Decision making in a case of mixed uncertainty: A normative model

We consider a case of uncertainty which is frequently met in various fields, e.g., in parametric statistics: Events {θ}, θ ∈ ∵, are members of family $\text{E}$ on which the decision maker possesses no information at all; however, conditionally on the realization of {θ}, he is able to affix probabilities to all members of another family of events, $\text{F}$. We assume that the decision maker: (1) has a rational behavior under complete ignorance, for decisions whose results only depend on events of $\text{E}$; (2) with {θ} known, maximizes his conditional expected utility for decisions whose results only depend on events of $\text{F}$; (3) has (unconditional) preferences which are consistent with his conditional ones. These assumptions are shown to be sufficient to ensure an approximate representation of the decision maker's preference by a real-valued function W which has the form $\text{W(f) = v[}\text{Inf}{}_{\mathrm{\theta \in \because }}\text{E}{}_{\mathrm{\theta }}\text{(u°f),}\text{Sup}{}_{\mathrm{\theta \in \because }}\text{E}{}_{\mathrm{\theta }}\text{(u°f)]}$, where u and v, respectively, characterize the decision maker's attitudes toward risk and toward complete ignorance.     

Decision making under internal uncertainty: the case of multiple-choice tests with different scoring rules

This paper assesses framing effects on decision making with internal uncertainty, i.e., partial knowledge, by focusing on examinees' behavior in multiple-choice (MC) tests with different scoring rules. In two experiments participants answered a general-knowledge MC test that consisted of 34 solvable and 6 unsolvable items. Experiment 1 studied two scoring rules involving Positive (only gains) and Negative (only losses) scores. Although answering all items was the dominating strategy for both rules, the results revealed a greater tendency to answer under the Negative scoring rule. These results are in line with the predictions derived from Prospect Theory (PT) [Econometrica 47 (1979) 263]. The second experiment studied two scoring rules, which allowed respondents to exhibit partial knowledge. Under the Inclusion-scoring rule the respondents mark all answers that could be correct, and under the Exclusion-scoring rule they exclude all answers that might be incorrect. As predicted by PT, respondents took more risks under the Inclusion rule than under the Exclusion rule. The results illustrate that the basic process that underlies choice behavior under internal uncertainty and especially the effect of framing is similar to the process of choice under external uncertainty and can be described quite accurately by PT.     

Decision making under time pressure: An independent test of sequential sampling models

Choice probability and choice response time data from a risk-taking decision-making task were compared with predictions made by a sequential sampling model. The behavioral data, consistent with the model, showed that participants were less likely to take an action as risk levels increased, and that time pressure did not have a uniform effect on choice probability. Under time pressure, participants were more conservative at the lower risk levels but were more prone to take risks at the higher levels of risk. This crossover interaction reflected a reduction of the threshold within a single decision strategy rather than a switching of decision strategies. Response time data, as predicted by the model, showed that participants took more time to make decisions at the moderate risk levels and that time pressure reduced response time across all risk levels, but particularly at the those risk levels that took longer time with no pressure. Finally, response time data were used to rule out the hypothesis that time pressure effects could be explained by a fast-guess strategy.     

Decision making under conflict: Decision time as a measure of conflict strength

Conflict and choice are closely related in that choice produces conflict and conflict is resolved by making a choice. Although conflict was invoked in psychological approaches to decision making early on (Lewin, 1931/1964), no generally accepted measure of conflict strength has been established (Tversky & Shafir, 1992). The present study introduces a model (multiattribute decision field theory) that predicts a decision time pattern depending on the conflict situation. In a risky decision-making experiment with multiattribute choice alternatives, decision time is investigated as a possible measure of conflict strength. It is shown that the model can be fitted to a complex choice pattern.     

