Stochastic Dominance and Prospect Dominance with Subjective Weighting Functions

Laboratory experiments with and without real money repeatedly reveal that even if all subjects observe the same pair of cumulative distributions F and G, they act as if they were other cumulative probability functions F* and G* different for different investors. Namely, the subjects assign (subjective) weights to the various probabilities. In their breakthrough article Kahneman and Tversky [1979] suggest that in making decisions under uncertainty, the subjects apply a monotonic transformation (p) where p are the probabilities, and investors make decisions by comparing (p) corresponding to the two distributions under consideration rather than by comparing the true probabilities, p, themselves.     

Individual behavior under risk and under uncertainty: An experimental study

These experiments are concerned with individual behavior under risk and under uncertainty. By exploiting the isolation effect the experiments were able to offer to 134 subjects the possibility of actually gaining or losing an important sum of money.The experimental data show that under risk as well as under complete ignorance the subjects' attitudes towards prospects of gains and towards prospects of losses are totally unrelated.The data also show that when facing prospects of gains, the subjects generally take the exact probabilities of the events into account, whereas, when facing prospects of losses many of then have only recourse to coarser categories of plausibility, or even no longer use their information at all.     

Risk,uncertainty and hidden information

People are less willing to accept bets about an event when they do not know the true probability of that event. Such uncertainty aversion has been used to explain certain economic phenomena. This paper considers how far standard private information explanations (with strategic decisions to accept bets) can go in explaining phenomena attributed to uncertainty aversion. This paper shows that if two individuals have different prior beliefs about some event, and two sided private information, then each individuals willingness to bet will exhibit a bid ask spread property. Each individual is prepared to bet for the event, at sufficiently favorable odds, and against, at sufficiently favorable odds, but there is an intermediate range of odds where each individual is not prepared to bet either way. This is only true if signals are distributed continuously and sufficiently smoothly. It is not true, for example, in a finite signal model.     

Risky investment decisions: How are individuals influenced by their groups?

We investigate the effect of group versus individual decision-making in the context of risky investment decisions in which all subjects are fully informed of the probabilities and payoffs. Although there is full information, the lottery choices pose cognitive challenges so that people may not be sure of their expected utility-maximizing choice. Making such decisions in a group context provides real-time information in which group members can observe others’ choices and revise their own decisions. Our experimental results show that simply observing what others in the group do has a significant impact on behavior. Coupling real-time information with group decisions based on the median value, i.e., majority rule, makes the median investment choice focal, leading people with low values to increase investments and those with high values to decrease investments. Group decisions based on the minimum investment amount produce more asymmetric effects.     

Experimental evidence on the irreversebility effect

This paper presents the results of an experimental investigation on how increased expected information affects subjects' choices. We show that Claude Henry's (1974) result (the Irreversibility Effect) is strongly supported by our experimental data. According to the Irreversibility Effect a rational (expected utility maximizing) agent who anticipates more information before making his future choices, will take a less irreversible position today. In our experiment, present and future choices are framed respectively as portfolio and investment decisions. The degree of irreversibility (or flexibility) chosen by experimental subjects in response to additional information indicated that subjects react to anticipated information as predicted by theory.     

Equivalent decision trees and their associated strategy sets

The purpose of this paper is to examine the structure of individual decisions under uncertainty in extensive (i.e., decision-tree) form at a sufficient level of generality to encompass many traditional as well as novel criteria of general choice under uncertainty. Considerations both of structure and of strategic effect arise. In § 2 we define weak and strong forms of strategic equivalence of decision trees and describe partial-normalization procedures by which all economically defined complete pure strategies may be identified for the decider and for chance. In § 3 we examine characteristics of locally randomized, behavior strategies for the decider as the degree of normalization is varied, and we deduce useful properties of the function which specifies an outcome lottery for each behavior strategy of the decider in conjuction with a deterministic or stochastic selection by Chance. In § 4 we list a wide variety of choice criteria which may be invoked within the framework developed here.     

Evaluating second-order probability judgments with strictly proper scoring rules

Empirical studies have demonstrated that uncertainty about event probabilities, also known as ambiguity or second-order uncertainty, can affect decision makers choice preferences. Despite the importance of second-order uncertainty in decision making, almost no effort has been directed towards the development of methods that evaluate the accuracy of second-order probabilities. In this paper, we describe conditions under which strictly proper scoring rules can be used to assess the accuracy of second-order probability judgments. We investigate the effectiveness of using a particular strictly proper scoring rule the ranked probability score - to discourage biased assessments of second-order uncertainty.     

