Economic irrationality is optimal during noisy decision making

(Ir)rationality of Moral Judgment

Chaotic responses to COVID-19, political polarization, and pervasive misinformation raise the question of whether some or many individuals exercise irrational moral judgment. We provide the first mathematically correct test for transitivity of moral preferences. Transitivity is the most prominent rationality criterion of the behavioral, biological, and economic sciences. However, transitivity is conceptually, mathematically, and statistically difficult to evaluate empirically. We tested three parsimonious, order-constrained, probabilistic characterizations: First, the weak utility model treats an individual's choices as noisy reflections of a single, deterministic, underlying transitive preference; second, a variant severely limits the allowable response noise; and third, by the general random utility hypothesis, individuals' choices reveal uncertain, but transitive, moral preferences. Among 28 individuals, everyone's data were consistent with the weak utility model and general random utility model, thus supporting both operationalizations. Tightening the bounds on error rates in noisy responses yielded a poorly performing model, thus rejecting the model according to which choices are highly consistent with a single transitive preference. Bayesian model selection favored probabilistic transitive preferences and hence the equivalent random utility hypothesis. This suggests that there is some order underlying the apparent chaos: Rather than presume widespread disregard for moral principles, policymakers may build on navigating and reconciling extreme heterogeneity compounded with individual uncertainty.

Early versus late noise differentially enhances or degrades context-dependent choice

Noise is a fundamental problem for information processing in neural systems. In decision-making, noise is thought to cause stochastic errors in choice. However, little is known about how noise arising from different sources may contribute differently to value coding and choice behaviors. Here, we examine how noise arising early versus late in the decision process differentially impacts context-dependent choice behavior. We find in model simulations that under early noise, contextual information enhances choice accuracy, while under late noise, context degrades choice accuracy. Furthermore, we verify these opposing predictions in experimental human choice behavior. Manipulating early and late noise - by inducing uncertainty in option values and controlling time pressure - produces dissociable positive and negative context effects. These findings reconcile controversial experimental findings in the literature, suggesting a unified mechanism for context-dependent choice. More broadly, these findings highlight how different sources of noise can interact with neural computations to differentially modulate behavior.

Better generalization through distraction? Concurrent load reduces the size of the inverse base-rate effect

The inverse base-rate effect (IBRE) is an irrational phenomenon in predictive learning. It occurs when people try to generalize what they have experienced to novel and ambiguous events. This irrational generalization manifests as a preference for rare, unlikely outcomes in the face of ambiguity. At least two formal mathematical models of this irrational preference (EXIT, NNRAS) lead to a counter-intuitive prediction: the effect reduces under concurrent load. We tested this prediction across two experiments ( N 1 = 72, M age = 20.12; N 2 = 160, M age = 20.88). We confirm the prediction, but only when participants were under an obvious time constraint. This empirical confirmation is as surprising as the prediction itself-irrationality reduces under increased task demands. Further, our data are more consistent with the NNRAS model than with EXIT, the most prominent model of the IBRE to date.

Origins of noise in both improving and degrading decision making

Noise is a fundamental problem for information processing in neural systems. In decision-making, noise is thought to cause stochastic errors in choice. However, little is known about how noise arising from different sources may contribute differently to value coding and choice behaviors. Here, we examine how noise arising early versus late in the decision process differentially impacts context-dependent choice behavior. We find in model simulations that under early noise, contextual information enhances choice accuracy, while under late noise, context degrades choice accuracy. Furthermore, we verify these opposing predictions in experimental human choice behavior. Manipulating early and late noise - by inducing uncertainty in option values and controlling time pressure - produces dissociable positive and negative context effects. These findings reconcile controversial experimental findings in the literature, suggesting a unified mechanism for context-dependent choice. More broadly, these findings highlight how different sources of noise can interact with neural computations to differentially modulate behavior.

Significance

The current study addresses the role of noise origin in decision-making, reconciling controversies around how decision-making is impacted by context. We demonstrate that different types of noise - either arising early during evaluation or late during option comparison - leads to distinct results: with early noise, context enhances choice accuracy, while with late noise, context impairs it. Understanding these dynamics offers potential strategies for improving decision-making in noisy environments and refining existing neural computation models. Overall, our findings advance our understanding of how neural systems handle noise in essential cognitive tasks, suggest a beneficial role for contextual modulation under certain conditions, and highlight the profound implications of noise structure in decision-making.