Decision making under time pressure, modeled in a prospect theory framework

The current research examines the effects of time pressure on decision behavior based on a prospect theory framework. In Experiments 1 and 2, participants estimated certainty equivalents for binary gains-only bets in the presence or absence of time pressure. In Experiment 3, participants assessed comparable bets that were framed as losses. Data were modeled to establish psychological mechanisms underlying decision behavior. In Experiments 1 and 2, time pressure led to increased risk attractiveness, but no significant differences emerged in either probability discriminability or outcome utility. In Experiment 3, time pressure reduced probability discriminability, which was coupled with severe risk-seeking behavior for both conditions in the domain of losses. No significant effects of control over outcomes were observed. Results provide qualified support for theories that suggest increased risk-seeking for gains under time pressure.     

Decision making under stress: scanning of alternatives under controllable and uncontrollable threats

This study tested the proposition that deficient decision making under stress is due, to a significant extent, to the individual's failure to fulfill adequately an elementary requirement of the decision-making process, that is, the systematic consideration of all relevant alternatives. One hundred one undergraduate students (59 women and 42 men), aged 20-40, served as subjects in this experiment. They were requested to solve decision problems, using an interactive computer paradigm, while being exposed to controllable stress, uncontrollable stress, or no stress at all. There was no time constraint for the performance of the task. The controllability of the stressor was found to have no effect on the participants' performance. However, those who were exposed to either controllable or uncontrollable stress showed a significantly stronger tendency to offer solutions before all available alternatives had been considered and to scan their alternatives in a nonsystematic fashion than did participants who were not exposed to stress. In addition, patterns of alternative scanning were found to be correlated with the correctness of solutions to decision problems.     

Decision biases in intertemporal choice and choice under uncertainty: Testing a common account

Two experiments were performed to test a psychophysical account of parallels between biases in risky choice and intertemporal choice. Experiment 1 demonstrated the common difference effect in intertemporal choice and the common ratio effect in risky choice. As was predicted, these two biases were uncorrelated with each other, although each was correlated across monetary/health domains. This result is consistent with the supposition that these two biases result from psychophysical properties of two different dimensions (time and probability, respectively). Experiment 2 examined the magnitude effect in intertemporal choice and the peanuts effect in risky choice. These two biases were correlated with each other but were uncorrelated across monetary/health domains. This result is consistent with the supposition that these two biases result from psychophysical properties of the same dimension (utility of money or health).     

Simplified approaches for multicriteria decision making under uncertainty

The problem of uncertainty in the outcome of decisions has tended to be glossed over by many MCDM methods, with the exception of multiattribute utility theory (MAUT). MAUT does, however, require quite complicated preference elicitations and knowledge of the full multivariate distribution of outcomes. Results from a series of simulation studies indicate that the preference orderings of MAUT are only minimally changed when using a simple additive aggregation of marginal utilities, especially in relation to the natural imprecisions inherent in preference elicitation. It is shown in the simulations that by far the most critical aspect of multicriteria decision analysis under uncertainty is not the form of aggregation, but the correct elicitation of marginal utilities which properly represent decision maker preferences over gambles. We relate the results obtained here to other results on the approximation of distributions by three- or five-point discrete distributions, and suggest that the use of deterministic MCDM methods of any form (not necessarily value function techniques), applied to an extended formulation in which each criterion measure is repeated for three or five ‘scenarios’, can be justified.     

Decision making and free will: a neuroscience perspective

A thorough analysis of the question of whether we possess "free will" requires that we take into account the process of exercising that will: that is, the neural mechanisms of decision making. Much of what we know about these mechanisms indicates that decision making is greatly influenced by implicit processes that may not even reach consciousness. Moreover, there exist conditions, for example certain types of brain injury or drug addiction, in which an individual can be said to have a disorder of the will. Examples such as these demonstrate that the idea of freedom of will on which our legal system is based is not supported by the neuroscience of decision making. Using the criminal law as an example, we discuss how new discoveries in neuroscience can serve as a tool for reprioritizing our society's legal intuitions in a way that leads us to a more effective and humane system.     

