Thinking styles and risky decision‐making: Further exploration of the affect–probability weighting link

People usually overweight small probabilities and underweight large probabilities leading to the familiar inverse S‐shaped weighting function. This research explores the link between affect and the structure of probability weighting from the perspective of thinking dispositions, a concept central to dual system theories of reasoning. The effects of affective priming and cognitive load on both probability weighting and the value function are also examined. The evidence suggests that thinking styles do have predictive implications for risky decision‐making. Participants with a more affective thinking style tend to be more risk‐seeking in small probability gambles. However, increasing access to the affective system by affective priming or cognitive load manipulations tend to reduce risk‐seeking behavior in small probability gambles as well as reduce risk averse behavior in large probability gambles. Previous research, manipulating the affective nature of lottery outcomes, found evidence for an increase in curvature (more overweighting of small probabilities and more underweighting of large probabilities) of the weighting function for affect‐rich outcomes, lending support to a hope‐and‐fear deconstruction of probability weighting. The present research suggests that increased anticipatory emotions characterized by the elevation of the weighting function (more overweighting at all probabilities) is also important and could sometimes be more significant than hope‐and‐fear in decision‐making under risk. An integrated approach incorporating the impact of affect on all three, the elevation and curvature of probability weighting as well as the curvature of the value function explains the empirical findings. Copyright © 2010 John Wiley & Sons, Ltd.     

The role of motivation and volition in economic decisions: Evidence from eye movements and pupillometry

Economic decisions usually involve high stakes, real consequences, and some degree of personal risk. This article explores the impact of motivational and volitional states on economic decision processes in an incentivized lottery choice task. We investigated the patterns of decision time, choice, information search, and pupil dilation dependent on an experimental manipulation of motivation and volition, that is, the deliberative and the implemental mindset. The results indicated that choice preferences in economic decisions were robust and remained unaffected by motivational and volitional states, but decision processes were notably impacted. Decision makers in a deliberative state of mind searched for information more extensively and made slower decisions than the baseline. The implemental mindset was associated with more attention paid to the probability attributes of the gambles relative to the deliberative mindset. Furthermore, we observed that gamble outcomes that entailed no win at all (i.e., zero outcomes) played an important role for information search. These outcomes were largely disregarded in terms of predecisional information search but elicited pupillary responses similar to very high outcome lotteries. These results inform the current debate about the zero effect in risky choice. We also discuss the potential of eye-tracking studies of risky choice to dissolve ambiguities concerning the contributions of effort and arousal to modulating pupillary response. Implications for theoretical advances in decision research are discussed.     

How do we evaluate future gambles? Experimental evidence on path dependency in risky intertemporal choice

This study reports three experiments which demonstrate path dependency in risky intertemporal choice. Consider a lottery to be resolved and paid in a future time period. One can obtain the present value of this lottery in three different ways: (1) eliciting directly the present certainty equivalent (CE) of the future lottery (direct path); (2) eliciting the future CE and then discounting this amount to the present (risk‐time path); and (3) eliciting the present value of the risky prospect and then determining the CE of this current lottery (time‐risk path). Standard rational choice models such as the discounted expected utility model, assume a multiplicative model, where all three methods mentioned above would yield the same value. We conducted three studies to examine if this is the case: Experiments 1 and 2 were based on a set of matching‐task questions and Experiment 3 used a process‐tracing design to analyze the natural sequence of decision making by the subjects. These three studies show that the evaluation of future gambles is path‐dependent. The present values elicited under the time‐risk and direct paths are, on average, higher than those reported under the risk‐time path. In addition, we found evidence for a two‐stage evaluation of risky future prospects: When evaluating a future gamble, individuals first assess the present value of the gamble (time discounting) and then they determine a certainty equivalent (probability discounting). Copyright © 2008 John Wiley & Sons, Ltd.     