Frequent winners explain apparent skewness preferences in experience-based decisions

Do people's attitudes toward the (a)symmetry of an outcome distribution affect their choices? Financial investors seek return distributions with frequent small returns but few large ones, consistent with leading models of choice in economics and finance that assume right-skewed preferences. In contrast, many experiments in which decision-makers learn about choice options through experience find the opposite choice tendency, in favor of left-skewed options. To reconcile these seemingly contradicting findings, the present work investigates the effect of skewness on choices in experience-based decisions. Across seven studies, we show that apparent preferences for left-skewed outcome distributions are a consequence of those distributions having a higher value in most direct outcome comparisons, a "frequent-winner effect." By manipulating which option is the frequent winner, we show that choice tendencies for frequent winners can be obtained even with identical outcome distributions. Moreover, systematic choice tendencies in favor of right- or left-skewed options can be obtained by manipulating which option is experienced as the frequent winner. We also find evidence for an intrinsic preference for right-skewed outcome distributions. The frequent-winner phenomenon is robust to variations in outcome distributions and experimental paradigms. These findings are confirmed by computational analyses in which a reinforcement-learning model capturing frequent winning and intrinsic skewness preferences provides the best account of the data. Our work reconciles conflicting findings of aggregated behavior in financial markets and experiments and highlights the need for theories of decision-making sensitive to joint outcome distributions of the available options.

What's in a sample? Epistemic uncertainty and metacognitive awareness in risk taking

In a fundamentally uncertain world, sound information processing is a prerequisite for effective behavior. Given that information processing is subject to inevitable cognitive imprecision, decision makers should adapt to this imprecision and to the resulting epistemic uncertainty when taking risks. We tested this metacognitive ability in two experiments in which participants estimated the expected value of different number distributions from sequential samples and then bet on their own estimation accuracy. Results show that estimates were imprecise, and this imprecision increased with higher distributional standard deviations. Importantly, participants adapted their risk-taking behavior to this imprecision and hence deviated from the predictions of Bayesian models of uncertainty that assume perfect integration of information. To explain these results, we developed a computational model that combines Bayesian updating with a metacognitive awareness of cognitive imprecision in the integration of information. Modeling results were robust to the inclusion of an empirical measure of participants' perceived variability. In sum, we show that cognitive imprecision is crucial to understanding risk taking in decisions from experience. The results further demonstrate the importance of metacognitive awareness as a cognitive building block for adaptive behavior under (partial) uncertainty.

The ephemeral stories of our lives

Johnson et al. make a persuasive case that qualitative, story-like reasoning plays a crucial role in everyday thought and decision-making. This commentary questions the cohesiveness of this type of reasoning and the representations that generate it. Perhaps narratives do not underpin, but are ephemeral products of thought, created when we need to justify our actions to ourselves and others.

Unlocking a new dimension in the speed-accuracy trade-off

Why do we sometimes spend too much time on seemingly impossible-to-solve tasks instead of just moving on? Masís et al. provide a new perspective on the speed-accuracy trade-off (SAT), showing that, although prolonging deliberation looks suboptimal in the short run, it is a long-term investment that helps organisms reach proficient performance more rapidly.

Toward an Atlas of Canonical Cognitive Mechanisms

A central goal in Cognitive Science is understanding the mechanisms that underlie cognition. Here, we contend that Cognitive Science, despite intense multidisciplinary efforts, has furnished surprisingly few mechanistic insights. We attribute this slow mechanistic progress to the fact that cognitive scientists insist on performing underdetermined exercises, deriving overparametrized mechanistic theories of complex behaviors and seeking validation of these theories to the elusive notions of optimality and biological plausibility. We propose that mechanistic progress in Cognitive Science will accelerate once cognitive scientists start focusing on simpler explananda that will enable them to chart an atlas of elementary cognitive operations. Looking forward, the next challenge for Cognitive Science will be to understand how these elementary cognitive processes are pieced together to explain complex behavior.

EEG-representational geometries and psychometric distortions in approximate numerical judgment

When judging the average value of sample stimuli (e.g., numbers) people tend to either over- or underweight extreme sample values, depending on task context. In a context of overweighting, recent work has shown that extreme sample values were overly represented also in neural signals, in terms of an anti-compressed geometry of number samples in multivariate electroencephalography (EEG) patterns. Here, we asked whether neural representational geometries may also reflect a relative underweighting of extreme values (i.e., compression) which has been observed behaviorally in a great variety of tasks. We used a simple experimental manipulation (instructions to average a single-stream or to compare dual-streams of samples) to induce compression or anti-compression in behavior when participants judged rapid number sequences. Model-based representational similarity analysis (RSA) replicated the previous finding of neural anti-compression in the dual-stream task, but failed to provide evidence for neural compression in the single-stream task, despite the evidence for compression in behavior. Instead, the results indicated enhanced neural processing of extreme values in either task, regardless of whether extremes were over- or underweighted in subsequent behavioral choice. We further observed more general differences in the neural representation of the sample information between the two tasks. Together, our results indicate a mismatch between sample-level EEG geometries and behavior, which raises new questions about the origin of common psychometric distortions, such as diminishing sensitivity for larger values.

