The formation of preference in risky choice

Deliberation during online bargaining reveals strategic information

A standard assumption in game theory is that decision-makers have preplanned strategies telling them what actions to take for every contingency. In contrast, nonstrategic decisions often involve an on-the-spot comparison process, with longer response times (RT) for choices between more similarly appealing options. If strategic decisions also exhibit these patterns, then RT might betray private information and alter game theory predictions. Here, we examined bargaining behavior to determine whether RT reveals private information in strategic settings. Using preexisting and experimental data from eBay, we show that both buyers and sellers take hours longer to accept bad offers and to reject good offers. We find nearly identical patterns in the two datasets, indicating a causal effect of offer size on RT. However, this relationship is half as strong for rejections as for acceptances, reducing the amount of useful private information revealed by the sellers. Counter to our predictions, buyers are discouraged by slow rejections-they are less likely to counteroffer to slow sellers. We also show that a drift-diffusion model (DDM), traditionally limited to decisions on the order of seconds, can account for decisions on the order of hours, sometimes days. The DDM reveals that more experienced sellers are less cautious and more inclined to accept offers. In summary, strategic decisions are inconsistent with preplanned strategies. This underscores the need for game theory to incorporate RT as a strategic variable and broadens the applicability of the DDM to slow decisions.

Bayesian confidence in optimal decisions

The optimal way to make decisions in many circumstances is to track the difference in evidence collected in favor of the options. The drift diffusion model (DDM) implements this approach and provides an excellent account of decisions and response times. However, existing DDM-based models of confidence exhibit certain deficits, and many theories of confidence have used alternative, nonoptimal models of decisions. Motivated by the historical success of the DDM, we ask whether simple extensions to this framework might allow it to better account for confidence. Motivated by the idea that the brain will not duplicate representations of evidence, in all model variants decisions and confidence are based on the same evidence accumulation process. We compare the models to benchmark results, and successfully apply four qualitative tests concerning the relationships between confidence, evidence, and time, in a new preregistered study. Using computationally cheap expressions to model confidence on a trial-by-trial basis, we find that a subset of model variants also provide a very good to excellent account of precise quantitative effects observed in confidence data. Specifically, our results favor the hypothesis that confidence reflects the strength of accumulated evidence penalized by the time taken to reach the decision (Bayesian readout), with the penalty applied not perfectly calibrated to the specific task context. These results suggest there is no need to abandon the DDM or single accumulator models to successfully account for confidence reports. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Attention biases the process of risky decision-making: Evidence from eye-tracking

Attention determines what kind of option information is processed during risky choices owing to the limitation of visual attention. This paper reviews research on the relationship between higher-complexity risky decision-making and attention as illustrated by eye-tracking to explain the process of risky decision-making by the effect of attention. We demonstrate this process from three stages: the pre-phase guidance of options on attention, the process of attention being biased, and the impact of attention on final risk preference. We conclude that exogenous information can capture attention directly to salient options, thereby altering evidence accumulation. In particular, for multi-attribute risky decision-making, attentional advantages increase the weight of specific attributes, thus biasing risk preference in different directions. We highlight the significance of understanding how people use available information to weigh risks from an information-processing perspective via process data.

Risky decisions are influenced by individual attributes as a function of risk preference

It has long been assumed in economic theory that multi-attribute decisions involving several attributes or dimensions - such as probabilities and amounts of money to be earned during risky choices - are resolved by first combining the attributes of each option to form an overall expected value and then comparing the expected values of the alternative options, using a unique evidence accumulation process. A plausible alternative would be performing independent comparisons between the individual attributes and then integrating the results of the comparisons afterwards. Here, we devise a novel method to disambiguate between these types of models, by orthogonally manipulating the expected value of choice options and the relative salience of their attributes. Our results, based on behavioral measures and drift-diffusion models, provide evidence in favor of the framework where information about individual attributes independently impacts deliberation. This suggests that risky decisions are resolved by running in parallel multiple comparisons between the separate attributes - possibly alongside an additional comparison of expected value. This result stands in contrast with the assumption of standard economic theory that choices require a unique comparison of expected values and suggests that at the cognitive level, decision processes might be more distributed than commonly assumed. Beyond our planned analyses, we also discovered that attribute salience affects people of different risk preference type in different ways: risk-averse participants seem to focus more on probability, except when monetary amount is particularly high; risk-neutral/seeking participants, in contrast, seem to focus more on monetary amount, except when probability is particularly low.

