Craig R. Fox

Ambiguity Aversion and Comparative Ignorance

Decisions under uncertainty depend not only on the degree of uncertainty but also on its source, as illustrated by Ellsbergs observation of ambiguity aversion. In this article we propose the comparative ignorance hypothesis, according to which ambiguity aversion is produced by a comparison with less ambiguous events or with more knowledgeable individuals. This hypothesis is supported in a series of studies showing that ambiguity aversion, present in a comparative context in which a person evaluates both clear and vague prospects, seems to disappear in a noncomparative context in which a person evaluates only one of these prospects in isolation.

Weighing risk and uncertainty

Decision theory distinguishes between risky prospects, where the probabilities associated with the possible outcomes are assumed to be known, and uncertain prospects, where these probabilities are not assumed to be known. Studies of choice between risky prospects have suggested a nonlinear transformation of the probability scale that overweights low probabilities and underweights moderate and high probabilities. The present article extends this notion from risk to uncertainty by invoking the principle of bounded subadditivity: An event has greater impact when it turns impossibility into possibility, or possibility into certainty, than when it merely makes a possibility more or less likely. A series of studies provides support for this principle in decision under both risk and uncertainty and shows that people are less sensitive to uncertainty than to risk. Finally, the article discusses the relationship between probability judgments and decision weights and distinguishes relative sensitivity from ambiguity aversion. Decisions are generally made without definite knowledge of their consequences. The decisions to invest in the stock market, to undergo a medical operation, or to go to court are generally made without knowing in advance whether the market will go up, the operation will be successful, or the court will decide in ones favor. Decision under uncertainty, therefore, calls for an evaluation of two attributes: the desirability of possible outcomes and their likelihood of occurrence. Indeed, much of the study of decision making is concerned with the assessment of these values and the manner in which they are—or should be— combined. In the classical theory of decision under risk, the utility of each outcome is weighted by its probability of occurrence. Consider a simple prospect of the form (x, p) that offers a probability p to win

Mind the gap: bridging economic and naturalistic risk-taking with cognitive neuroscience

jc and a probability 1 — p to win nothing. The expected utility of this prospect is given by pu(x) + (1 — p)w(O), where u is the utility function for money. Expected utility theory has been developed to explain attitudes toward risk, namely, risk aversion and risk seeking. Risk aversion is denned as a preference for a sure outcome over a prospect with an equal or greater expected value. Thus, choosing a sure

Options traders exhibit subadditive decision weights

100 over an even chance to win

Partition Priming in Judgment Under Uncertainty

200 or nothing is an expression of risk aversion. Risk seeking is exhibited if a prospect is preferred to a sure outcome with equal or greater expected value. It is commonly assumed that people are risk averse, which is explained in expected utility theory by a concave utility function. The experimental study of decision under risk has shown that people often violate both the expected utility model and the

Political Extremism Is Supported by an Illusion of Understanding

Economists define risk in terms of the variability of possible outcomes, whereas clinicians and laypeople generally view risk as exposure to possible loss or harm. Neuroeconomic studies using relatively simple behavioral tasks have identified a network of brain regions that respond to economic risk, but these studies have had limited success predicting naturalistic risk-taking. By contrast, more complex behavioral tasks developed by clinicians (e.g. Balloon Analogue Risk Task and Iowa Gambling Task) correlate with naturalistic risk-taking but resist decomposition into distinct cognitive constructs. We propose here that to bridge this gap and better understand neural substrates of naturalistic risk-taking, new tasks are needed that: are decomposable into basic cognitive and/or economic constructs; predict naturalistic risk-taking; and engender dynamic, affective engagement.

Chapter 11 – Prospect Theory and the Brain

Professional options traders priced risky prospects as well as uncertain prospects whose outcomes depended on future values of various stocks. The prices of the risky prospects coincided with their expected value, but the prices of the uncertain prospects violated expected utility theory. An event had greater impact on prices when it turned an impossibility into a possibility or a possibility into a certainty than when it merely made a possibility more or less likely, as predicted by prospect theory. This phenomenon is attributed to the subadditivity of judged probabilities.

Typical Versus Atypical Unpacking and Superadditive Probability Judgment

We show that likelihood judgments are biased toward an ignorance-prior probability that assigns equal credence to each mutually exclusive event considered by the judge. The value of the ignorance prior depends crucially on how the set of possibilities (i.e., the state space) is subjectively partitioned by the judge. For instance, asking “what is the probability that Sunday will be hotter than any other day next week?” facilitates a two-fold case partition, (Sunday hotter, Sunday not hotter), thus priming an ignorance prior of 1/2. In contrast, asking “what is the probability that the hottest day of the week will be Sunday?” facilitates a seven-fold class partition, (Sunday hottest, Monday hottest, etc.), priming an ignorance prior of 1/7. In four studies, we observed systematic partition dependence: Judgments made by participants presented with either case or class formulations of the same query were biased toward the corresponding ignorance prior.

Subjective Knowledge in Consumer Financial Decisions

People often hold extreme political attitudes about complex policies. We hypothesized that people typically know less about such policies than they think they do (the illusion of explanatory depth) and that polarized attitudes are enabled by simplistic causal models. Asking people to explain policies in detail both undermined the illusion of explanatory depth and led to attitudes that were more moderate (Experiments 1 and 2). Although these effects occurred when people were asked to generate a mechanistic explanation, they did not occur when people were instead asked to enumerate reasons for their policy preferences (Experiment 2). Finally, generating mechanistic explanations reduced donations to relevant political advocacy groups (Experiment 3). The evidence suggests that people’s mistaken sense that they understand the causal processes underlying policies contributes to political polarization.

Decreasing ventromedial prefrontal cortex activity during sequential risk-taking: an FMRI investigation of the balloon analog risk task.

Publisher Summary This chapter highlights the behavioral and neuroscience work on the prospect theory and the neuroscience of behavioral decision-making. Several applications of prospect theory from neuroeconomics to decision analysis to behavioral finance require individual assessment of value and weighting functions. In order to measure the shape of the value and weighting functions exhibited by participants in the laboratory, one must first discuss how these functions can be formally modeled. The field of neuroeconomics is providing a rapidly increasing amount of data regarding the phenomena that lie at the heart of prospect theory, such as framing effects and loss aversion. It is clear that the demonstrations of neural correlates of several of the fundamental behavioral phenomena underlying prospect theory (loss aversion, framing effects, and probability weighting distortions) provide strong evidence to even the most entrenched rational choice theorists that these anomalies are real. The data have also started to provide more direct evidence regarding specific claims of the theory.