The relationship between individual expectations and behaviors: Mortality expectations and smoking decisions

Using data from the Health and Retirement Study, we assess the accuracy of subjective beliefs about mortality and objectively estimated probabilities for individuals in the same sample. Overall, subjective beliefs and objective probabilities are very close. However, there are differences conditional on behaviors, with current smokers being relatively optimistic and never smokers relatively pessimistic in their assessments. In the aggregate, individuals accurately predict longevity, but at the individual level, subjective beliefs provide information in addition to the estimated objective probabilities in predicting actual events, which may arise from the effect of past or anticipated decisions on these beliefs.

Does television terrify tourists? Effects of US television news on demand for tourism in Israel

We analyze the impact on US tourist flows to Israel of variations in both the actual intensity of the Israeli-Palestinian conflict and the intensity implicit in US television news coverage. Conditional on actual events, changes in reported conflict intensity could influence tourists because alternative sources of information are costly; this explanation is consistent with a rational choice model. However, television news could influence tourist behavior because of its emotional impact, or because it causes the conflict to be brought to mind more readily, increasing the subjective probability of conflict events. We find that tourists respond to variations in actual Israeli casualties and reported Palestinian casualties; both effects are large. Reports of Israeli casualties and unreported Palestinian casualties have no significant impact on tourist flows. These asymmetries are consistent with asymmetric information costs within a rational choice framework, but are more difficult to square with the alternative explanations for media influence.

The influence of fear in decisions: Experimental evidence

This article studies decisions made under conditions of fear, when a catastrophic outcome is introduced in a lottery. It reports on experimental results and seeks to compare the predictions of the expected utility (EU) framework with those of a new axiomatic treatment of choice under uncertainty that takes explicit account of emotions such as fear (Chichilnisky 1996, 2000, 2002, 2009). Results provide evidence that fear influences the cognitive process of decision-making by leading some subjects to focus excessively on catastrophic events. Such heterogeneity in subjects’ behavior, while not consistent with EU-based functions, is fully consistent with the new type of utility function implied by the new axioms.     

Coherent decision analysis with inseparable probabilities and utilities

This article explores the extent to which a decision maker's probabilities can be measured separately from his/her utilities by observing his/her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partitioned into a set of belief gambles, which reveals probabilities distorted by marginal utilities for money, and a set of preference gambles, which reveals utilities reciprocally distorted by marginal utilities for money. However, the information in these gambles still enables us to solve the decision maker's problem: his/her utility-maximizing decision is the one that avoids arbitrage (i.e., incoherence or Dutch books).     

Uncertainty,information and resolution of medical malpractice disputes

This study assesses the role of defendant liability in determining whether the plaintiff receives payment, relationship of compensation to economic loss, and stage of dispute resolution. An options pricing model explains how information acquired affects both decisions to drop or continue and settlement values, as well as the role of pecuniary motives for claiming. Cases in which a panel of physician evaluators thought defendant(s) to be innocent were much more likely to be dropped, as were cases in which innocence became more apparent as the case developed. Compensation was much less than economic loss on average. Questionable defendant liability meant reduced compensation.The research was supported in part by a grant from The Robert Wood Johnson Foundation entitled, Resolution of Malpractice Claims: Birth- and Emergency Room-Related Injuries (Grant No. 14045). We thank Mingliang Zhang, Lars Runquist, and Stephen van Wert for research assistance.     

Deriving Harsanyi’s Utilitarianism from De Finetti’s Book-Making Argument

The book-making argument was introduced by de Finetti as a principle to prove the existence and uniqueness of subjective probabilities. It has subsequently been accepted as a principle of rationality for decisions under uncertainty. This note shows that the book-making argument has relevant applications to welfare: it gives a new foundation for utilitarianism that is alternative to Harsanyi’s, it generalizes foundations based on the theorem of the alternative, and it avoids arguments based on expected utility.     