Behavioural and neural responses of crabs show evidence for selective attention in predator avoidance

Selective attention, the ability to focus on a specific stimulus and suppress distractions, plays a fundamental role for animals in many contexts, such as mating, feeding, and predation. Within natural environments, animals are often confronted with multiple stimuli of potential importance. Such a situation significantly complicates the decision-making process and imposes conflicting information on neural systems. In the context of predation, selectively attending to one of multiple threats is one possible solution. However, how animals make such escape decisions is rarely studied. A previous field study on the fiddler crab, Gelasimus dampieri, provided evidence of selective attention in the context of escape decisions. To identify the underlying mechanisms that guide their escape decisions, we measured the crabs' behavioural and neural responses to either a single, or two simultaneously approaching looming stimuli. The two stimuli were either identical or differed in contrast to represent different levels of threat certainty. Although our behavioural data provides some evidence that crabs perceive signals from both stimuli, we show that both the crabs and their looming-sensitive neurons almost exclusively respond to only one of two simultaneous threats. The crabs' body orientation played an important role in their decision about which stimulus to run away from. When faced with two stimuli of differing contrasts, both neurons and crabs were much more likely to respond to the stimulus with the higher contrast. Our data provides evidence that the crabs' looming-sensitive neurons play an important part in the mechanism that drives their selective attention in the context of predation. Our results support previous suggestions that the crabs' escape direction is calculated downstream of their looming-sensitive neurons by means of a population vector of the looming sensitive neuronal ensemble.

The repulsion effect in preferential choice and its relation to perceptual choice

People rely on the choice context to guide their decisions, violating fundamental principles of rational choice theory and exhibiting phenomena called context effects. Recent research has uncovered that dominance relationships can both increase or decrease the choice share of the dominating option, marking the two ends of an attraction-repulsion continuum. However, empirical links between the two opposing effects are scarce and theoretical accounts are missing altogether. The present study (N = 55) used eye tracking alongside a within-subject design that contrasts a perceptual task and a preferential-choice analog in order to bridge this gap and uncover the underlying information-search processes. Although individuals differed in their perceptual and preferential choices, they generally engaged in alternative-wise comparisons and a repulsion effect was present in both conditions that became weaker the more predominant the attribute-wise comparisons were. Altogether, our study corroborates the notion that repulsion effects are a robust and general phenomenon that theoretical accounts need to take seriously.

Implicit Counterfactual Effect in Partial Feedback Reinforcement Learning: Behavioral and Modeling Approach

Context remarkably affects learning behavior by adjusting option values according to the distribution of available options. Displaying counterfactual outcomes, the outcomes of the unchosen option alongside the chosen one (i.e., providing complete feedback), would increase the contextual effect by inducing participants to compare the two outcomes during learning. However, when the context only consists of the juxtaposition of several options and there is no such explicit counterfactual factor (i.e., only partial feedback is provided), it is not clear whether and how the contextual effect emerges. In this research, we employ Partial and Complete feedback paradigms in which options are associated with different reward distributions. Our modeling analysis shows that the model that uses the outcome of the chosen option for updating the values of both chosen and unchosen options in opposing directions can better account for the behavioral data. This is also in line with the diffusive effect of dopamine on the striatum. Furthermore, our data show that the contextual effect is not limited to probabilistic rewards, but also extends to magnitude rewards. These results suggest that by extending the counterfactual concept to include the effect of the chosen outcome on the unchosen option, we can better explain why there is a contextual effect in situations in which there is no extra information about the unchosen outcome.

Decision neuroscience and neuroeconomics: Recent progress and ongoing challenges

In the past decade, decision neuroscience and neuroeconomics have developed many new insights in the study of decision making. This review provides an overarching update on how the field has advanced in this time period. Although our initial review a decade ago outlined several theoretical, conceptual, methodological, empirical, and practical challenges, there has only been limited progress in resolving these challenges. We summarize significant trends in decision neuroscience through the lens of the challenges outlined for the field and review examples where the field has had significant, direct, and applicable impacts across economics and psychology. First, we review progress on topics including reward learning, explore-exploit decisions, risk and ambiguity, intertemporal choice, and valuation. Next, we assess the impacts of emotion, social rewards, and social context on decision making. Then, we follow up with how individual differences impact choices and new exciting developments in the prediction and neuroforecasting of future decisions. Finally, we consider how trends in decision-neuroscience research reflect progress toward resolving past challenges, discuss new and exciting applications of recent research, and identify new challenges for the field. This article is categorized under: Psychology > Reasoning and Decision Making Psychology > Emotion and Motivation.

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.