Measuring utility with diffusion models

The drift diffusion model (DDM) is a prominent account of how people make decisions. Many of these decisions involve comparing two alternatives based on differences of perceived stimulus magnitudes, such as economic values. Here, we propose a consistent estimator for the parameters of a DDM in such cases. This estimator allows us to derive decision thresholds, drift rates, and subjective percepts (i.e., utilities in economic choice) directly from the experimental data. This eliminates the need to measure these values separately or to assume specific functional forms for them. Our method also allows one to predict drift rates for comparisons that did not occur in the dataset. We apply the method to two datasets, one comparing probabilities of earning a fixed reward and one comparing objects of variable reward value. Our analysis indicates that both datasets conform well to the DDM. We find that utilities are linear in probability and slightly convex in reward.

The effect of perceptual organization on numerical and preference-based decisions shows inter-subject correlation

Individual differences in cognitive processing have been the subject of intensive research. One important type of such individual differences is the tendency for global versus local processing, which was shown to correlate with a wide range of processing differences in fields such as decision making, social judgments and creativity. Yet, whether these global/local processing tendencies are correlated within a subject across different domains is still an open question. To address this question, we develop and test a novel method to quantify global/local processing tendencies, in which we directly set in opposition the local and global information instead of instructing subjects to specifically attend to one processing level. We apply our novel method to two different domains: (1) a numerical cognition task, and (2) a preference task. Using computational modeling, we accounted for classical effects in choice and numerical-cognition. Global/local tendencies in both tasks were quantified using a salience parameter. Critically, the salience parameters extracted from the numerical cognition and preference tasks were highly correlated, providing support for robust perceptual organization tendencies within an individual.

Complex economic decisions from simple neurocognitive processes: the role of interactive attention

Neurocognitive theories of value-based choice propose that people additively accumulate choice attributes when making decisions. These theories cannot explain the emergence of complex multiplicative preferences such as those assumed by prospect theory and other economic models. We investigate an interactive attention mechanism, according to which attention to attributes (like payoffs) depends on other attributes (like probabilities) attended to previously. We formalize this mechanism using a Markov attention model combined with an accumulator decision process, and test our model on eye-tracking and mouse-tracking data in risky choice. Our tests show that interactive attention is necessary to make good choices, that most participants display interactive attention and that allowing for interactive attention in accumulation-based decision models improves their predictions. By equipping established decision models with sophisticated attentional dynamics, we extend these models to describe complex economic choice, and in the process, we unify two prominent theoretical approaches to studying value-based decision making.

The composition of the choice set modulates probability weighting in risky decisions

Probability distortion-the tendency to underweight larger probabilities and overweight smaller ones-is a robust empirical phenomenon and an important driver of suboptimal choices. We reveal a novel contextual effect on probability distortion that depends on the composition of the choice set. Probability distortion was larger in a magnitude-diverse choice set (in which participants encountered more unique magnitudes than probabilities) but declined, resulting in more veridical weighting, in a probability-diverse choice set (more unique probabilities than magnitudes). This effect was consistent in two, large, independent datasets (N = 481, N = 100) and held for a subset of lotteries that were identical in the two contexts. It also developed gradually as a function of exposure to the choice set, was independent of attentional biases to probability versus magnitude information, and was specific to probability weighting, leaving risk attitudes unaffected. The results highlight the importance of context when processing probabilistic information.

Gaze-dependent evidence accumulation predicts multi-alternative risky choice behaviour

Choices are influenced by gaze allocation during deliberation, so that fixating an alternative longer leads to increased probability of choosing it. Gaze-dependent evidence accumulation provides a parsimonious account of choices, response times and gaze-behaviour in many simple decision scenarios. Here, we test whether this framework can also predict more complex context-dependent patterns of choice in a three-alternative risky choice task, where choices and eye movements were subject to attraction and compromise effects. Choices were best described by a gaze-dependent evidence accumulation model, where subjective values of alternatives are discounted while not fixated. Finally, we performed a systematic search over a large model space, allowing us to evaluate the relative contribution of different forms of gaze-dependence and additional mechanisms previously not considered by gaze-dependent accumulation models. Gaze-dependence remained the most important mechanism, but participants with strong attraction effects employed an additional similarity-dependent inhibition mechanism found in other models of multi-alternative multi-attribute choice.

Evidence integration and decision confidence are modulated by stimulus consistency

Evidence integration is a normative algorithm for choosing between alternatives with noisy evidence, which has been successful in accounting for vast amounts of behavioural and neural data. However, this mechanism has been challenged by non-integration heuristics, and tracking decision boundaries has proven elusive. Here we first show that the decision boundaries can be extracted using a model-free behavioural method termed decision classification boundary, which optimizes choice classification based on the accumulated evidence. Using this method, we provide direct support for evidence integration over non-integration heuristics, show that the decision boundaries collapse across time and identify an integration bias whereby incoming evidence is modulated based on its consistency with preceding information. This consistency bias, which is a form of pre-decision confirmation bias, was supported in four cross-domain experiments, showing that choice accuracy and decision confidence are modulated by stimulus consistency. Strikingly, despite its seeming sub-optimality, the consistency bias fosters performance by enhancing robustness to integration noise.

