric values for health status or health-related quality of life, the effective quantification of subjective health outcomes is still a challenge. Here, two of the best measurement tools, the discrete choice and the Rasch model, are combined to create a new model for deriving health values. First, existing techniques to value health states are briefly discussed followed by a reflection on the recent revival of interest in patients’ experience with regard to their possible role in health measurement. Subsequently, three basic principles for valid health measurement are reviewed, namely unidimensionality, interval level, and invariance. In the main section, the basic operation of measurement is then discussed in the framework of probabilistic discrete choice analysis (random utility model) and the psychometric Rasch model. It is then shown how combining the main features of these two models yields an integrated measurement model, called the multi-attribute preference response (MAPR) model, which is introduced here. This new model transforms subjective individual rank data into a metric scale using responses from patients who have experienced certain health states. Its measurement mechanism largely prevents biases such as adaptation and coping. Several extensions of the MAPR model are presented. The MAPR model can be applied to a wide range of research problems. If extended with the self-selection of relevant health domains for the individual patient, this model will be more valid than existing valuation techniques.

A previously reported positive influence of a distractor alternative on decision accuracy was driven by an unintended covariation between key variables, beyond which the distractor has a modest negative influence on accuracy, possibly mirroring asymmetric multiattribute context effects.

Subjective uncertainty is characterized by ambiguity if the decision maker has an imprecise knowledge of the probabilities of payoff relevant events. In such an instance, the decision maker's beliefs are better represented by a set of probability functions than by a unique probability function. An ambiguity averse decision maker adjusts his choice on the side of caution in response to his imprecise knowledge of the odds. The non-additive expected utility model allows a formal characterization of such behavior. Using this model, this paper shows that ambiguity aversion can explain the existence of incomplete contracts. The setting for the demonstration is the investment hold-up model which has been the focus of much of the recent research on the implications of incomplete contracts.

This paper highlights a previously unnoticed property of commonly-used discrete choice models, which is that they feature parallel demand curves. Specifically, we show that in additive random utility models, inverse aggregate demand curves shift in parallel with respect to variety if and only if the random utility shocks follow the Gumbel (Type 1 Extreme Value) distribution. Using results from Extreme Value Theory, we provide conditions for other distributions to generate parallel demands asymptotically, as the number of varieties increases. We establish these results in the benchmark case of symmetric products, illustrate them using numerical simulations and show that they hold in extended versions of the model with correlated tastes and asymmetric products. Lastly, we provide a “proof of concept” of parallel demands as an economic tool by showing how to use parallel demands to identify the change in consumer surplus from an exogenous change in product variety.