Asymmetric reinforcement learning facilitates human inference of transitive relations

Humans and other animals are capable of inferring never-experienced relations (for example, A > C) from other relational observations (for example, A > B and B > C). The processes behind such transitive inference are subject to intense research. Here we demonstrate a new aspect of relational learning, building on previous evidence that transitive inference can be accomplished through simple reinforcement learning mechanisms. We show in simulations that inference of novel relations benefits from an asymmetric learning policy, where observers update only their belief about the winner (or loser) in a pair. Across four experiments (n = 145), we find substantial empirical support for such asymmetries in inferential learning. The learning policy favoured by our simulations and experiments gives rise to a compression of values that is routinely observed in psychophysics and behavioural economics. In other words, a seemingly biased learning strategy that yields well-known cognitive distortions can be beneficial for transitive inferential judgements.

Ciranka, Linde-Domingo et al. show that inference of transitive orderings from pairwise relations benefits from a seemingly biased learning strategy, where observers update their belief about one of the pair members but not the other.

A Normative Account of Confirmation Bias During Reinforcement Learning

Reinforcement learning involves updating estimates of the value of states and actions on the basis of experience. Previous work has shown that in humans, reinforcement learning exhibits a confirmatory bias: when the value of a chosen option is being updated, estimates are revised more radically following positive than negative reward prediction errors, but the converse is observed when updating the unchosen option value estimate. Here, we simulate performance on a multi-arm bandit task to examine the consequences of a confirmatory bias for reward harvesting. We report a paradoxical finding: that confirmatory biases allow the agent to maximize reward relative to an unbiased updating rule. This principle holds over a wide range of experimental settings and is most influential when decisions are corrupted by noise. We show that this occurs because on average, confirmatory biases lead to overestimating the value of more valuable bandits and underestimating the value of less valuable bandits, rendering decisions overall more robust in the face of noise. Our results show how apparently suboptimal learning rules can in fact be reward maximizing if decisions are made with finite computational precision.

Building and Understanding the Minimal Self

Within the methodologically diverse interdisciplinary research on the minimal self, we identify two movements with seemingly disparate research agendas - cognitive science and cognitive (developmental) robotics. Cognitive science, on the one hand, devises rather abstract models which can predict and explain human experimental data related to the minimal self. Incorporating the established models of cognitive science and ideas from artificial intelligence, cognitive robotics, on the other hand, aims to build embodied learning machines capable of developing a self "from scratch" similar to human infants. The epistemic promise of the latter approach is that, at some point, robotic models can serve as a testbed for directly investigating the mechanisms that lead to the emergence of the minimal self. While both approaches can be productive for creating causal mechanistic models of the minimal self, we argue that building a minimal self is different from understanding the human minimal self. Thus, one should be cautious when drawing conclusions about the human minimal self based on robotic model implementations and vice versa. We further point out that incorporating constraints arising from different levels of analysis will be crucial for creating models that can predict, generate, and causally explain behavior in the real world.

Normative Principles for Decision-Making in Natural Environments

The decisions we make are shaped by a lifetime of learning. Past experience guides the way that we encode information in neural systems for perception and valuation, and determines the information we retrieve when making decisions. Distinct literatures have discussed how lifelong learning and local context shape decisions made about sensory signals, propositional information, or economic prospects. Here, we build bridges between these literatures, arguing for common principles of adaptive rationality in perception, cognition, and economic choice. We discuss how a single common framework, based on normative principles of efficient coding and Bayesian inference, can help us understand a myriad of human decision biases, including sensory illusions, adaptive aftereffects, choice history biases, central tendency effects, anchoring effects, contrast effects, framing effects, congruency effects, reference-dependent valuation, nonlinear utility functions, and discretization heuristics. We describe a simple computational framework for explaining these phenomena. Expected final online publication date for the Annual Review of Psychology, Volume 73 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A rational reinterpretation of dual-process theories

Highly influential "dual-process" accounts of human cognition postulate the coexistence of a slow accurate system with a fast error-prone system. But why would there be just two systems rather than, say, one or 93? Here, we argue that a dual-process architecture might reflect a rational tradeoff between the cognitive flexibility afforded by multiple systems and the time and effort required to choose between them. We investigate what the optimal set and number of cognitive systems would be depending on the structure of the environment. We find that the optimal number of systems depends on the variability of the environment and the difficulty of deciding when which system should be used. Furthermore, we find that there is a plausible range of conditions under which it is optimal to be equipped with a fast system that performs no deliberation ("System 1") and a slow system that achieves a higher expected accuracy through deliberation ("System 2"). Our findings thereby suggest a rational reinterpretation of dual-process theories.

