Pairs Of Gambles Research Articles

A user study of visualisations of spatio-temporal eye tracking data

AbstractEye movements have a spatial (where people look), but also a temporal (when people look) component. Various types of visualizations have been proposed that take this spatio-temporal nature of the data into account, but it is unclear how well each one can be interpreted and whether such interpretation depends on the question asked about the data or the nature of the dataset that is being visualised. In this study, four spatio-temporal visualization techniques for eye movements (chord diagram, scan path, scarf plot, space-time cube) were compared in a user study. Participants $$(N = 25)$$ ( N = 25 ) answered three questions (what region first, what region most, which regions most between) about each visualization, which was based on two types of datasets (eye movements towards adverts, eye movements towards pairs of gambles). Accuracy of the answers depended on a combination of the dataset, the question that needed to answered, and the type of visualization. For most questions, the scan path, which did not use area of interest (AOI) information, resulted in lower accuracy than the other graphs. This suggests that AOIs improve the information conveyed by graphs. No effects of experience with reading graphs (for work or not for work) or education on accuracy of the answer was found. The results therefore suggest that there is no single best visualisation of the spatio-temporal aspects of eye movements. When visualising eye movement data, a user study may therefore be beneficial to determine the optimal visualization of the dataset and research question at hand. Graphical abstract

Shallow Value Weighting Predicts Problem Gambling: A Parameter Estimation Analysis Using Cumulative Prospect Theory.

Problem gambling is a non-substance-based addictive disorder that can cause significant distress and dramatic consequences. Despite extensive research in neuroscience and clinical/social psychology, few contributions have been made from formal models of behavioural economics. We apply Cumulative Prospect Theory (CPT) to provide a formal analysis of cognitive distortions in problem gambling. In two experiments, participants made decisions between pairs of gambles and completed a standard gambling assessment. We estimated the parameter values specified by CPT for each participant and used those estimates to predict gambling severity. In Experiment 1, severe gambling behaviour was associated with a shallow valuation curve, a reversal of loss aversion, and decreased influence of subjective value on decisions (i.e., more noise or variability in preference). Experiment 2 replicated the effect of shallow valuation but did not demonstrate reversed loss version or noisier decisions. Neither experiment provided evidence of differences in probability weighting. We explore implications of the findings and conclude that problem gambling at least partially reflects a fundamental distortion to subjective valuation.

The Certainty Effect for Gains and Losses Emerges in Joint Evaluation but Not Always in Separate Evaluation

Abstract Six studies investigated people's attitudes toward uncertainty. Participants rated the attractiveness of pairs of gambles in either a gain or a loss frame. We varied the level of uncertainty, the monetary outcomes, and the evaluation mode of the gambles (i.e., joint versus separate evaluation). Experiments 1a and 1b compared a sure gain (loss) to a risky gain (loss), with both gambles having identical expected value. Experiments 2a and 2b included an almost sure (i.e., 98%) gain (loss) and risky gain (loss). When gambles entailed gains, a risky gamble became less attractive when evaluated in joint than in separate evaluation. The opposite pattern emerged when gambles entailed losses. The difference between a risky and a sure (or almost sure) gamble was weaker (or eliminated) in separate evaluation. Experiments 3a and 3b presented a risky gamble alone or with other gambles with varying probability and outcomes to be gained or lost. When gambles entailed gains (losses), a risky gamble became less (more) attractive and was chosen less (more) frequently when paired with gambles offering a higher probability of gaining (losing) smaller amounts. Overall, affective reactions and preferences for uncertain gambles depend on the decision context, and the certainty effect can disappear in separate evaluation.

Now for sure or later with a risk? Modeling risky intertemporal choice as accumulated preference.

Research on risky and intertemporal decision-making often focuses on descriptive models of choice. This class of models sometimes lack a psychological process account of how different cognitive processes give rise to choice behavior. Here, we attempt to decompose these processes using sequential accumulator modeling (i.e., the linear ballistic accumulator model). Participants were presented with pairs of gambles that either involve different levels of probability or delay (Experiment 1) or a combination of these dimensions (both probability and delay; Experiment 2). Response times were recorded as a measure of preferential strength. We then combined choice data and response times, and utilized variants of the linear ballistic accumulator to explore different assumptions about how preferences are formed. Specifically, we show that a model that allows for the subjective evaluation of a fixed now/certain option to change as a function of the delayed/risky option with which it is paired provides the best account of the combined choice and response time (RT) data. The work highlights the advantages of using cognitive process models in risky and intertemporal choice, and points toward a common framework for understanding how people evaluate time and probability.

