Coherent choice functions under uncertainty

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility.     

The effects of statistical training on choice heuristics in choice under uncertainty

Kahneman and Tversky (1984) proposed that decision makers perceive choice uncertainty in two ways: (1) as a distribution of possible outcomes or (2) as a single uncertain outcome. Using statistical training as a factor that influences these perceptions, and thus the type of decision approach individuals use, we found that individuals with different levels of experience displayed differences in the decisions they made and in the choice heuristics used to make those decisions. Statistically naive individuals were more likely to prefer loss-minimizing alternatives, use a more non-compensatory heuristic, and spend more time on loss-related information than their statistically experienced counterparts. When a distributional cue, indicating the distributional nature of choice outcomes, was presented to both experience groups, the naive group was found to use a decision approach similar to the experienced group and to make similar decisions. The results are discussed in terms of the need to include factors that alter individuals' approaches to uncertainty in future behavioral models of uncertain choice.     

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).     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

Of matchers and maximizers: How competition shapes choice under risk and uncertainty

In a world of limited resources, scarcity and rivalry are central challenges for decision makers—animals foraging for food, corporations seeking maximal profits, and athletes training to win, all strive against others competing for the same goals. In this article, we establish the role of competitive pressures for the facilitation of optimal decision making in simple sequential binary choice tasks. In two experiments, competition was introduced with a computerized opponent whose choice behavior reinforced one of two strategies: If the opponent probabilistically imitated participant choices, probability matching was optimal; if the opponent was indifferent, probability maximizing was optimal. We observed accurate asymptotic strategy use in both conditions irrespective of the provision of outcome probabilities, suggesting that participants were sensitive to the differences in opponent behavior. An analysis of reinforcement learning models established that computational conceptualizations of opponent behavior are critical to account for the observed divergence in strategy adoption. Our results provide a novel appraisal of probability matching and show how this individually ‘irrational’ choice phenomenon can be socially adaptive under competition.     

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.     

Belief, knowledge, and uncertainty: A cognitive perspective on subjective probability

This paper presents a cognitive analysis of subjective probability judgments and proposes that these are assessments of belief-processing activities. The analysis is motivated by an investigation of the concepts of belief, knowledge, and uncertainty. Judgment and reasoning are differentiated, Toulmin's (1958) theory of argument being used to explicate the latter. The paper discusses a belief-processing model in which reasoning is used to translate data into conclusions, while judgmental processes qualify those conclusions with degrees of belief. The model sheds light on traditional interpretations of probability and suggests that different characteristics of belief—likelihood and support—are addressed by different representational systems. In concluding, the paper identifies new lines of research implied by its analysis.     

Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time

Diffusion processes (e.g., Wiener process, Ornstein-Uhlenbeck process) are powerful approaches to model human information processes in a variety of psychological tasks. Lack of mathematical tractability, however, has prevented broad applications of these models to empirical data. This tutorial explains step by step, using a matrix approach, how to construct these models, how to implement them on a computer, and how to calculate the predictions made by these models. In particular, we present models for binaries choices for unidimensional and multiattribute choice alternatives; for simple reaction time tasks; and for three alternatives choice problems.     

Precision of probability information and prominence of outcomes: A description and evaluation of decisions under uncertainty

Information about event probability upon which decisions depend may be more or less precise. The first section of this paper reports three experiments that investigated the relationship between this type of imprecision and the prominence that outcomes obtain in decisions. Participants had to rank order sets of six lotteries according to attractiveness. While the lotteries’ values were always precisely known precision of information about lottery chances varied. These experiments showed that increasing ambiguity tied decisions closer to lottery values. The second section shows that modeling participants’ decisions with the contingent weighting model suggests that this outcome prominence effect was not necessarily caused by any change in the respective weighting of probability and outcome information, but that it had probably occurred for purely mathematical reasons. The third part of this paper explores, by means of a computer simulation, (i) which weighting strategy is optimal when probabilities are imprecise and (ii) how participants’ decision behavior compared to a simple, but better adapted strategy. It shows that the weighting of probability information should not change with decreasing precision and it implies that participants’ performance suffered most from a lack of strategic consequence. Implications for decision making policy in general are discussed.     