Collective Choice May Tell Nothing About Anyone’s Individual Preferences

As has been known for over a century, aggregated preferences of a group may bear little or no similarity to the preference of any single individual, regardless of the aggregation method. Yet, it remains routine to fit or test theories of individual decision making on pooled data, and it remains routine to cast theories of individual decision making at the aggregate level. This mindset may have disastrous policy and business implications. A population of individuals who all satisfy one theory may behave collectively as though they satisfied a competing theory. A collection of individuals satisfying a given theory may collectively satisfy a version of the same theory with qualitatively different scientific or decision analytic implications. Because the resulting artifacts apply at the population level, replications, large samples, and high-quality data can do nothing to detect or repair them.

Confirmation bias is adaptive when coupled with efficient metacognition

Biases in the consideration of evidence can reduce the chances of consensus between people with different viewpoints. While such altered information processing typically leads to detrimental performance in laboratory tasks, the ubiquitous nature of confirmation bias makes it unlikely that selective information processing is universally harmful. Here, we suggest that confirmation bias is adaptive to the extent that agents have good metacognition, allowing them to downweight contradictory information when correct but still able to seek new information when they realize they are wrong. Using simulation-based modelling, we explore how the adaptiveness of holding a confirmation bias depends on such metacognitive insight. We find that the behavioural consequences of selective information processing are systematically affected by agents' introspective abilities. Strikingly, we find that selective information processing can even improve decision-making when compared with unbiased evidence accumulation, as long as it is accompanied by good metacognition. These results further suggest that interventions which boost people's metacognition might be efficient in alleviating the negative effects of selective information processing on issues such as political polarization.

This article is part of the theme issue ‘The political brain: neurocognitive and computational mechanisms’.

Optimal utility and probability functions for agents with finite computational precision

When making economic choices, such as those between goods or gambles, humans act as if their internal representation of the value and probability of a prospect is distorted away from its true value. These distortions give rise to decisions which apparently fail to maximize reward, and preferences that reverse without reason. Why would humans have evolved to encode value and probability in a distorted fashion, in the face of selective pressure for reward-maximizing choices? Here, we show that under the simple assumption that humans make decisions with finite computational precision--in other words, that decisions are irreducibly corrupted by noise--the distortions of value and probability displayed by humans are approximately optimal in that they maximize reward and minimize uncertainty. In two empirical studies, we manipulate factors that change the reward-maximizing form of distortion, and find that in each case, humans adapt optimally to the manipulation. This work suggests an answer to the longstanding question of why humans make "irrational" economic choices.

Retrospective Valuation of Experienced Outcome Encoded in Distinct Reward Representations in the Anterior Insula and Amygdala

Our ability to evaluate an experience retrospectively is important because it allows us to summarize its total value, and this summary value can then later be used as a guide in deciding whether the experience merits repeating, or whether instead it should rather be avoided. However, when an experience unfolds over time, humans tend to assign disproportionate weight to the later part of the experience, and this can lead to poor choice in repeating, or avoiding experience. Using model-based computational analyses of fMRI recordings in 27 male volunteers, we show that the human brain encodes the summary value of an extended sequence of outcomes in two distinct reward representations. We find that the overall experienced value is encoded accurately in the amygdala, but its merit is excessively marked down by disincentive anterior insula activity if the sequence of experienced outcomes declines temporarily. Moreover, the statistical strength of this neural code can separate efficient decision-makers from suboptimal decision-makers. Optimal decision-makers encode overall value more strongly, and suboptimal decision-makers encode the disincentive markdown (DM) more strongly. The separate neural implementation of the two distinct reward representations confirms that suboptimal choice for temporally extended outcomes can be the result of robust neural representation of a displeasing aspect of the experience such as temporary decline.SIGNIFICANCE STATEMENT One of the numerous foibles that prompt us to make poor decisions is known as the "Banker's fallacy," the tendency to focus on short-term growth at the expense of long-term value. This effect leads to unwarranted preference for happy endings. Here, we show that the anterior insula in the human brain marks down the overall value of an experience as it unfolds over time if the experience entails a sequence of predominantly negative temporal contrasts. By contrast, the amygdala encodes overall value accurately. These results provide neural indices for the dichotomy of decision utility and experienced utility popularized as Thinking fast and slow by Daniel Kahneman.

Asynchronous time-space model for evolutionary market

An economic system is thought to be evolutionary growing. Economists investigate human decision-making by monetary value. However, the emergent property of the economy has not been explained. A model considering the extent of the monetary value is required. In this paper, a time-space model is proposed to elucidate the economic evolution of a market. Since the market activities are always open and realtime, the model of time and space is complicated. For the complexity, the probabilistic boundary and expectations under a low-possibility are introduced. Then, time and space cannot be separated and are defined as an asynchronous relationship. We apply this time-space model to the adaptive agent models of single and double auctions. The results of the numerical simulation indicate the intermittency in a broad area of the control parameter. This result concludes that the extent of monetary value can be a basis of the evolutionary market.

