Preference reversals are diminished when gambles are presented as relative frequencies

Preference reversals are a well-documented example of suboptimal decision making. Typical preference reversals experiments have involved monetary bets presented in probability format. Research on other examples of decision making have shown that irrational or suboptimal choices are diminished or eliminated entirely when the probabilities are presented as relative frequencies (e.g., Gigerenzer & Hoffrage, 1995). The aim of the present experiment was to determine if the way in which information is presented to participants affects participants' preferences. When the options were presented in the standard probability format 59% of participants' preferences were reversed. However, reversals were significantly decreased in the frequency format group, with only 40% of participants' responses being inconsistent. Although preference reversals were not eliminated when the gambles were presented as frequencies they were significantly diminished and may not be such a robust example of irrational decision making after all.     

An approach to and computational results on testing the form of a decision maker's utility function

In this paper we consider the problem of identifying the form of a decision maker's (DM) utility function. We consider a set of alternatives each defined by a number of criteria and we assume that the DM's preferences are consistent with some underlying utility function. We present some theory and develop approaches to test whether the DM's preferences are consistent with a linear, a quasi-concave, a quasi-convex or a general monotonic function. We present our computational experience showing that in almost all cases the approaches correctly identify the form of the underlying utility function and require very little preference information of the DM.     

Decision by sampling: The role of the decision environment in risky choice

Decision by sampling (DbS) is a theory about how our environment shapes the decisions that we make. Here, I review the application of DbS to risky decision making. According to classical theories of risky decision making, people make stable transformations between outcomes and probabilities and their subjective counterparts using fixed psychoeconomic functions. DbS offers a quite different account. In DbS, the subjective value of an outcome or probability is derived from a series of binary, ordinal comparisons with a sample of other outcomes or probabilities from the decision environment. In this way, the distribution of attribute values in the environment determines the subjective valuations of outcomes and probabilities. I show how DbS interacts with the real-world distributions of gains, losses, and probabilities to produce the classical psychoeconomic functions. I extend DbS to account for preferences in benchmark data sets. Finally, in a challenge to the classical notion of stable subjective valuations, I review evidence that manipulating the distribution of attribute values in the environment changes our subjective valuations just as DbS predicts.     

A Representation Theorem for a Decision Theory With Conditionals

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Ambiguity Attitudes over Time

Previous research demonstrates that individuals exhibit a stronger level of ambiguity aversion for high probabilities than for low probabilities. Given that risky and ambiguous prospects are often unresolved until a future date (e.g., investment decisions, new product launches, and medical interventions), this study examines the impact of time on ambiguity preferences at different probability levels. Our experimental results indicate that although ambiguity preferences for low‐probability events remain constant, a robust effect of time occurs for high‐probability events. More specifically, temporal distance mitigates ambiguity aversion. This effect is consistent for different elicitation methods (preference rating and probability–ambiguity trade‐off tasks). We propose a dual‐process model (affective versus cognitive processing styles) to explain our results. Affective processing for high‐probability lotteries resolved in the current period increases ambiguity aversion, while cognitive processing leads to less ambiguity‐averse choices for future lotteries. Copyright © 2015 John Wiley & Sons, Ltd.     

Leader‐driven distortion of probability and payoff information affects choices between risky prospects

Research indicating that decision makers often distort new information to favor nascent preferences has focused primarily on riskless choice rather than risky choice. In addition, the critical assumption that information distortion mediates the link between the initially preferred alternative and the final choice has not been tested in a compelling manner. In an experiment designed to fill these gaps, participants made six choices involving pairs of hypothetical three‐outcome monetary gambles. We manipulated initial preferences by varying the order in which gamble features were presented. Multilevel regressions indicated that participants distorted their evaluations of precise probabilities and payoffs in the direction of their emerging preferences and that they used their biased evaluations to update those preferences. As expected, information distortion mediated the effect of initial preferences on final choices and final preference strength. In a follow‐up experiment, we compared a standard measure of information distortion (based on comparisons to mean ratings in a no‐choice control task) to a more personalized measure (based on participants' own ratings in the control task) and found the mean‐based measure to be superior for the probability and payoff information in question. Other findings in Experiment 2 corroborated the results of Experiment 1. In both studies, the distortion of quantitative inputs in a simple task highlights the non‐normative circularity of the choice process. Copyright © 2010 John Wiley & Sons, Ltd.     