Salience-Driven Value Construction for Adaptive Choice under Risk.

Decisions we face in real life are inherently risky and can result in one of many possible outcomes. However, most of what we know about choice under risk is based on studies that use options with only two possible outcomes (simple gambles), so it remains unclear how the brain constructs reward values for more complex risky options faced in real life. To address this question, we combined experimental and modeling approaches to examine choice between pairs of simple gambles and pairs of three-outcome gambles in male and female human subjects. We found that subjects evaluated individual outcomes of three-outcome gambles by multiplying functions of reward magnitude and probability. To construct the overall value of each gamble, however, most subjects differentially weighted possible outcomes based on either reward magnitude or probability. These results reveal a novel dissociation between how reward information is processed when evaluating complex gambles: valuation of each outcome is based on a combination of reward information whereas weighting of possible outcomes mainly relies on a single piece of reward information. We show that differential weighting of possible outcomes could enable subjects to make decisions more easily and quickly. Together, our findings reveal a plausible mechanism for how salience, in terms of possible reward magnitude or probability, can influence the construction of subjective values for complex gambles. They also point to separable neural mechanisms for how reward value controls choice and attention to allow for more adaptive decision making under risk.SIGNIFICANCE STATEMENT Real-life decisions are inherently risky and can result in one of many possible outcomes, but how does the brain integrate information from all these outcomes to make decisions? To address this question, we examined choice between pairs of gambles with multiple outcomes using various computational models. We found that subjects evaluated individual outcomes by multiplying functions of reward magnitude and probability. To construct the overall value of each gamble, however, they differentially weighted possible outcomes based on either reward magnitude or probability. By doing so, they were able to make decisions more easily and quickly. Our findings illustrate how salience, in terms of possible reward magnitude or probability, can influence the construction of subjective values for more adaptive choice.

Predictive decision making under risk and uncertainty: A support vector machines model

In this paper, a decision making model using support vector machine (SVM) approach is presented. Here, human attitude towards risk and uncertainty is identified via optimizing SVM certainty classification model. In particular, individuals are given different pairs of gambles in order to reveal their preference. Unlike traditional methods used to estimate the utility function through direct inquiry of the certainty equivalents, pair-wise comparisons are used here in the training process to predict human preferences and to compute the utility parameters. The presented study is characterized by first, the use of SVM in the field of decision making to classify individuals’ choices, second, it uses such model to search for the optimal utility parameters, third, the model can be used to guide the decision makers towards better decisions. In contrast to existing utility models, the SVM utility approach is characterized by its tolerance to misclassification in the training and testing data sets which makes it cope with the existing violations such as the common consequence, common ratio and violation of betweenness in the utility theory. To demonstrate the merits of the model, different data sets were used from well known literature studies and new conducted surveys that elicit individual preferences. The data is split into training and testing sets. The results demonstrated a notable consistency in the computed utility parameters and remarkable predictions without the need to strict certainty equivalent estimation. The model can be beneficial in predictive decision making under risk and uncertainty.

The effects of surrounding positive and negative experiences on risk taking

AbstractTwo experiments explored how the context of recently experiencing an abundance of positive or negative outcomes within a series of choices influences risk preferences. In each experiment, choices were made between a series of pairs of hypothetical 50/50 two-outcome gambles. Participants experienced a control set of mixed outcome gamble pairs intermingled with a randomly assigned set of (a) all-gain, (b) all-loss, or (c) a mixture of all-gain and all-loss gamble pairs. In both experiments, a positive experience led to reduced risk taking in the control set and a negative experience led to increased risk taking. These patterns persisted even after the all-gain and all-loss gamble pairs were no longer present. In addition, we showed that the good luck attributed to positive experiences was associated with decreased, rather than increased, risk taking. These results ran counter to the house money effect, and could not readily be accounted for by changes in assets. We suggest that the goals associated with the predominant valence are likely to be assimilated and applied to other choices within a given situation. We also discuss the need to learn more about the characteristics of choice bracketing and mental accounting that influence which aspects of situational context will be included or excluded from consideration when making each choice.

