Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatter-expert colleagues. This paper reviews the state-of-the-art, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.

The field of modern financial economics assumes that people behave with extreme rationality, but they do not. Furthermore, people’s deviations from rationality are often systematic. Behavioral finance relaxes the traditional assumptions of financial economics by incorporating these observable, systematic, and very human departures from rationality into standard models of financial markets. We highlight two common mistakes investors make: excessive trading and the tendency to disproportionately hold on to losing investments while selling winners. We argue that these systematic biases have their origins in human psychology. The tendency for human beings to be overconfident causes the first bias in investors, and the human desire to avoid regret prompts the second. There is one important caveat to the notion that we live in a new economy, and that is human psychology... which appears essentially immutable.

We consider a panel of experts asked to assign probabilities to events, both logically simple and complex. The events evaluated by different experts are based on overlapping sets of variables but may otherwise be distinct. The union of all the judgments will likely be probabilistic incoherent. We address the problem of revising the probability estimates of the panel so as to produce a coherent set that best represents the group's expertise.

Forward-looking agents care about expected future utility flows, and hence have higher current felicity if they are optimistic. This paper studies utility-based biases in beliefs by supposing that beliefs maximize average felicity, optimally balancing this benefit of optimism against the costs of worse decision making. A small optimistic bias in beliefs typically leads to first-order gains in anticipatory utility and only second-order costs in realized outcomes. In a portfolio choice example, investors overestimate their return and exhibit a preference for skewness; in general equilibrium, investors ’ prior beliefs are endogenously heterogeneous. In a consumption-saving example, consumers are both overconfident and overoptimistic. (JEL D1, D8, E21, G11, G12) Modern psychology views human behavior as a complex interaction of cognitive and emotional responses to external stimuli that sometimes results in dysfunctional outcomes. Modern economics takes a relatively simple

Milton Friedman argued that irrational traders will consistently lose money, won’t survive and, therefore, cannot influence long run equilibrium asset prices. Since his work, survival and price influence have been assumed to be the same. Often partial equilibrium analysis has been relied upon to examine the survival of irrational traders and to make inferences on their influence on prices. In this paper, we demonstrate that survival and influence on prices are two independent concepts. The price impact of irrational traders does not rely on their long-run survival and they can have a significant impact on asset prices even when their wealth becomes negligible. In addition, in contrast to a partial equilibrium analysis, general equilibrium considerations matter since the ability of irrational traders to impact prices even when their wealth is diminishing can significantly affect their chances for long-run survival. In sum, in a long-run equilibrium, we explicitly show that price impact can occur whether or not the irrational traders survive. In related work, we show that even if the irrational

Motivated by the behavior of internet stock prices in 1998-2000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a short-sale constraint, an asset owner has an option to sell the asset to other agents when they have more optimistic beliefs. This re-sale option has a recursive structure, that is a buyer of the asset gets the option to resell it, causing a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. The model generates prices that are above fundamentals, excessive trading, and excess volatility. We also give an example where the price of a subsidiary is larger than its parent firm. Our analysis shows that while Tobin's tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility.

∗This paper is an updated version of a previous working paper, “The Positive Role of Overconfidence and

Journal of Behavioral Decision Making, Vol. 10, 21±32 (1997) Whereas probabilistic calibration has been a central normative concept of accuracy in previous research on interval estimates, we suggest here that normative approaches for the evaluation of judgmental estimates should consider the communicative interaction between the individuals who produce the judgments and those who receive or use them for making decisions. We analyze precision and error in judgment and consider the role of the accuracy±informativeness trade-o€ (Yaniv and Foster, 1995) in the communication of estimates. The results shed light on puzzling ®ndings reported earlier in the literature concerning the calibration of subjective con®dence intervals. *c 1997 by John Wiley & Sons, Ltd. KEY WORDS judgmental estimation; subjective con®dence interval; graininess of judgment; accuracy-informativeness trade-o€ In the process of making our daily decisions, we commonly solicit from judges estimates and forecasts of uncertain quantities. For instance, estimates of the amount of driving are relevant for planning a

The behavioral revolution in economics tells us that human beings often have a difficult time making wise choices. The most widely chronicled difficulties occur in conjunction with decisions made under conditions of uncertainty, decisions that involve significant elements of time, and decisions in complex environments. Unfortunately,

People often have knowledge about the chances of events but are unable to express their knowledge in the form of coherent probabilities. This study proposed to correct incoherent judgment via an optimization procedure that seeks the (coherent) probability distribution nearest to a judge's estimates of chance. This method was applied to the chances of simple and complex meteorological events, as estimated by college undergraduates. No judge responded coherently, but the optimization method found close (coherent) approximations to their estimates. Moreover, the approximations were reliably more accurate than the original estimates, as measured by the quadratic scoring rule. Methods for correcting incoherence facilitate the analysis of expected utility and allow human judgment to be more easily exploited in the construction of expert systems. Suppose you think the probability that the Internet will expand next year is.90. Suppose you also think the probability that the Internet will expand and PC makers will be profitable is.91. Then you have assigned a greater chance to a conjunction rather than to one of its conjuncts; hence, your judgments are incoherent. You may, nonetheless, prove to be more insightful than someone with