Indeterminate Preferences

It is commonly assumed that preferences are determinate; that is, that an agent who has a preference knows that she has the preference in question and is disposed to act upon it. This paper argues the dubiousness of that assumption. An account of indeterminate preferences in terms of self-predicting subjective probabilities is given, and a decision rule for choices involving indeterminate preferences is proposed. Wolfgang Spohn’s and Isaac Levi’s arguments against self-predicting probabilities are also considered, in light of Wlodek Rabinowicz’s recent criticism.     

The Effect of Temporal Distance on Attitudes toward Imprecise Probabilities and Imprecise Outcomes

Many personal, managerial, and societal decisions involve uncertain or ambiguous consequences that will occur in the future. Yet, previous empirical research on ambiguity preferences has focused mainly on decisions with immediate outcomes. To close this gap in the literature, this paper examines ambiguity attitudes toward future prospects, particularly how they may differ from the attitudes toward comparable prospects in the present. On the basis of a recent paradigm, we first distinguish between two types of ambiguity: imprecise probabilities and imprecise outcomes. Then, in accordance with construal level theory, which shows that temporal distance increases the relative importance of outcomes over probabilities in evaluating prospects, we conjecture that temporal distance would moderate attitudes toward imprecise probabilities but amplify attitudes toward imprecise outcomes. Through a series of experiments, we demonstrate that when the prospects are in the future, individuals are less averse toward imprecise probabilities and more seeking toward imprecise outcomes. However, the effect is most prominent for prospects where both the probability and outcome dimensions are concurrently imprecise. The paper ends with a discussion on how dimension salience may have contributed to this result. Copyright © 2012 John Wiley & Sons, Ltd.     

Representation of subjective preferences under ambiguity

The objective of this paper is to show how potentially incomplete preferences of a decision maker (DM) on acts can be modelled formally in a subjective ambiguity perspective. We identify acts as functions from a state space Ω to bounded support (finitely additive) probabilities over a set X of prizes. Then, we characterize preferences over equibounded acts a which have a numerical representation by the family of functionals , where u is a cardinal utility on X (representing the risk attitude of the DM) and Π is a unique pointwise closed convex set of probabilities on all events in Ω (representing the ambiguity perceived by the DM). To this end, in addition to the usual independence and continuity assumptions, we add completeness and dominance for preferences restricted to constant acts; moreover, we consider two other properties (subjective monotonicity and coherence) related with the preferences of a DM who is not able, owing to his partial knowledge, to evaluate any event in Ω.     

The loss‐bet paradox: Actuaries,accountants, and other numerate people rate numerically inferior gambles as superior

Psychologists have convincingly demonstrated that preferences are not always stable and, instead, are often “constructed” based on information available in the judgment or decision context. In 4 studies with experts (accountants and actuaries in Studies 1 and 2, respectively) and a diverse lay population (Studies 3 and 4), the evidence was consistent with the highly numerate being more likely than the less numerate to construct their preferences by rating a numerically inferior bet as superior (i.e., the bets effect). Thus, the effect generalizes beyond a college student sample, and preference construction differs by numeracy. Contrary to prior thinking about preference construction, however, high expertise and high ability (rather than low) consistently related to the paradoxical phenomenon. Results across studies including Study 3's experimental modifications of the task supported the hypothesized number comparison process (and not a lack of expertise with monetary outcomes and probabilities or numeracy‐related differences in attention to numbers) as the effect's underlying cause. The bets effect was not attenuated by Study 4's instructions to think about what would be purchased with bet winnings. Task results combined with free‐response coding supported the notion that highly numerate participants have a systematic and persistent inclination for doing simple and complex number operations that drive their judgments (even after controlling for nonnumeric intelligence). Implications for 3 types of dual‐process theories are discussed. The results were inconsistent with default‐interventionist theories, consistent or unclear with respect to fuzzy trace theory, and consistent with interactive theories.     

