Competence effects for choices involving gains and losses

We investigate how choices for uncertain gain and loss prospects are affected by the decision maker’s perceived level of knowledge about the underlying domain of uncertainty. Specifically, we test whether Heath and Tversky’s (J Risk Uncertain 4:5–28, 1991) competence hypothesis extends from gains to losses. We predict that the commonly-observed preference for high knowledge over low knowledge prospects for gains reverses for losses. We employ an empirical setup in which participants make hypothetical choices between gain or loss prospects in which the outcome depends on whether a high or low knowledge event occurs. We infer decision weighting functions for high and low knowledge events from choices using a representative agent preference model. For gains, we replicate the results of Kilka and Weber (Manage Sci 47:1712–1726, 2001), finding that decision makers are more attracted to choices that they feel more knowledgeable about. However, for losses, we find limited support for our extension of the competence effect.     

How to deal with partially analyzable acts?

In some situations, a decision is best represented by an incompletely analyzed act: conditionally on a given event A, the consequences of the decision on sub-events are perfectly known and uncertainty becomes probabilizable, whereas the plausibility of this event itself remains vague and the decision outcome on the complementary event [`(A)]{\bar{A}} is imprecisely known. In this framework, we study an axiomatic decision model and prove a representation theorem. Resulting decision criteria aggregate partial evaluations consisting of (i) the conditional expected utility associated with the analyzed part of the decision, and (ii) the best and worst consequences of its non-analyzed part. The representation theorem is consistent with a wide variety of decision criteria, which allows for expressing various degrees of knowledge on (A, [`(A)]{A, \bar{A}}) and various types of attitude toward ambiguity and uncertainty. This diversity is taken into account by specific models already existing in the literature. We exploit this fact and propose some particular forms of our model incorporating these models as sub-models and moreover expressing various types of beliefs concerning the relative plausibility of the analyzed and the non-analyzed events ranging from probabilities to complete ignorance that include capacities.     

Uncertainty Aversion Vs. Competence: An Experimental Market Study

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to test for the presence of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments.      

The Likelihood Method for Decision under Uncertainty

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism.     

Recent developments in modeling preferences: Uncertainty and ambiguity

In subjective expected utility (SEU), the decision weights people attach to events are their beliefs about the likelihood of events. Much empirical evidence, inspired by Ellsberg (1961) and others, shows that people prefer to bet on events they know more about, even when their beliefs are held constant. (They are averse to ambiguity, or uncertainty about probability.) We review evidence, recent theoretical explanations, and applications of research on ambiguity and SEU.Thanks to Jonathan Baron, James Dow, Peter Fishburn, Itzhak Gilboa, Gordon Hazen, Howard Kunreuther, Tomas Phillipson, David Schmeidler, Amos Tversky, the editor, and several anonymous referees for corrections and helpful comments. Camerer's contribution to this work was supported by the National Science Foundation, grant no. SES 88-09299. Weber's contribution was supported by the Deutsche Forschungsge-meinschaft, grant no. WE 993/5-1.     

The impossibility of experimental elicitation of subjective probabilities

We show that if decision makers may have stakes in certain events then the experimental elicitation of their subjective probabilities of these events is impossible.We thank Eyal Sulganik for helpful comments on an earlier draft of this paper.     

A multiattribute decision time theory

In this study, we analyze choice in the presence of some conflict that affects the decision time (response time), a subject that has been documented in the literature. We axiomatize a multiattribute decision time (MDT) representation, which is a dynamic extension of the classic multiattribute expected utility theory that allows potentially incomplete preferences. Under this framework, one alternative is preferred to another in a certain period if and only if the weighted sum of the attribute-dependent expected utility induced by the former alternative is larger than that induced by the latter for all attribute weights in a closed and convex set. MDT uniquely determines the decision time as the earliest period at which the ranking between alternatives becomes decisive. The comparative statics result indicates that the decision time provides useful information to locate indifference curves in a specific setting. MDT also explains various empirical findings in economics and other relevant fields.     

Known, Unknown, and Unknowable Uncertainties

In normative decision theory, the weight of an uncertain event in a decision is governed solely by the probability of the event. A large body of empirical research suggests that a single notion of probability does not accurately capture peoples' reactions to uncertainty. As early as the 1920s, Knight made the distinction between cases where probabilities are known and where probabilities are unknown. We distinguish another case –- the unknowable uncertainty –- where the missing information is unavailable to all. We propose that missing information influences the attractiveness of a bet contingent upon an uncertain event, especially when the information is available to someone else. We demonstrate that the unknowable uncertainty –- falls in preference somewhere in between the known and the known uncertainty.     

Ambiguity and decision modeling: A preference-based approach

In this article, we develop a model that permits a decision maker's preferences to depend on the decision maker's ambiguity about the probability of an event that is relevant for decision-making purposes. We deal with ambiguity through preference modeling, with ambiguity leading to modifications in the utilities of outcomes. The behavior of ambiguity premiums and probability premiums as the payoffs are varied depends on the nature of the modifications in utilities. Particular forms of the model that arise under different sets of assumptions about preferences include additive, bilinear, and ratio forms. We conclude with a brief example and some thoughts about potential generalizations and implications of the model.     