The same but different: an empirical investigation of the reducibility principle

According to classical utility theory the valuation of any lottery should depend only on its outcomes and their respective probabilities, and should not be affected by the nature, complexity and structure of the chance mechanism. Previous research has documented systematic violations of this principle. For example, most subjects prefer lotteries in which the payoffs are contingent on the joint occurrence of multiple (high probability) events to simple lotteries, and lotteries in which the earlier stages offer higher probabilities than the later stages. We review the various violations of this principle and suggest a classification into two major types associated with misunderstanding of chance mechanisms and attitude towards the chance mechanism and process. In the present study 40 subjects were presented with 30 pairs of binary gambles. In any given pair the lotteries had identical outcomes and equal ‘reduced’ probabilities (and thus equal expected values). However, the chance mechanisms varied along a variety of factors such as the size of the sample space, the number of stages, temporal ordering, order of probabilities, their transparency and time constraints. Half the subjects saw lotteries involving gains and the other half considered only losses. After choosing one lottery in each pair, the subjects were asked to explain and justify their choices. The findings revealed systematic violations of the reducibility principle: subjects displayed a preference for lotteries with larger sample spaces, and for lotteries that allow quicker resolutions in the earlier stages. A clear distinction between some patterns of preferences in the gains and loss domains was revealed. In gambles involving gains subjects preferred to have the highest probability on the first stage (and the lowest probability on the last stage), but displayed the opposite preferences for losses. A content analysis of the subjects' stated reasons for their choices identified eight major categories. The most frequently invoked were hope, fun, simplicity, stress and time. Copyright © 2001 John Wiley & Sons, Ltd.     

Additivity of risk in portfolios

A collection of gambles constituting a portfolio may itself be represented as a single gamble played once. A portfolio may be constructed by requiring each component gamble to be played once, and there is a theory of additive risk which requires that the perceived risk of the portfolio be an additive function of the perceived riskiness of the component gambles. Alternatively, a portfolio may be constructed as a probability mixture of the component gambles, and there is a theory of expected risk which requires that the perceived risk of the portfolio be the average of the riskiness of the component gambles. Existing evidence suggests that both of these theories cannot be true. A test of additivity of portfolios under both kinds of composition functions was made under two forms of display, the components displayed separately and fused as a single gamble. This experiment supports expected risk and rejects additive risk, especially under fused display.     

The Influence of Positive Affect on the Decision Rule in Risk Situations: Focus on Outcome (and Especially Avoidance of Loss) Rather Than Probability

Two experiments examined the influence of positive affect on probability estimation and choice. Participants in whom positive affect had been induced, as well as no-manipulation controls, were asked to make both numerical evaluations of verbal probabilities in three-outcome gambles and actual betting decisions about similar gambles. Results from Experiment 1 showed the phenomenon labeledcautious optimism:Positive affect participants significantly overestimated the probabilities associated with phrases for winning relative to their estimates of probability of losing for the same phrases (optimism), while participants in a control condition did not; yet, in actual gambling situations, affect condition participants were much less likely to gamble than were controls when a real loss was possible (caution). Results of the betting task from Experiment 2 further indicated that affect participants used a betting-decision rule that was different from that of controls: They bet less than controls in gambles where potential losses were large, even though probability of loss was small, and they bet more than controls in gambles where the amount of the potential loss was small, even though the probability of loss was moderate or large. These findings suggest that positive affect can promote an overt shift from a decision rule focusing primarily on probabilities to one focusing on utilities or outcome values, especially for losses. Taken together, the results are compatible with an interpretation of the influence of positive affect in terms of an elaboration of positive cognitive material, and purposive behavior in decisions, rather than in terms of mere response bias.     

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.     

Le renversement de préférence… renversé !