Empirical comparison of Markov and quantum models of decision making

There are at least two general theories for building probabilistic-dynamical systems: one is Markov theory and another is quantum theory. These two mathematical frameworks share many fundamental ideas, but they also differ in some key properties. On the one hand, Markov theory obeys the law of total probability, but quantum theory does not; on the other hand, quantum theory obeys the doubly stochastic law, but Markov theory does not. Therefore, the decision about whether to use a Markov or a quantum system depends on which of these laws are empirically obeyed in an application. This article derives two general methods for testing these theories that are parameter free, and presents a new experimental test. The article concludes with a review of experimental findings from cognitive psychology that evaluate these two properties.     

Hierarchical models of simple mechanisms underlying confidence in decision making

Choice confidence is a central measure in psychological decision research, often being reported on a probabilistic scale. Simple mechanisms that describe the psychological processes underlying choice confidence, including those based on error and confirmation biases, have typically received support via fits to data averaged over subjects. While averaged data ease model development, they can also destroy important aspects of the confidence data distribution. In this paper, we develop a hierarchical model of raw confidence judgments using the beta distribution, and we implement two simple confidence mechanisms within it. We use Bayesian methods to fit the hierarchical model to data from a two-alternative confidence experiment, and we use a variety of Bayesian tools to diagnose shortcomings of the simple mechanisms that are overlooked when applied to averaged data. Bugs code for estimating the models is also supplied.     

Decision making under risk condition in patients with Parkinson's disease: a behavioural and fMRI study

We aimed to study whether previously described impairment in decision making under risky conditions in patients with Parkinson's disease (PD) is affected by deficits in using information about potential incentives or by processing feedback (in terms of fictitious gains and losses following each decision). Additionally, we studied whether the neural correlates of using explicit information in decision making under risk differ between PD patients and healthy subjects. We investigated ten cognitively intact PD patients and twelve healthy subjects with the Game of Dice Task (GDT) to assess risky decision making, and with an fMRI paradigm to analyse the neural correlates of information integration in the deliberative decision phase. Behaviourally, PD patients showed selective impairment in the GDT but not on the fMRI task that did not include a feedback component. Healthy subjects exhibited lateral prefrontal, anterior cingulate and parietal activations when integrating decision-relevant information. Despite similar behavioural patterns on the fMRI task, patients exhibited reduced parietal activation. Behavioural results suggest that PD patients' deficits in risky decision making are dominated by impaired feedback utilization not compensable by intact cognitive functions. Our fMRI results suggest similarities but also differences in neural correlates when using explicit information for the decision process, potentially indicating different strategy application even if the interfering feedback component is excluded.     

Decision making, impulsivity and time perception

Time is an important dimension when individuals make decisions. Specifically, the time until a beneficial outcome can be received is viewed as a cost and is weighed against the benefits of the outcome. We propose that impulsive individuals experience time differently, that is with a higher cost. Impulsive subjects, therefore, overestimate the duration of time intervals and, as a consequence, discount the value of delayed rewards more strongly than do self-controlled individuals. The literature on time perception and impulsivity, however, is not clear cut and needs a better theoretical foundation. Here, we develop the theoretical background on concepts of time perception, which could lead to an empirically based notion of the association between an altered sense of time and impulsivity.     

A comparison of three simple test theory models

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of minimal models available to test analysts.This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.     

Corporate foreign exchange risk management: A study in decision making under uncertainty

This paper examines the management of foreign exchange risk in multinational corporations in light of the conclusions of previous empirical and theoretical investigations into decision making under uncertainty. Cognitive perceptions of risk and uncertainty are shown to underlie the hedging decisions made by corporate treasury managers, which are often demonstrably sub-optimal in a Bayesian expected utility framework. The findings suggest that simple principal-agent approaches to explaining seemingly sub-optimal corporate risk management preferences are inadequate inasmuch as they fail to account for the markedly different perspectives on risk and uncertainty taken by financial economists (qua economists) and corporate financial risk managers.     