Allais from Experience: Choice Consistency, Rare Events, and Common Consequences in Repeated Decisions

AbstractThe Allais Paradox is a well‐known bias in which people's preferences result in contradictory choices between two normatively identical gamble pairs. Studies have shown that these preference reversals depend on how information is described and presented. In an experiment, we investigate the Allais gambles in several formats including an experiential paradigm, where participants make selections from two blank buttons and get an outcome as a result of a draw from distributions of outcomes in the selected gamble. Results indicate that a large proportion of Allais reversals are found in the traditional descriptive format, they are reduced when gambles are presented in a descriptive table format, and they disappear when choices are made from experience. Although a majority of participants made consistent choices from experience, the proportion of individual reversals is similar to that of descriptive choices. Detailed analyses of experiential choice suggest interesting behavioral differences between participants classified as consistent and those classified as reversals: consistent participants explore and maximize more than reversal participants. Furthermore, consistent participants demonstrate a different switching behavior after experiencing a rare outcome than do reversal participants. We find that, both, overweighting or underweighting of rare outcomes may occur within the course of an individual's experience; depending on the timing of those experiences, the magnitude of the outcomes observed, and the general accumulated value of the gambles. Copyright © 2015 John Wiley & Sons, Ltd.

An empirical assessment of the form of utility functions.

Utility functions, which relate subjective value to physical attributes of experience, are fundamental to most decision theories. Seven experiments were conducted to test predictions of the most widely assumed mathematical forms of utility (power, log, and negative exponential), and a function proposed by Rachlin (1992). For pairs of gambles for real monetary gains, undergraduate and nonstudent subjects either reported an equalizing amount for 1 outcome that made the gambles subjectively equal or chose between gambles where the amounts were varied across trial, which allowed the equalizing amount to be estimated from their pattern of choices. Using a novel method that eliminates several limitations of previous research, I manipulated the outcomes across trials such that each type of utility function predicted a linear relationship between the equalizing amounts and the amounts of the other outcomes, and made point predictions for either the slope or intercept of that relationship. In a meta-analysis across experiments, systematic departures from the point predictions were observed for each type of utility function. Thus, the data imply that despite their historical importance and incorporation in many psychological and economic decision theories, the most widely assumed models of utility are incorrect.

Preference reversals: The impact of truth-revealing monetary incentives

Researchers vigorously debate the impact of incentives in preference reversal experiments. Do incentives alter behavior and generate economically consistent choices? Lichtenstein and Slovic (1971) document inconsistencies (reversals) in revealed preference in gamble pairs across paired choice and individual pricing tasks. The observed pattern is inconsistent with stable underlying preferences expressed with simple errors. Lichtenstein and Slovic (1973) and Grether and Plott (1979) introduce incentives, but aggregate reversal rates change little. These results fostered numerous replications and assertions that models of non-stable preferences are required to explain reversals. Contrary to this research, we find that incentives can generate more economically consistent behavior. Our reevaluation of existing experimental data shows that incentives have a clear impact by better aligning aggregate choices and prices. The effect is sufficiently large that, with truth-revealing incentives, a stable-preferences-with-error model not only explains behavior, but fits the data as well as any model possibly could.

Cognitive Models of Choice: Comparing Decision Field Theory to the Proportional Difference Model

People often face preferential decisions under risk. To further our understanding of the cognitive processes underlying these preferential choices, two prominent cognitive models, decision field theory (DFT; Busemeyer & Townsend, 1993) and the proportional difference model (PD; González-Vallejo, 2002), were rigorously tested against each other. In two consecutive experiments, the participants repeatedly had to choose between monetary gambles. The first experiment provided the reference to estimate the models' free parameters. From these estimations, new gamble pairs were generated for the second experiment such that the two models made maximally divergent predictions. In the first experiment, both models explained the data equally well. However, in the second generalization experiment, the participants' choices were much closer to the predictions of DFT. The results indicate that the stochastic process assumed by DFT, in which evidence in favor of or against each option accumulates over time, described people's choice behavior better than the trade-offs between proportional differences assumed by PD.