Preference reversal (PR) occurs when pairs of lottery gambles are evaluated under two different conditions: to choose the gamble preferred to play and assign minimum selling price to each gamble. The preference order is then reversed from one condition to another: while it receives the lowest selling price, the gamble less risked is preferred in condition of play. Many times replicated, this result is considered as a cognitive bias. Recent research suggests that it could be related only to the procedure used to present the gambles (i.e., the evaluation mode): either by pair (joint evaluation or JE) in condition of play, or one by one (separate evaluation or SE) in the pricing task. Then, by reversing the evaluation mode in each condition, PR should be reversed, as it is shown in this study: although the phenomenon still occurs when subjects evaluate gambles in the classical paradigm, we observe an inversion of PR when they have, on the one hand, to play in SE, and on the other hand, to sell in JE. Furthermore, an analysis not often used in this literature provides new elements, which can attest to the cognitive mechanisms underlying the phenomenon: by recording the online information (self-paced display time paradigm) we show the effect of an anchoring and adjustment process when riskiest gambles are preferred.     

Modeling dynamic inconsistency with a changing reference point

A rational principle of decision making called dynamic consistency was tested by presenting decision makers with a sequence of two gambles. The first gamble was obligatory. Before playing the first gamble, participants were asked to make a planned choice as to whether they would take the second gamble. After experiencing the actual results of the first gamble, decision makers were asked to make a final choice regarding the second gamble. Dynamic consistency requires agreement between the planned and final choices. Violations of dynamic consistency were observed, e.g. anticipating a gain in the first gamble, decision makers planned to take the second gamble; after experiencing the gain, they changed their minds and rejected the second gamble. Two models of dynamic inconsistency were compared. One assumes that experience shifts the reference point and changes the utility associated with the gamble; another assumes that experience changes the subjective probability associated with the gamble. The reference point model provided the best account for the findings. Copyright © 2003 John Wiley & Sons, Ltd.     

Valuing information and options: an experimental study

Participants in four studies were faced with everyday‐life decision scenarios involving risk, such as purchasing an airline ticket whose price may change. They were asked to state their maximum willingness to pay (WTP) for resolving the uncertainty with either perfect information or an option. The two are strategically equivalent, therefore, should be valued in the same way. Across all experiments, individuals tend to value the option more than the information. In addition, the distributions of responses reveal frequent and gross violations of normative bounds. Contrary to normative predictions, no relationship is found between individuals' valuation of the gamble and their reported WTP for information or option. Furthermore, although participants pay attention to the probabilities of outcomes in valuing the gambles, they ignore the probabilities in valuing uncertainty resolution. Several reasoning heuristics that participants use to come up with a value of information are identified, and it appears that the Information and Option contexts tend to trigger different heuristics. Shift in reference point and regret are consistent with the Information–Option valuation discrepancy. Copyright © 2007 John Wiley & Sons, Ltd.     

Risky decision: Attention and path dependency as a function of response mode

It was previously shown and was here replicated that the amount of money required to induce a subject to exchange one gamble for a second and then the second for a third depends on the second (intermediate) gamble. This path dependency cannot be explained by any of the algebraic models (including SEU), nor can it be explained as a simple attention effect. A model was put forward which explains the effect in terms of differential masking depending on a kind of stimulus—response compatibility. The effect of response mode on path dependency was examined in this study; similarity judgements showed no consistent path dependency nor did difference in rated attractiveness of gambles presented in pairs, but rated attractiveness was different for gambles presented singly. Since it might be that monetary response emphasises the monetary aspects, that is, the winning amount of the gamble, it was thought that a probability response would emphasise the probability of winning. However, when subjects were asked to set the probability of winning $ 12 which would induce them to exchange one gamble for another, not only was no path dependency observed, but the subjects' responses seemed to depend only on the difference in expected value of the gambles. This suggests the possibility of developing response-display modes which would eliminate or at least attenuate the inconsistencies observed in risky decision processes.     