Decision making and neuropsychiatry

Abnormal decision making is a central feature of neuropsychiatric disorders. Recent investigations of the neural substrates underlying decision making have involved qualitative assessment of the cognition of decision making in clinical lesion studies (in patients with frontal lobe dementia) and neuropsychiatric disorders such as mania, substance abuse and personality disorders. A neural network involving the orbitofrontal cortex, ventral striatum and modulatory ascending neurotransmitter systems has been identified as having a fundamental role in decision making and in the neural basis of neuropsychiatric diseases. This network accounts for the dissociations among decision-making deficits in different clinical populations. Ultimately, a more refined and sophisticated characterization of such deficits might guide the early diagnosis and cognitive and therapeutic rehabilitation of these patients.     

Pragmatic approach to decision making under uncertainty: The case of the disjunction effect

The disjunction effect (Tversky & Shafir, 1992 Tversky, A. and Shafir, E. 1992. The disjunction effect in choice under uncertainty. Psychological Science, 3: 305–309. [Crossref], [Web of Science ®] , [Google Scholar]) occurs when decision makers prefer option x (versus y) when knowing that event A occurs and also when knowing that event A does not occur, but they refuse x (or prefer y) when not knowing whether or not A occurs. This form of incoherence violates Savage's (1954 Savage, L. J. 1954. The foundations of statistics, New York: Wiley.  [Google Scholar]) sure-thing principle, one of the basic axioms of the rational theory of decision making. The phenomenon was attributed to a lack of clear reasons for accepting an option (x) when subjects are under uncertainty. Through a pragmatic analysis of the task and a consequent reformulation of it, we show that the effect does not depend on the presence of uncertainty, but on the introduction of non-relevant goals into the text problem, in both the well-known Gamble problem and the Hawaii problem.     

Dynamic decision making: a comparison of approaches

This paper is concerned with a specific type of problem, namely dynamic decisions, for which most techniques fail to provide adequate solutions. Here, we present two of the most promising optimization techniques, partially observable Markov decision processes (POMDP) and dynamic decision networks (DDN), while arguing which is the most suitable for this problem domain. Copyright © 2000 John Wiley & Sons, Ltd.     

The effects of trial repetition and individual characteristics on decision making under uncertainty

The authors examined participants' preferences between certain and uncertain outcomes in a multistage gambling task and the effects of individual difference characteristics on those preferences. In Study 1, 144 participants made choices in single-stage gambles under gain and loss conditions and replicated the certainty effect in a previous study (D. Kahneman & A. Tversky, 1979). In Study 2, 94 participants engaged in a multistage gambling task using the same decision problems as those in Study 1. They also answered a questionnaire consisting of the Japanese version (M. Kamahara, K. Higuchi, & N. Shimizu, 2001) of the Locus of Control Scale (J. B. Rotter, 1966), the Reflection-Impulsivity Scale (K. Takigiku & A. Sakamoto, 2001), and a Japanese version (M. Terasaki, K. Shiomi, Y. Kishimoto, & K. Hiraoka, 1987) of the Sensation-Seeking Scale (M. Zuckerman, 1994). The results indicated that the certainty effect (Kahneman & Tversky) disappears in multistage gambling tasks and that differences in reflection-impulsivity and in gender influence the process of decision making under gain conditions. These results are discussed in terms of the decision strategies and cognitive biases involved in the multistage gambling task.     

Magnitude comparison revisited: An alternative approach to binary choice under uncertainty

Two generations of psychologists have been interested in understanding binary choice under uncertainty. In the 1970s and 1980s, researchers assumed that people rely on a two-stage magnitude comparison process to make these decisions (Banks, 1977; Moyer & Dumais, 1978). More recently, the focus has shifted to approaches that rely on probabilistic cues and simple heuristics (Gigerenzer & Goldstein, Psychological Review 103, 650-669, 1996). Here, we test competing predictions derived from these two very different approaches and conclude that the magnitude comparison process plays a central role in this task. In support of this conclusion, we present an experiment in which participants were timed as they decided which of two vehicles was more expensive. Pairs composed of one luxury vehicle (e.g., BMW 323i) and one nonluxury vehicle (e.g., Toyota 4Runner) were critical because the magnitude comparison approach correctly predicted that reaction times would decrease with subjective distance, whereas the heuristics approach incorrectly predicted that there would be no relation.