A circuit mechanism for decision-making biases and NMDA receptor hypofunction

Decision-making biases can be features of normal behaviour, or deficits underlying neuropsychiatric symptoms. We used behavioural psychophysics, spiking-circuit modelling and pharmacological manipulations to explore decision-making biases during evidence integration. Monkeys showed a pro-variance bias (PVB): a preference to choose options with more variable evidence. The PVB was also present in a spiking circuit model, revealing a potential neural mechanism for this behaviour. To model possible effects of NMDA receptor (NMDA-R) antagonism on this behaviour, we simulated the effects of NMDA-R hypofunction onto either excitatory or inhibitory neurons in the model. These were then tested experimentally using the NMDA-R antagonist ketamine, a pharmacological model of schizophrenia. Ketamine yielded an increase in subjects' PVB, consistent with lowered cortical excitation/inhibition balance from NMDA-R hypofunction predominantly onto excitatory neurons. These results provide a circuit-level mechanism that bridges across explanatory scales, from the synaptic to the behavioural, in neuropsychiatric disorders where decision-making biases are prominent.

Efficient sampling and noisy decisions

Human decisions are based on finite information, which makes them inherently imprecise. But what determines the degree of such imprecision? Here, we develop an efficient coding framework for higher-level cognitive processes in which information is represented by a finite number of discrete samples. We characterize the sampling process that maximizes perceptual accuracy or fitness under the often-adopted assumption that full adaptation to an environmental distribution is possible, and show how the optimal process differs when detailed information about the current contextual distribution is costly. We tested this theory on a numerosity discrimination task, and found that humans efficiently adapt to contextual distributions, but in the way predicted by the model in which people must economize on environmental information. Thus, understanding decision behavior requires that we account for biological restrictions on information coding, challenging the often-adopted assumption of precise prior knowledge in higher-level decision systems.

Psychological mechanisms of loss aversion: A drift-diffusion decomposition

Decision makers often reject mixed gambles offering equal probabilities of a larger gain and a smaller loss. This important phenomenon, referred to as loss aversion, is typically explained by prospect theory, which proposes that decision makers give losses higher utility weights than gains. In this paper we consider alternative psychological mechanisms capable of explaining loss aversion, such as a fixed utility bias favoring rejection, as well as a bias favoring rejection prior to gamble valuation. We use a drift diffusion model of decision making to conceptually distinguish, formally define, and empirically measure these mechanisms. In two preregistered experiments, we show that the pre-valuation bias provides a very large contribution to model fits, predicts key response time patterns, reflects prior expectations regarding gamble desirability, and can be manipulated independently of the valuation process. Our results indicate that loss aversion is the result of multiple different psychological mechanisms, and that the pre-valuation bias is a fundamental determinant of this well-known behavioral tendency. These results have important implications for how we model behavior in risky choice tasks, and how we interpret its relationship with various psychological, clinical, and neurobiological variables.

Selective Integration during Sequential Sampling in Posterior Neural Signals

Decisions are typically made after integrating information about multiple attributes of alternatives in a choice set. Where observers are obliged to consider attributes in turn, a computational framework known as "selective integration" can capture salient biases in human choices. The model proposes that successive attributes compete for processing resources and integration is biased towards the alternative with the locally preferred attribute. Quantitative analysis shows that this model, although it discards choice-relevant information, is optimal when the observers' decisions are corrupted by noise that occurs beyond the sensory stage. Here, we used electroencephalography (EEG) to test a neural prediction of the model: that locally preferred attributes should be encoded with higher gain in neural signals over the posterior cortex. Over two sessions, human observers judged which of the two simultaneous streams of bars had the higher (or lower) average height. The selective integration model fits the data better than a rival model without bias. Single-trial analysis showed that neural signals contralateral to the preferred attribute covaried more steeply with the decision information conferred by locally preferred attributes. These findings provide neural evidence in support of selective integration, complementing existing behavioral work.

Evolutionary Processes in Quantum Decision Theory

The review presents the basics of quantum decision theory, with an emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. How an operationally-testable, rational choice between alternatives differs from a choice decorated by irrational feelings is elucidated. Quantum-classical correspondence is emphasized. A model of quantum intelligence network is described. Dynamic inconsistencies are shown to be resolved in the frame of the quantum decision theory.