Rank-dependent,subjective expected-utility representations

Gambles are recursively generated from pure payoffs, events, and other gambles, and a preference order over them is assumed. Weighted average utility representations are studied that are strictly increasing in each payoff and for which the weights depend both on the events underlying the gamble and the preference ranking over the several component payoffs. Basically two results are derived: a characterization of monotonicity in terms of the weights, and an axiomatization of the representation. The latter rests on two important conditions: a decomposition of gambles into binary ones and a necessary commutativity condition on events in a particular class of binary gambles. A number of unsolved problems are cited.     

Race, racial resentment, attentiveness to the news media, and public opinion toward the Jena Six

Objective. We outline the role of race, racial resentment, and attentiveness to news in structuring public opinion toward the prosecution of the Jena Six, the name given to six African-American high school students who beat a white student, five of whom were subsequently charged with attempted second-degree murder.Method. We rely on a telephone survey of 428 registered voters collected in the aftermath of the protests in Jena, Louisiana.Results. Public reactions were heavily filtered by race and associated with measures of racial resentment. African Americans followed news about the protests more closely, believed race was the most important consideration in the decision to prosecute, and believed the decision to prosecute was the wrong decision. Racially conservative white respondents were less likely to believe race was the most important consideration in the decision to prosecute and were more likely to believe that the decision to prosecute was the right decision. Consistent with theories of agenda setting and framing, attentiveness to the news influenced perceptions regarding the importance of race in the decision to prosecute but not whether the decision was the right decision.Conclusions. At least within the context of the Deep South, race and racial attitudes continue to be an important predictor of public reactions to racially charged events. Attentiveness to the news influenced the lens through which events were interpreted, but not perceptions of whether the outcome was the right decision.     

Are beliefs a matter of taste? A case for objective imprecise information

We argue, in the spirit of some of Jean-Yves Jaffray’s work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker’s attitude toward imprecise information.     

Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory

This paper extends de Finetti’s betting-odds method for assessing subjective beliefs to ambiguous events. Thus, a tractable manner for measuring decision weights under ambiguity is obtained. De Finetti’s method is so transparent that decision makers can evaluate the relevant tradeoffs in complex situations. The resulting data can easily be analyzed, using nonparametric techniques. Our extension is implemented in an experiment on predicting next-day’s performance of the Dow Jones and Nikkei stock indexes, where we test the existence and nature of rank dependence, finding usual patterns. We also find violations of rank dependence.

Expanding state space and extension of beliefs

This article provides a simple decision theoretic model in which elements of the world successively enter the decision maker??s scope and the state space expands over time, which is intended to be the closest correspondence to the standard subjective expected utility theory. We propose a dynamic consistency condition that after any expansion of the scope, the preference ranking should remain unchanged over acts to which the expansion is irrelevant. Together with other natural axioms, it characterizes a model in which the decision maker??s belief extends over time in order that the marginal distribution of the new belief induced over the old state space coincides with the old belief. It is extended to encompass both expansion of scope and learning events, and we characterize the model with an additional property that the decision maker??s belief updating follows Bayes?? rule when she learns events.     

The price for information about probabilities and its relation with risk and ambiguity

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker??s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.     

Subjectively weighted linear utility

An axiomatized theory of nonlinear utility and subjective probability is presented in which assessed probabilities are allowed to depend on the consequences associated with events. The representation includes the expected utility model as a special case, but can accommodate the Ellsberg paradox and other types of ambiguity sensitive behavior, while retaining familiar properties of subjective probability, such as additivity for disjoint events and multiplication of conditional probabilities. It is an extension, to the states model of decision making under uncertainty, of Chew's weighted linear utility representation for decision making under risk.     

The axioms and algebra of ambiguity

This paper continues a study of event ambiguity as a primitive concept. Axioms are described for a comparative ambiguity relation on an arbitrary event set that are necessary and sufficient for a representation of the relation by a functional that is nonnegative, vanishes at the empty event, and satisfies complementary equality and submodularity. Uniqueness characteristics of representing functionals are discussed. The theory is extended to multifactor events, where marginal ambiguity and additive representations arise.     

Representability of Ordinal Relations on a Set of Conditional Events

Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the case of binary relations representable by a coherent conditional probability.     

Resilience and Thriving: Issues, Models, and Linkages

This article addresses distinctions underlying concepts of resilience and thriving and issues in conceptualizing thriving. Thriving (physical or psychological) may reflect decreased reactivity to subsequent stressors, faster recovery from subsequent stressors, or a consistently higher level of functioning. Psychological thriving may reflect gains in skill, knowledge, confidence, or a sense of security in personal relationships. Psychological thriving resembles other instances of growth. It probably does not depend on the occurrence of a discrete traumatic event or longer term trauma, though such events may elicit it. An important question is why some people thrive, whereas others are impaired, given the same event. A potential answer rests on the idea that differences in confidence and mastery are self-perpetuating and self-intensifying. This idea suggests a number of variables whose role in thriving is worth closer study, including personality variables such as optimism, contextual variables such as social support, and situational variables such as the coping reactions elicited by the adverse event.