Insurance with undiversifiable risk: Contract structure and organizational form of insurance firms

Previous explanations of the contract choice and organizational form of insurance firms do not explain, by themselves, the recent proliferation of mutuals and new contract designs. We first present risk-bearing arguments to address these phenomena. We present two forms of insurance. The first is a conventional transfer of risk whereas the second decomposes risk between idiosyncratic and nonidiosyncratic. We show that the latter form leads to more active trade in insurance markets with correlated exposures. Moreover, the decomposed form dominates the simple transfer. These results qualify and extend the work of Borch (1962) and Marshall (1974). Market responses to the recent liability insurance crisis are compatible with these predictions.This research was conducted while G. Dionne was visiting the University of Pennsylvania under grants from Huebner Foundation and CRSH Canada. N. Doherty wishes to acknowledge with thanks support from the National Science Foundation under grant #88-09299. We wish to thank Patricia Danzon, Beverly Dahlby, Claude Fluet, James Garven, Scott Harrington, Howard Kunreuther, Clifford Smith Jr., George Theall, Kip Viscusi, and a referee for helpful comments.     

Subjective Probability Weighting and the Discovered Preference Hypothesis

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. I thank Peter P. Wakker for useful comments and suggestions.     

The impact of risk attitude,uncertainty and disequilibria on optimal production and inventory

Summary The empirical facts seem to indicate that in real economies the effect of uncertainty tends to decrease production. The limitations of empirical investigations presented should be stressed: they were performed mainly on an aggregate level, they mainly refer to Austrian manufacturing, they rely heavily on questionnaires. Above all empirical investigation will never be able to decide normative questions or to explain the behavior in the general equilibrium. Nevertheless in the short run, given all the rigidities and disequilibria which exist, uncertainty tends to lower optimal production even in absence of risk aversion. Risk aversion becomes important for large, for once-for-all decisions, but it is not the only channel through which uncertainty changes decisions.Technological concavity created by concave marginal revenues or by convex marginal costs, marginal costs of uncertainty in disequilibria model or asymmetric costs of revisions of the preliminary decision are able to bias the decision downward in a real world economy without invokingPaper presented to the 2nd Conference on the Foundations of Risk and Utility (FUR), Venezia, 1984.     

Decomposing Hindsight Bias

Traditional accounts of hindsight bias inadequately distinguish primary hindsight bias from both secondary and tertiary hindsight bias. A subject exhibits primary bias when she assigns a higher ex ante probability estimate to actual outcomes, secondary bias when she believes that she herself would have made the same estimate of the prior probability of an event before receiving outcome information as she made after receiving it, and tertiary bias when she believes that third parties lacking outcome information were unreasonable if they did not make the same prior probability judgments that subjects now possessing such information make.In our experiments, we find that when people can readily calculate the actual ex ante probability of an outcome, they don't reassess that probability when told what outcomes actually occurred. They reassess only in situations in which they are unable to assess prior probabilities or when given information that the outcome was not simply a result of sampling or chance but the result of an imperceptible feature of the initial situation. Observed primary bias may therefore often be rational.     

Subjects' Access to Cognitive Processes: Demand Characteristics and Verbal Report

The present paper examines the arguments and data presented by Nisbett and Wilson (1977a; 1977b; Wilson & Nisbett, 1978) relevant to their thesis that subjects do not have access to their own cognitive processes. It is concluded that their review of previous research is selective and incomplete and that the data they present in behalf of their thesis does not withstand a demand characteristics analysis. Furthermore, their use of observer-subject similarity as evidence of subjects' inability to access cognitive processes makes tests of their hypothesis confounded and, at the same time, reveals limitations in the application of the pre-inquiry quasi-control to research on social behavior. Problems with postexperiment questionnaires, such as the demand characteristics of the inquiry procedure are also considered. Although there are difficulties in assessing subjects' cognitive processes, many of these may be overcome through the application of novel techniques and research conducted on more traditional methods. In contrast to the view that subjects have limited access to cognitive processes and that their verbal reports are not valid, it is concluded that subjects' verbalizations are a rich source of psychological data which must be pursued if we are to tap their cognitive processes and are to gain an adequate understanding of human behavior.     

One-reason decision-making: Modeling violations of expected utility theory

People violate expected utility theory and this has been traditionally modeled by augmenting its weight-and-add framework by nonlinear transformations of values and probabilities. Yet individuals often use one-reason decision-making when making court decisions or choosing cellular phones, and institutions do the same when creating rules for traffic safety or fair play in sports. We analyze a model of one-reason decision-making, the priority heuristic, and show that it simultaneously implies common consequence effects, common ratio effects, reflection effects, and the fourfold pattern of risk attitude. The preferences represented by the priority heuristic satisfy some standard axioms. This work may provide the basis for a new look at bounded rationality.