On the composition of risk preference and belief

Prospect theory assumes nonadditive decision weights for preferences over risky gambles. Such decision weights generalize additive probabilities. This article proposes a decomposition of decision weights into a component reflecting risk attitude and a new component depending on belief. The decomposition is based on an observable preference condition and does not use other empirical primitives such as statements of judged probabilities. The preference condition is confirmed by most of the experimental findings in the literature. The implied properties of the belief component suggest that, besides the often-studied ambiguity aversion (a motivational factor reflecting a general aversion to unknown probabilities), perceptual and cognitive limitations play a role: It is harder to distinguish among various levels of likelihood, and to process them differently, when probabilities are unknown than when they are known.     

封面故事、选项框架和损益概率对风险偏好的影响

以股市投资为背景设计决策问题,考查了问题的封面故事类型、备择选项框架和风险项的概率水平对327名股民被试和465名大学生被试的风险偏好的影响。结果表明,股民被试的风险偏好不同于大学生被试,前者在所有实验处理上呈现出稳定的风险回避倾向。大学生被试在不同类型的封面故事下呈现出不同的风险偏好。在传统的坏封面故事下,风险偏好只受到备择选项框架的影响,不受损益概率的影响,即出现经典的框架效应现象。在好封面故事下,风险偏好受到备择选项框架、损益概率及两者交互作用的影响,即在高概率水平上出现框架效应现象,在低概率水平上出现框架效应反转现象     

Patterns of Preference for Numerical and Verbal Probabilities

We report results of an experiment designed to test a principle formulated by Budescu and Wallsten (1995), that, when communicating uncertainty information, mode choices are sensitive to sources and degrees of vagueness. In addition, we examined subjects’ efficacy in using such uncertainty information as a function of communication mode, source, and vagueness. In phase one of the experiment, subjects in a dyad used precise (numerical) or imprecise (verbal) expressions to communicate to a remote partner precise or vague uncertainty about the likelihoods of events. Spinner outcomes were used to generate precise uncertainty while answers to almanac questions were used to elicit vague uncertainty. In phase two, subjects saw the events paired with their partners’ estimates of similar events, and were asked to gamble on one event from each pair. Communication mode preferences were measured as the relative frequency that subjects chose the numerical mode to either express or receive uncertainty information regarding the events. Efficacy was measured as the relative frequency that subjects choose from the pair the event associated with the objectively more probable uncertainty expression. Underlying uncertainty interacted with direction of communication to affect preferences for modes of expression of the probabilities. Subjects preferred precise (numerical) information, especially for precise events (spinners). For vague events (questions), their preference for precise (numerical) information was stronger when receiving than when communicating information. Similar preferences were reflected in the efficiency of subsequent gamble decisions based on the probability estimates. Specifically, decisions were more efficacious (i.e. consistent with Expected Utility) when degrees of precision in events and estimates matched. © 1997 by John Wiley & Sons, Ltd.     

Group transformation: How demonstrability promotes intra-group cooperation in social dilemmas

Intra-group cooperation in a social dilemma is increased after a group has discussed and reached a decision, especially if the dilemma is easily understood (‘demonstrable’). This paper examines how demonstrability affects the decision of a group that consists entirely of participants who are initially non-cooperative. Thirty-eight 6-person groups with unanimous prior preference for cooperation or non-cooperation discussed a prisoner’s dilemma before making a group decision. When demonstrability was low groups reflected the prior (either cooperative or non-cooperative) preferences of their members. When demonstrability was high we found that groups showed no effect of prior preference. Specifically, groups of prior non-cooperators made more cooperative group decisions and subsequently their members remained cooperative when asked to express preferences individually. The combined advantages of group process and high demonstrability for facilitating optimal cooperation are discussed.     