Duplex decomposition and general segregation of lotteries of a gain and a loss: An empirical evaluation

We investigate the empirical validity of two hypotheses, duplex decomposition (DD) and general segregation (GS), regarding decomposition of a binary gamble of a gain and a loss into two unitary gambles in which one consequence of each gamble is no change from the status quo. Four binary lotteries (money gambles with specified probabilities) and four decomposed lotteries designed to test GS and four decomposed lotteries to test DD were constructed, and certainty equivalents (CEs) were estimated for each lottery. Respondents’ indifference between a binary lottery and a decomposed lottery was determined by evaluating the equality between the CE of a mixed binary lottery and the CE of the corresponding decomposed lottery. Given the variability of estimates of CEs and the lack of a clear statistical definition for the equality between two CEs, we applied several criteria: we counted responses where the difference between two CEs was either ±2% (the strictest criterion), ±4%, ±6%, or ±8% (the most lenient criterion) of the range of lottery outcomes. The results showed that under the strictest criterion, GS held for 25% of the responses and DD for 22%. Under the most lenient criterion, GS held for 56% of the responses and DD for 52%. Depending upon the criterion used, between 39 and 75% of the responses were consistent with at least one of the hypotheses. Several methodological problems in determining the indifference between two lotteries are discussed.     

An eye‐tracking study on information processing in risky decisions: Evidence for compensatory strategies based on automatic processes

Many everyday decisions have to be made under risk and can be interpreted as choices between gambles with different outcomes that are realized with specific probabilities. The underlying cognitive processes were investigated by testing six sets of hypotheses concerning choices, decision times, and information search derived from cumulative prospect theory, decision field theory, priority heuristic and parallel constraint satisfaction models. Our participants completed 40 decision tasks of two gambles with two non‐negative outcomes each. Information search was recorded using eye‐tracking technology. Results for choices, decision time, the amount of information searched for, fixation durations, the direction of the information search, and the distribution of fixations conflict with the prediction of the non‐compensatory priority heuristic and indicate that individuals use compensatory strategies. Choice proportions are well in line with the predictions of cumulative prospect theory. Process measures indicate that individuals thereby do not rely on deliberate calculations of weighted sums. Information integration processes seem to be better explained by models that partially rely on automatic processes such as decision field theory or parallel constraint satisfaction models. Copyright © 2010 John Wiley & Sons, Ltd.     

Changing plans: Dynamic inconsistency and the effect of experience on the reference point

This article presents a new test of a principle of decision making calleddynamic consistency. This principle was tested in an experiment in which participants were asked to make decisions about a second gamble within a sequence of two gambles. Participants were first asked to make a planned choice about the second gamble. The planned choice was madebefore the first gamble was played and was conditioned on the anticipated outcomes of the first gamble.After the first gamble was played, the same participants were asked to make a final choice about the second gamble, conditioned on the experienced outcome of the first gamble. The results showed that participants’ final choices were frequently inconsistent with their plans, even when the anticipated and experienced outcomes were identical. These inconsistencies occurred in a systematic direction. Experiencing an anticipated gain resulted with a change toward risk aversion, and experiencing an anticipated loss resulted in a change toward risk seeking. These results are explained in terms of the effect of actual experience on the reference point used for the evaluation of the decision problem.     

Attention in risky choice

Previous research on the processes involved in risky decisions has rarely linked process data to choice directly. We used a simple measure based on the relative amount of attentional deployment to different components (gains/losses and their probabilities) of a risky gamble during the choice process, and we related this measure to the actual choice. In an experiment we recorded the decisions, decision times, and eye movements of 80 participants who made decisions on 11 choice problems. We used the number of eye fixations and fixation transitions to trace the deployment of attention during the choice process and obtained the following main results. First, different components of a gamble attracted different amounts of attention depending on participants' actual choice. This was reflected in both the number of fixations and the fixation transitions. Second, the last-fixated gamble but not the last-fixated reason predicted participants' choices. Third, a comparison of data obtained with eye tracking and data obtained with verbal protocols from a previous study showed a large degree of convergence regarding the process of risky choice. Together these findings tend to support dimensional decision strategies such as the priority heuristic.     

