[show abstract][hide abstract] ABSTRACT: This paper presents preference axiomatizations of expected utility for nonsimple lotteries while avoiding continuity constraints. We use results by Fishburn (1975), Wakker (1993), and Kopylov (2010) to generalize results by Delbaen et al. (2011). We explain the logical relations between these contributions for risk versus uncertainty, and for finite versus countable additivity, indicating what are the most general axiomatizations of expected utility existing today.
Journal of Mathematical Economics 01/2013; 49(1):28–30. · 0.32 Impact Factor
[show abstract][hide abstract] ABSTRACT: Behavioral conditions such as compound invariance for risky choice and constant decreasing relative impatience for intertemporal choice have surprising implications for the underlying decision model. They imply a multiplicative separability of outcomes and either probability or time. Hence the underlying model must be prospect theory or discounted utility on the domain of prospects with one nonzero outcome. We indicate implications for richer domains with multiple outcomes, and with both risk and time involved.
Journal of Mathematical Psychology. 01/2013; 57(s 3–4):68–77.
[show abstract][hide abstract] ABSTRACT: This paper presents a general technique for comparing the concavity of different utility functions when probabilities need not be known. It generalizes: (a) Yaariʼs comparisons of risk aversion by not requiring identical beliefs; (b) Kreps and Porteusʼ information-timing preference by not requiring known probabilities; (c) Klibanoff, Marinacci, and Mukerjiʼs smooth ambiguity aversion by not using subjective probabilities (which are not directly observable) and by not committing to (violations of) dynamic decision principles; (d) comparative smooth ambiguity aversion by not requiring identical second-order subjective probabilities. Our technique completely isolates the empirical meaning of utility. It thus sheds new light on the descriptive appropriateness of utility to model risk and ambiguity attitudes.
Games and Economic Behavior 07/2012; 75(2):481–489. · 0.83 Impact Factor
[show abstract][hide abstract] ABSTRACT: Time discounting and quality of life are two important factors in evaluations of medical interventions. The measurement of these two factors is complicated because they interact. Existing methods either simply assume one factor given, based on heuristic assumptions, or invoke complicating extraneous factors, such as risk, that generate extra biases. The authors introduce a method for measuring discounting (and then quality of life) that involves no extraneous factors and that avoids distorting interactions. Their method is considerably simpler and more realistic for subjects than existing methods. It is entirely choice based and thus can be founded on economic rationality requirements. An experiment demonstrates the feasibility of this method and its advantages over classical methods.
Medical Decision Making 06/2012; 32(4):583-93. · 2.89 Impact Factor
[show abstract][hide abstract] ABSTRACT: In a large representative sample, we measure ambiguity attitudes and investigate their relation with stock market participation. Our tractable measurement of the general population’s ambiguity attitudes is made possible by a simplification of the recently introduced source method. In addition to ambiguity aversion, the results from our representative sample confirm a-insensitivity, a new component of ambiguity attitudes recently found in laboratory studies. A-insensitivity means that people do not sufficiently discriminate between different levels of likelihood, often treating them as fifty-fifty. Contrary to common expectation, ambiguity aversion, when measured using classical stimuli, is not significantly associated with stock market participation, except for those subjects who perceive stock returns as highly ambiguous. A-insensitivity, however, is negatively related to both stock market participation and private business ownership. These surprising findings can be explained by reference dependent ambiguity. Our results show the empirical relevance of a-insensitivity and reference dependence for real-world economic decisions.
[show abstract][hide abstract] ABSTRACT: Two experiments show that violations of expected utility due to ambiguity, found in general decision experiments, also affect belief aggregation. Hence we use modern ambiguity theories to analyze belief aggregation, thus obtaining more refined and empirically more valid results than traditional theories can provide. We can now confirm more reliably that conflicting (heterogeneous) beliefs where some agents express certainty are processed differently than informationally equivalent imprecise homogeneous beliefs. We can also investigate new phenomena related to ambiguity. For instance, agents who express certainty receive extra weight (a cognitive effect related to ambiguity-generated insensitivity) and generate extra preference value (source preference; a motivational effect related to ambiguity aversion). Hence, incentive compatible belief elicitations that prevent manipulation are especially warranted when agents express certainty. For multiple prior theories of ambiguity, our findings imply that the same prior probabilities can be treated differently in different contexts, suggesting an interest of corresponding generalizations.
Journal of Risk and Uncertainty 01/2012; 44(2):115-147. · 1.53 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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. This paper was accepted by George Wu, decision analysis.
[show abstract][hide abstract] ABSTRACT: 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.
Journal of Mathematical Psychology - J MATH PSYCHOL. 01/2011;
[show abstract][hide abstract] ABSTRACT: Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical
primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty
today, prospect theory, preference foundations have as yet been provided only for prospects taking finitely many values. In
applications, however, prospects often are complex and involve infinitely many values, as in normal and lognormal distributions.