Extreme malleability of preferences: Absolute preference sign changes under uncertainty

Malleability of preferences is a central tenet of behavioral decision theory. How malleable preferences really are, however, is a topic of debate. Do preference reversals imply preference construction? We argue that to claim preferences are construed, a demonstration of more extreme preference malleability than simple preference reversals is required: absolute preference sign changes within participants. If respondents value a prospect positively in 1 condition but negatively in a different condition, preferences cannot be considered stable. Such absolute preference sign changes are possible under uncertainty. In 2 incentive‐compatible experiments, we found participants were willing to pay to take part in a gamble and also demanded to be compensated to take part in a subsequent gamble with identical outcomes and probabilities. Such absolute preference sign changes within participants led to simultaneous risk aversion and risk seeking for the same risky prospect, suggesting that, at least in the domain of risky decisions, consumers' preferences are indeed malleable and construed.     

Ambiguity seeking in multi-attribute decisions: Effects of optimism and message framing

This paper investigates the influence of message framing and personality variables on preferences over ambiguity in the context of multi-attribute decision scenarios. Undergraduate subjects responded to scenarios in which one of two medical treatments was associated with ambiguous probabilities of treatment effects. Probabilities were either positively or negatively framed. Subjects indicated their degree of preference for one treatment over the other. Subjects' optimism, trait anxiety, health locus of control, need for cognitive structure, and current mood were measured. In two separate studies, subjects preferred ambiguity when probabilities were positively framed, and were neutral toward ambiguity when probabilities were negatively framed. Also, in both studies the preference for ambiguity in positively framed scenarios was greater for more optimistic subjects. The unexpected finding of ambiguity seeking may be associated with the use of different decision strategies in multi-attribute versus single-attribute decisions.     

Managers' variance investigation decisions: an experimental examination of probabilistic and outcome ambiguity

Information ambiguity is prevalent in organizations and may influence management decisions. This study examines, given imprecise probabilities or outcomes, how managers decide which department's performance to investigate further when they are provided with performance benchmarks expressed in numerical intervals. Seventy‐nine MBA students participated in two experiments involving investigation decisions. We presented participants with interval benchmarks of a firm's expenses. Being below or above the benchmark should have been seen as equally negative. We found that, when facing outcome ambiguity, our participants consistently preferred to investigate further those departments whose performance was described as having an ambiguous outcome (when the outcome's range was centered either below or above the interval benchmark). However, when facing probabilistic ambiguity, there were two predominant choice patterns: consistently choosing to investigate the department whose performance is described with an ambiguous probability, or consistently choosing to investigate the department with unambiguous performance. To gain further insight, we conducted a follow‐up study collecting written protocols of participants' reasons for making choices involving ambiguous performance information. The results show that our participants displayed similar decision‐making processes when facing outcome ambiguity and probabilistic ambiguity. Copyright © 2001 John Wiley & Sons, Ltd.     

Desirability foundations of robust rational decision making

Recent work has formally linked the traditional axiomatisation of incomplete preferences à la Anscombe-Aumann with the theory of desirability developed in the context of imprecise probability, by showing in particular that they are the very same theory. The equivalence has been established under the constraint that the set of possible prizes is finite. In this paper, we relax such a constraint, thus de facto creating one of the most general theories of rationality and decision making available today. We provide the theory with a sound interpretation and with basic notions, and results, for the separation of beliefs and values, and for the case of complete preferences. Moreover, we discuss the role of conglomerability for the presented theory, arguing that it should be a rationality requirement under very broad conditions.

     

On the shape of the probability weighting function

Empirical studies have shown that decision makers do not usually treat probabilities linearly. Instead, people tend to overweight small probabilities and underweight large probabilities. One way to model such distortions in decision making under risk is through a probability weighting function. We present a nonparametric estimation procedure for assessing the probability weighting function and value function at the level of the individual subject. The evidence in the domain of gains supports a two-parameter weighting function, where each parameter is given a psychological interpretation: one parameter measures how the decision maker discriminates probabilities, and the other parameter measures how attractive the decision maker views gambling. These findings are consistent with a growing body of empirical and theoretical work attempting to establish a psychological rationale for the probability weighting function.