Confidence drives a neural confirmation bias

A prominent source of polarised and entrenched beliefs is confirmation bias, where evidence against one's position is selectively disregarded. This effect is most starkly evident when opposing parties are highly confident in their decisions. Here we combine human magnetoencephalography (MEG) with behavioural and neural modelling to identify alterations in post-decisional processing that contribute to the phenomenon of confirmation bias. We show that holding high confidence in a decision leads to a striking modulation of post-decision neural processing, such that integration of confirmatory evidence is amplified while disconfirmatory evidence processing is abolished. We conclude that confidence shapes a selective neural gating for choice-consistent information, reducing the likelihood of changes of mind on the basis of new information. A central role for confidence in shaping the fidelity of evidence accumulation indicates that metacognitive interventions may help ameliorate this pervasive cognitive bias.

Judgments of effort exerted by others are influenced by received rewards

Estimating invested effort is a core dimension for evaluating own and others’ actions, and views on the relationship between effort and rewards are deeply ingrained in various societal attitudes. Internal representations of effort, however, are inherently noisy, e.g. due to the variability of sensorimotor and visceral responses to physical exertion. The uncertainty in effort judgments is further aggravated when there is no direct access to the internal representations of exertion – such as when estimating the effort of another person. Bayesian cue integration suggests that this uncertainty can be resolved by incorporating additional cues that are predictive of effort, e.g. received rewards. We hypothesized that judgments about the effort spent on a task will be influenced by the magnitude of received rewards. Additionally, we surmised that such influence might further depend on individual beliefs regarding the relationship between hard work and prosperity, as exemplified by a conservative work ethic. To test these predictions, participants performed an effortful task interleaved with a partner and were informed about the obtained reward before rating either their own or the partner’s effort. We show that higher rewards led to higher estimations of exerted effort in self-judgments, and this effect was even more pronounced for other-judgments. In both types of judgment, computational modelling revealed that reward information and sensorimotor markers of exertion were combined in a Bayes-optimal manner in order to reduce uncertainty. Remarkably, the extent to which rewards influenced effort judgments was associated with conservative world-views, indicating links between this phenomenon and general beliefs about the relationship between effort and earnings in society.

The role of expecting feedback during decision-making under risk

Sometimes choice is followed by outcome feedback and other times it is not. It remains unknown whether humans prefer gambling when they expect feedback to be revealed. Regarding this question, decision-making theories make alternative predictions. Some theories have proposed that choice is influenced by whether one expects to be disappointed in the future. Given that feedback is sometimes disappointing, these theories predict increased aversion towards gambling when feedback is expected compared to when feedback is not expected. The opposite effect is predicted by theories of curiosity, which postulate reduction of uncertainty as an important behavioural drive. Given that feedback reduces uncertainty, these theories predict that gambling will be favoured when feedback is expected. To examine whether expecting feedback influences gambling behaviour, we recorded functional neuroimaging data while participants performed a novel decision-making task requiring to chose between a sure option and a gamble. Crucially, participants expected to receive feedback in some trials but not in other trials. Consistent with theories of curiosity, we found that expecting feedback increased gambling propensity. At the neural level, at option presentation the increased value of gambling during feedback was reflected in activity in the ventral striatum. This suggests that, together with its established role in signalling reward, the ventral striatum also processes a form of epistemic value. Our study demonstrates that gambling becomes more attractive when feedback is expected and suggests that striatal activity could signal the value of feedback information.

Selective Integration: An Attentional Theory of Choice Biases and Adaptive Choice

Human choice behavior shows a range of puzzling anomalies. Even simple binary choices are modified by accept/reject framing and by the presence of decoy options, and they can exhibit circular (i.e., intransitive) patterns of preferences. Each of these phenomena is incompatible with many standard models of choice but may provide crucial clues concerning the elementary mental processes underpinning our choices. One promising theoretical account proposes that choice-related information is selectively gathered through an attentionally limited window favoring goal-consistent information. We review research showing attentional-mediated choice biases and present a computationally explicit model—selective integration—that accounts for these biases.

Pessimistic outcome expectancy does not explain ambiguity aversion in decision-making under uncertainty

When faced with a decision, most people like to know the odds and prefer to avoid ambiguity. It has been suggested that this aversion to ambiguity is linked to people's assumption of worst possible outcomes. We used two closely linked behavioural tasks in 78 healthy participants to investigate whether such pessimistic prior beliefs can explain ambiguity aversion. In the risk-taking task, participants had to decide whether or not they place a bet, while in the beliefs task, participants were asked what they believed would be the outcome. Unexpectedly, we found that in the beliefs task, participants were not overly pessimistic about the outcome in the ambiguity condition and in fact closer to optimal levels of decision-making than in the risk conditions. While individual differences in pessimism could explain outcome expectancy, they had no effect on ambiguity aversion. Consequently, ambiguity aversion is more likely caused by general caution than by expectation of negative outcomes despite pessimism-dependent subjective weighting of probabilities.