This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility
and only require finite additivity of the underlying probability distributions, leaving the restriction to countably additive
distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect
theory (rank-dependent utility and Choquet expected utility) that all required countable additivity. We now obtain genuine
generalizations of de Finetti’s and Savage’s finitely additive setups to unbounded utility.
KeywordsProspect theory–Preference foundations–Continuous distributions–Unbounded utility
Journal of Risk and Uncertainty 01/2011; 42(3):195-210. · 1.53 Impact Factor
[show abstract][hide abstract] ABSTRACT: This paper finds preference reversals in measurements of ambiguity aversion, even if psychological and informational circumstances are kept constant. The reversals are of a fundamentally different nature than the reversals found before because they cannot be explained by context-dependent weightings of attributes. We offer an explanation based on Sugden's random-reference theory, with different elicitation methods generating different random reference points. Then measurements of ambiguity aversion that use willingness to pay are confounded by loss aversion and hence overestimate ambiguity aversion. This paper was accepted by Teck Ho, decision analysis.
[show abstract][hide abstract] ABSTRACT: When process fairness deviates from outcome fairness, dynamic inconsistencies can arise as in nonexpected utility. Resolute choice (Machina) can restore dynamic consistency under nonexpected utility without using Strotz's precommitment. It can similarly justify dynamically consistent process fairness.
[show abstract][hide abstract] ABSTRACT: In economic decisions we often have to deal with uncertain events for which no probabilities are known. Several normative models have been proposed for such decisions. Empirical studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically that can capture the richness of ambiguity attitudes. The theoretical key in our method is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak.
[show abstract][hide abstract] ABSTRACT: This paper introduces time-tradeoff (TTO) sequences as a general tool to analyze intertemporal choice. We give several applications. For empirical purposes, we can measure discount functions without requiring any measurement of or assumption about utility. We can quantitatively measure time inconsistencies and simplify their qualitative tests. TTO sequences can be administered and analyzed very easily, using only pencil and paper. For theoretical purposes, we use TTO sequences to axiomatize (quasi-)hyperbolic discount functions. We demonstrate the feasibility of measuring TTO sequences in an experiment, in which we tested the axiomatizations. Our findings suggest rejections of several currently popular discount functions and call for the development of new ones. It is especially desirable that such discount functions can accommodate increasing impatience.
[show abstract][hide abstract] ABSTRACT: We often deal with uncertain events for which no probabilities are known. Several normative models have been proposed. Descriptive studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically. The theoretical key is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak. (JEL D81)
American Economic Review 01/2010; 101(2):695-723. · 2.69 Impact Factor
[show abstract][hide abstract] ABSTRACT: Similarity measures have been studied extensively in many domains, but usually with well-structured data sets. In many psychological applications, however, such data sets are not available. It often cannot even be predicted how many items will be observed, or what exactly they will entail. This paper introduces a similarity measure, called the metric-frequency (MF) measure, that can be applied to such data sets. If it is not known beforehand how many items will be observed, then the number of items actually observed in itself carries information. A typical feature of the MF is that it incorporates such information. The primary purpose of our measure is that it should be pragmatic, widely applicable, and tractable, even if data are complex. The MF generalizes Tversky's set-theoretic measure of similarity to cases where items may be present or absent and at the same time can be numerical as with Shepard's metric measure, but need not be so. As an illustration, we apply the MF to family therapy where it cannot be predicted what issues the clients will raise in therapy sessions. The MF is flexible enough to be applicable to idiographic data.
British Journal of Mathematical and Statistical Psychology 03/2009; 62(Pt 3):663-82. · 1.26 Impact Factor
[show abstract][hide abstract] ABSTRACT: The commonly used hyperbolic and quasi-hyperbolic discount functions have been developed to accommodate decreasing impatience, which is the prevailing empirical finding in intertemporal choice, in particular for aggregate behavior. However, these discount functions do not have the flexibility to accommodate increasing impatience or strongly decreasing impatience. This lack of flexibility is particularly disconcerting for fitting data at the individual level, where various patterns of increasing impatience and strongly decreasing impatience will occur for a significant fraction of subjects. This paper presents discount functions with constant absolute (CADI) or constant relative (CRDI) decreasing impatience that can accommodate any degree of decreasing or increasing impatience. In particular, they are sufficiently flexible for analyses at the individual level. The CADI and CRDI discount functions are the analogs of the well-known CARA and CRRA utility functions for decision under risk.
[show abstract][hide abstract] ABSTRACT: This article is a personal account of the author's experiences as an economist working in medical decision making. He discusses the differences between economic decision theory and medical decision making and gives examples of the mutual benefits resulting from interactions. In particular, he discusses the pros and cons of different methods for measuring quality of life (or, as economists would call it, utility), including the standard gamble, the time tradeoff, and the healthy-years equivalent methods.
Medical Decision Making 10/2008; 28(5):690-8. · 2.89 Impact Factor