Phineas gauged: decision-making and the human prefrontal cortex

Poor social judgment and decision-making abilities have often been attributed to people who have suffered injury to the ventromedial prefrontal cortex (VMPFC). However, few laboratory tests of decision-making have been conducted on these patients. The exception to this is the Iowa Gambling Task which has often, but not always, demonstrated differential performance between patients and controls. Results from patients with prefrontal cortex lesions on a novel test of decision-making are presented. Participants explored and chose from pairs of gambles that differed in their underlying distributions, primarily in the variance of their respective outcomes. In accordance with many findings from the behavioral decision-making literature, both young normal participants and older patient controls demonstrated a marked avoidance of risk and selected largely from secure, low variance gambles. In contrast, patients with ventromedial lesions were divided into two clear sub-groups. One group behaved similarly to normals, showing a risk-averse strategy. The other group displayed a distinctive risk-seeking behavior pattern, choosing predominantly from the high-variance, high-risk decks. This research demonstrates some of the advantages of using methods and theories from traditional decision-making research to study the behavior of patients, as well as the benefits of examining individual participants, and provides new insights into the nature of the decision-making deficit in patients with ventromedial prefrontal cortex lesions.

Do generalized expected utility theories capture persisting properties of individual decision makers?

Expected utility theory and two generalizations of it (rank-dependent utility theory and cumulative prospect theory), which have been proposed to describe individuals' risky choice behavior, have been examined. A characteristic feature of these models is subjective weighting of outcomes and probabilities. This study investigates whether individually determined weighting functions (utility functions and weighting functions for probabilities) capture individual traits of decision makers. To verify this, temporal constancy of individual subjective weighting functions and predictability of individuals' future decisions were considered. Sixty-four subjects had to choose between the same 150 gamble pairs in three separate sessions, with an interval of one week between sessions. Descriptive analyses showed considerable temporal inconsistency in the individuals' decision behavior. It was, therefore, not surprising that the analysis of temporal constancy of individual weighting functions yielded frequent rejections of the constancy assumption. An additional analysis was conducted, predicting decision behavior in later sessions using individual weighting functions estimated from earlier sessions. This analysis takes the inconsistency into account explicitly and suggests that the models' weighting functions, indeed, seemed to capture persisting properties of the decision makers. While the assumption of subjective weighting of outcomes (as in expected utility theory) proved very important for predicting future decisions, the additional assumption of subjective weighting of probabilities (as in rank-dependent utility theory or cumulative prospect theory) improved predictability only to a minor degree.

Organizational Decision Making With Similar Alternatives

The role of the dominance criterion in organizational decision making was examined. Fifty-two participants were administered questionnaires containing four pairs of alternative gambles. The participants were asked to choose their preferred gamble in each pair. All of the pairs of gambles were equivalent and were presented in increasing order of masked dominance. Results indicated that individuals are less likely to use the dominance criterion as dominance between alternatives is increasingly masked. In addition, the results are consistent with a hypothesized comparison heuristic of choosing the alternative with a larger number of preferred outcomes.

Tests of consequence monotonicity in decision making under uncertainty.

Consequence monotonicity means that if 2 gambles differ only in 1 consequence, the one having the better consequence is preferred. This property has been sustained in direct comparisons but apparently fails for some gamble pairs when they are ordered in terms of judged monetary certainty equivalents. In Experiments 1 and 3 a judgment procedure was compared with 2 variants of a choice procedure. Slightly fewer nonmonotonicities were found in one of the choice procedures, and, overall, fewer violations occurred than in previous studies. Experiments 2 and 3 showed that the difference was not due to procedural or stimulus presentation differences. Experiment 4 tested a noise model that suggested that the observed violations were due primarily to noise in estimating certainty equivalents, and so, despite some proportion of observed violations, consequence monotonicity cannot be rejected in that case.