The effects of active choice,shock duration,shock experience,and probability on the choice between immediate and delayed shock

The choice between immediate and delayed shock was investigated in three experiments with college students. Some Ss were required to choose between a longer-duration shock immediately and a shorter-duration shock later. Immediate, as opposed to delayed, choices were more frequent when: (a) Ss were required to choose the immediate or the delayed shock in contrast to other procedures in which Ss were required to choose immediate shock or passively wait for automatic shock to occur, (b) the duration of the immediate shock was reduced, (c) the S was given prior experience with shock, and (d) the probability of the immediate shock was reduced. Under some circumstances, shock delay and anxiety increased the frequency of immediate choices.     

The role of uncertainty in attentional and choice exploration

Psychonomic Bulletin & Review - The exploitation-exploration (EE) trade-off describes how, when making a decision, an organism must often choose between a safe alternative with a known pay-off,...     

Thinking through uncertainty: nonconsequential reasoning and choice.

When thinking under uncertainty, people often do not consider appropriately each of the relevant branches of a decision tree, as required by consequentialism. As a result they sometimes violate Savage's sure-thing principle. In the Prisoner's Dilemma game, for example, many subjects compete when they know that the opponent has competed and when they know that the opponent has cooperated, but cooperate when they do not know the opponent's response. Newcomb's Problem and Wason's selection task are also interpreted as manifestations of nonconsequential decision making and reasoning. The causes and implications of such behavior, and the notion of quasi-magical thinking, are discussed.     

Cultural, social, and emotional determinants of decisions under uncertainty

Two experiments examined the factors that influence Chinese and United States college students’ decisions in both a simulated investment situation and an academic situation. Participants in each experiment were confronted with a choice between (a) an alternative that could have either a very positive outcome or a very negative one and (b) an alternative that was relatively safe. The decision that others had typically made in the situation was also indicated. Participants’ decisions in both experiments were mediated by the emotional reactions they experienced in response to alternative decision outcomes. Others’ decisions had a direct impact on decisions in the investment situation, but their impact in the academic situation was mediated by their influence on participants’ anticipated emotional reactions. Cultural differences in the impact of anticipated feelings and others’ decisions were not evident in the investment situation. However, they were apparent in the academic situation, which was more similar to ones that participants were likely to encounter in daily life.     

Effects of stimulus-response uncertainty on watchkeeping performance and choice reactions

The present study was conducted to assess the effects of S-R uncertainty on performance in watchkeeping and typical type-b choice-reaction situations. The assessment was based in part on measurements of S-R compatibility effects in the two performance conditions. Four levels of S-R uncertainty (1, 2, 3 and 4 bits/S-R event) were combined factorially with two levels of S-R compatibility (high and low) and the two kinds of tasks (watchkeeping and choice-reaction); 12 Ss were assigned at random to each of the 16 conditions. A matrix of lights was used as stimuli in the choice-reaction condition; Ss monitored the matrix for a I-h duration in the watchkeeping condition. In both tasks, Ss responded by pressing a corresponding key after the presentation of a stimulus or “critical signal.” Reaction time (RT) was found to be an increas ing linear function of S-R uncertainty in both tasks. and the effects of S-R compatibility were essentially identical in the two. However, choice reactions were significantly faster than watchkeeping responses, and the rate of gain of information in watchkeeping was greater than in the comparable choice-reaction situations. The results are interpreted as supporting the hypothesis that watchkeeping differs from the simpler choice-reaction task principally in presenting an additional source of (temporal) uncertainty for information processing.     

A re‐examination of probability matching and rational choice

In a typical probability learning task participants are presented with a repeated choice between two response alternatives, one of which has a higher payoff probability than the other. Rational choice theory requires that participants should eventually allocate all their responses to the high‐payoff alternative, but previous research has found that people fail to maximize their payoffs. Instead, it is commonly observed that people match their response probabilities to the payoff probabilities. We report three experiments on this choice anomaly using a simple probability learning task in which participants were provided with (i) large financial incentives, (ii) meaningful and regular feedback, and (iii) extensive training. In each experiment large proportions of participants adopted the optimal response strategy and all three of the factors mentioned above contributed to this. The results are supportive of rational choice theory. Copyright © 2002 John Wiley & Sons, Ltd.