A causal role for the right frontal eye fields in value comparison

Recent studies have suggested close functional links between overt visual attention and decision making. This suggests that the corresponding mechanisms may interface in brain regions known to be crucial for guiding visual attention - such as the frontal eye field (FEF). Here, we combined brain stimulation, eye tracking, and computational approaches to explore this possibility. We show that inhibitory transcranial magnetic stimulation (TMS) over the right FEF has a causal impact on decision making, reducing the effect of gaze dwell time on choice while also increasing reaction times. We computationally characterize this putative mechanism by using the attentional drift diffusion model (aDDM), which reveals that FEF inhibition reduces the relative discounting of the non-fixated option in the comparison process. Our findings establish an important causal role of the right FEF in choice, elucidate the underlying mechanism, and provide support for one of the key causal hypotheses associated with the aDDM.

Influence of the Manner of Information Presentation on Risky Choice

We are constantly faced with decisive situations in which the options are not presented simultaneously. How the information of options is presented might influence the subsequent decision-making. For instance, presenting the information of options in an alternative- or dimension-wise manner may affect searching patterns and thus lead to different choices. In this study, the effects of this manner of information presentation on risky choice according to two experiments (Experiment 1, N = 45; Experiment 2, N = 50) are systematically examined. Specifically, two tasks with different presentation are conducted. Participants could search the information of one option (alternative-wise task) or dimension (dimension-wise task) for each time. Results revealed that the participants assigned in the alternative-wise task exhibited more choices consistent with expected value theory and took a longer decision time than those in the dimension-wise task. Moreover, the effect of task on choice was mediated by the direction of information search. These findings suggest a relationship between information search pattern and risky choice and allow for a better understanding of the mechanisms and processes involved in risky choice.

Neural correlates of visual attention during risky decision evidence integration

Value-based decision-making is presumed to involve a dynamic integration process that supports assessing the potential outcomes of different choice options. Decision frameworks assume the value of a decision rests on both the desirability and risk surrounding an outcome. Previous work has highlighted neural representations of risk in the human brain, and their relation to decision choice. Key neural regions including the insula and anterior cingulate cortex (ACC) have been implicated in encoding the effects of risk on decision outcomes, including approach and avoidance. Yet, it remains unknown whether these regions are involved in the dynamic integration processes that precede and drive choice, and their relationship with ongoing attention. Here, we used concurrent fMRI and eye-tracking to discern neural activation related to visual attention preceding choice between sure-thing (i.e. safe) and risky gamble options. We found activation in both dorsal ACC (dACC) and posterior insula (PI) scaled in opposite directions with the difference in attention to risky rewards relative to risky losses. PI activation also differentiated foveations on both risky options (rewards and losses) relative to a sure-thing option. These findings point to ACC involvement in ongoing evaluation of risky but higher value options. The role of PI in risky outcomes points to a more general evaluative role in the decision-making that compares both safe and risky outcomes, irrespective of potential for gains or losses.

Using dynamic monitoring of choices to predict and understand risk preferences

Navigating conflict is integral to decision-making, serving a central role both in the subjective experience of choice as well as contemporary theories of how we choose. However, the lack of a sensitive, accessible, and interpretable metric of conflict has led researchers to focus on choice itself rather than how individuals arrive at that choice. Using mouse-tracking-continuously sampling computer mouse location as participants decide-we demonstrate the theoretical and practical uses of dynamic assessments of choice from decision onset through conclusion. Specifically, we use mouse tracking to index conflict, quantified by the relative directness to the chosen option, in a domain for which conflict is integral: decisions involving risk. In deciding whether to accept risk, decision makers must integrate gains, losses, status quos, and outcome probabilities, a process that inevitably involves conflict. Across three preregistered studies, we tracked participants' motor movements while they decided whether to accept or reject gambles. Our results show that 1) mouse-tracking metrics of conflict sensitively detect differences in the subjective value of risky versus certain options; 2) these metrics of conflict strongly predict participants' risk preferences (loss aversion and decreasing marginal utility), even on a single-trial level; 3) these mouse-tracking metrics outperform participants' reaction times in predicting risk preferences; and 4) manipulating risk preferences via a broad versus narrow bracketing manipulation influences conflict as indexed by mouse tracking. Together, these results highlight the importance of measuring conflict during risky choice and demonstrate the usefulness of mouse tracking as a tool to do so.