Probability of Regret: Anticipation of Uncertainty Resolution in Choice

In choice between uncertain options, uncertainty may be eventually resolved for all options, or just for the chosen option. The findings described here demonstrate that preference between uncertain options is systematically affected by expectations concerning uncertainty resolution: Prospects which are less likely to yield worse outcome than the alternative are selected more often when all options are to be resolved (complete resolution). Two experiments examined choice between statistically independent lotteries for which the chances of being worse off with the low-risk alternative were nearly as high, or higher than the chances of being worse-off with the high-risk alternative. For these gamble pairs it was found that subjects who expected complete resolution chose the high-risk high-gain option more often than subjects who expected only their selected gamble to be resolved. A third experiment suggests that the preference changes due to resolution are related to the probability of the low-risk gamble yielding the worse obtained outcome. The results are interpreted as compatible with the hypothesis that in choosing between uncertain options, people are more inclined to compare outcomes per states of the world if they expect to learn what would have happened with each option. In those cases, the outcome of a foregone option is more likely to serve as a salient comparison point for evaluating the outcome of the selected option. An alternative explanation is also discussed.

Consequences of Regret Aversion: Effects of Expected Feedback on Risky Decision Making

Previous research has considered the question of how anticipated regret affects risky decision making. Several studies have shown that anticipated regret forces participants towards the safe option, showing risk-aversion. We argue that these results are due to the previous confounding of the riskiness of the options with the feedback received. Our design unconfounds these factors, and we predict that participants will always tend to makeregret-minimizingchoices (rather than risk-minimizing choices). We present three experiments using a “choices between equally valued alternatives” paradigm. In these experiments we manipulate whether the risky or safe gamble is the regret-minimizing choice by manipulating which gamble(s) will be resolved. As predicted, participants tend to choose the regret-minimizing gamble in both gains and losses and in both relatively high risk and relatively low risk pairs of gambles. We consider the implications of these results for the role of regret in choice behavior.

Note—Further Tests of Aspiration Level Effects in Risky Choice Behavior

This Note extends the work reported in Payne, Laughhunn, and Crum (Payne, J. W., D. J. Laughhunn, R. Crum. 1980. Translation of gambles and aspiration level effects in risky choice behavior. Management Sci. 26 1039–1060.) on the need to incorporate a target return, reference point, or aspiration level concept in the analysis of risky choice behavior. Two experiments are reported. The first experiment provides a more complete test of the model of reference point effects developed by Payne, Laughhunn, and Crum. A translation of outcomes procedure, which adds a constant to all outcomes, was used to vary the relationship of pairs of gambles to an assumed target or reference point. The results fully support the model. The second experiment provides evidence of the conceptual validity of the model by using explicit instructions to vary the target levels of managers, while holding gamble values constant.

The effect of time pressure on risky choice behavior

Thirty six subjects chose individually between pairs of gambles under three time pressure conditions: High (8 seconds), Medium (16 seconds) and Low (32 seconds). The gambles in each pair were equated for expected value but differed in variance, amounts to win and lose and their respective probabilities. Information about each dimension could be obtained by the subject sequentially according to his preference. The results show that subjects are less risky under High as compared to Medium and Low time pressure, risk taking being measured by choices of gambles with lower variance or lower amounts to lose and win. Subjects tended to spend more time observing the negative dimensions (amount to lose and probability of losing), whereas under low time pressure they preffered observing their positive counterparts. Information preference was found to be related to choices. Filtration of information and acceleration of its processing appear to be the strategies of coping with time pressure.

Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior

Two recent models of risky decision making developed by Fishburn (Fishbijrn, P. C. 1977. Mean-risk analysis with risk associated with below-target returns. Amer. Econ. Rev. 67 116–126.) and by Kahneman and Tversky (Kahneman, D., A. Tversky. 1979. Prospect theory: an analysis of decisions under risk. Econometrica 47 262–291.) have emphasized the importance of a target return or a reference point in determining preferences and choices among gambles. Target returns and reference points represent variations on the concept of an aspiration level, an old idea in theories of decision making. Additional evidence on the need to incorporate such a concept in the analysis of risky choice behavior is presented in this paper. In three experiments, the relationship of pairs of gambles to an assumed reference point was varied by adding or subtracting a constant amount from all outcomes. The results demonstrate that such translations of outcomes can result in the reversal of choice within pairs of gambles. The effect of such translations on choice depended on whether the size of the translation was sufficient to insure that one gamble in a pair had outcome values either all above or all below the reference point, while the other gamble had outcome values both above and below the reference point. A model of the effects of a reference point on risky choice behavior is presented and the results are also discussed in terms of the Fishburn and Kahneman-Tversky models, as well as other theories of risky decision making.