Risky visuomotor choices during rapid reaching in childhood

Many everyday actions are implicit gambles because imprecisions in our visuomotor systems place probabilities on our success or failure. Choosing optimal action strategies involves weighting the costs and gains of potential outcomes by their corresponding probabilities, and requires stable representations of one's own imprecisions. How this ability is acquired during development in childhood when visuomotor skills change drastically is unknown. In a rewarded rapid reaching task, 6‐ to 11‐year‐old children followed ‘risk‐seeking’ strategies leading to overly high point‐loss. Adults' performance, in contrast, was close to optimal. Children's errors were not explained by distorted estimates of value or probability, but may reflect different action selection criteria or immature integration of value and probability information while planning movements. These findings provide a starting point for understanding children's risk‐taking in everyday visuomotor situations when suboptimal choices can be dangerous. Moreover, children's risky visuomotor decisions mirror those reported for non‐motor gambles, raising the possibility that common processes underlie development across decision‐making domains.     

Information overload or search-amplified risk? Set size and order effects on decisions from experience

How do changes in choice-set size influence information search and subsequent decisions? Moreover, does information overload influence information processing with larger choice sets? We investigated these questions by letting people freely explore sets of gambles before choosing one of them, with the choice sets either increasing or decreasing in number for each participant (from two to 32 gambles). Set size influenced information search, with participants taking more samples overall, but sampling a smaller proportion of gambles and taking fewer samples per gamble, when set sizes were larger. The order of choice sets also influenced search, with participants sampling from more gambles and taking more samples overall if they started with smaller as opposed to larger choice sets. Inconsistent with information overload, information processing appeared consistent across set sizes and choice order conditions, reliably favoring gambles with higher sample means. Despite the lack of evidence for information overload, changes in information search did lead to systematic changes in choice: People who started with smaller choice sets were more likely to choose gambles with the highest expected values, but only for small set sizes. For large set sizes, the increase in total samples increased the likelihood of encountering rare events at the same time that the reduction in samples per gamble amplified the effect of these rare events when they occurred—what we call search-amplified risk. This led to riskier choices for individuals whose choices most closely followed the sample mean.     

Dominance violations in judged prices of two- and three-outcome gambles

The dominance principle states that one should prefer the option with consequences that are at least as good as those of other options for any state of the world. When applied to judged prices of gambles, the dominance principle requires that increasing one or more outcomes of a gamble should increase the judged price of the gamble, with everything else held constant. Previous research has uncovered systematic violations of the dominance principle: people assign higher prices to a gamble with a large probability of winning an amount, Y, otherwise zero, than they do to a superior gamble with the same chance of winning Y, otherwise winning a small amount, X! These violations can be explained by a configural-weight theory in which two-outcome gambles are represented with two sets of decision weights; one set for outcomes having values of zero and another set for lower-valued outcomes that have nonzero values. The present paper investigates whether dominance violations are limited to two-outcome gambles. Results show that people violate the dominance principle with three-outcome gambles even with financial incentives. Furthermore, results could be predicted from the configural-weight theory. The data do not support the view that configural weighting is caused by a shift in strategy that would apply only to two-outcome gambles.     

Inducing Thought Processes: Bringing Process Measures and Cognitive Processes Closer Together

The challenge in inferring cognitive processes from observational data is to correctly align overt behavior with its covert cognitive process. To improve our understanding of this overt–covert mapping in the domain of decision making, we collected eye‐movement data during decisions between gamble‐problems. Participants were either free to choose or instructed to use a specific choice strategy (maximizing expected value or a choice heuristic). We found large differences in looking patterns between free and instructed choices. Looking patterns provided no support for the common assumption that attention is equally distributed between outcomes and probabilities, even when participants were instructed to maximize expected value. Eye‐movement data are to some extent ambiguous with respect to underlying cognitive processes. Copyright © 2017 John Wiley & Sons, Ltd.