Optimal policy for multi-alternative decisions

Everyday decisions frequently require choosing among multiple alternatives. Yet the optimal policy for such decisions is unknown. Here we derive the normative policy for general multi-alternative decisions. This strategy requires evidence accumulation to nonlinear, time-dependent bounds that trigger choices. A geometric symmetry in those boundaries allows the optimal strategy to be implemented by a simple neural circuit involving normalization with fixed decision bounds and an urgency signal. The model captures several key features of the response of decision-making neurons as well as the increase in reaction time as a function of the number of alternatives, known as Hick's law. In addition, we show that in the presence of divisive normalization and internal variability, our model can account for several so-called 'irrational' behaviors, such as the similarity effect as well as the violation of both the independence of irrelevant alternatives principle and the regularity principle.

The formation of preference in risky choice

A key question in decision-making is how people integrate amounts and probabilities to form preferences between risky alternatives. Here we rely on the general principle of integration-to-boundary to develop several biologically plausible process models of risky-choice, which account for both choices and response-times. These models allowed us to contrast two influential competing theories: i) within-alternative evaluations, based on multiplicative interaction between amounts and probabilities, ii) within-attribute comparisons across alternatives. To constrain the preference formation process, we monitored eye-fixations during decisions between pairs of simple lotteries, designed to systematically span the decision-space. The behavioral results indicate that the participants' eye-scanning patterns were associated with risk-preferences and expected-value maximization. Crucially, model comparisons showed that within-alternative process models decisively outperformed within-attribute ones, in accounting for choices and response-times. These findings elucidate the psychological processes underlying preference formation when making risky-choices, and suggest that compensatory, within-alternative integration is an adaptive mechanism employed in human decision-making.

A General Approach to Prior Transformation

We present a general method for setting prior distributions in Bayesian models where parameters of interest are re-parameterized via a functional relationship. We generalize the results of Heck and Wagenmakers (2016) by considering the case where the dimension of the auxiliary parameter space does not equal that of the primary parameter space. We present numerical methods for carrying out prior specification for statistical models that do not admit closed-form solutions. Taken together, these results provide researchers a more complete set of tools for setting prior distributions that could be applied to many cognitive and decision making models. We illustrate our approach by reanalyzing data under the Selective Integration model of Tsetsos et al. (2016). We find, via a Bayes factor analysis, that the selective integration model with all four parameters generally outperforms both the three-parameter variant (omitting early cognitive noise) and the w = 1 variant (omitting selective gating), as well as an unconstrained competitor model. By contrast, Tsetsos et al. found the three parameter variant to be the best performing in a BIC analysis (in the absence of a competitor). Finally, we also include a pedagogical treatment of the mathematical tools necessary to formulate our results, including a simple "toy" example that illustrates our more general points.

Variable time preference

We re-examine behavioral patterns of intertemporal choice with recognition that time preferences may be inherently variable, focusing in particular on the explanatory power of an exponential discounting model with variable discount factors - the variable exponential model. We provide analytical results showing that this model can generate systematically different choice patterns from an exponential discounting model with a fixed discount factor. The variable exponential model accounts for the common behavioral pattern of decreasing impatience, which is typically attributed to hyperbolic discounting. The variable exponential model also generates violations of strong stochastic transitivity in choices involving intertemporal dominance. We present the results of two experiments designed to evaluate the variable exponential model in terms of quantitative fit to individual-level choice data. Data from these experiments reveal that allowing for a variable discount factor significantly improves the fit of the exponential model, and that a variable exponential model provides a better account of individual-level choice probabilities than hyperbolic discounting models. In a third experiment we find evidence of strong stochastic transitivity violations when intertemporal dominance is involved, in accordance with the variable exponential model. Overall, our analytical and experimental results indicate that exponential discounting can explain intertemporal choice behavior that was supposed to be beyond its descriptive scope if the discount factor is permitted to vary at random. Our results also highlight the importance of allowing for different sources of randomness in choice modeling.

The standard Bayesian model is normatively invalid for biological brains

We show that the benchmark Bayesian framework that Rahnev & Denison (R&D) used to assess optimality is actually suboptimal under realistic assumptions about how noise corrupts decision making in biological brains. This model is therefore invalid qua normative standard. We advise against generally forsaking optimality and argue that a biologically constrained definition of optimality could serve as an important driver for scientific progress.

Perceptual suboptimality: Bug or feature?

Rahnev & Denison (R&D) argue that whether people are "optimal" or "suboptimal" is not a well-posed question. We agree. However, we argue that the critical question is why humans make suboptimal perceptual decisions in the first place. We suggest that perceptual distortions have a normative explanation - that they promote efficient coding and computation in biological information processing systems.

Decision Making through Integration of Sensory Evidence at Prolonged Timescales

When multiple pieces of information bear on a decision, the best approach is to combine the evidence provided by each one. Evidence integration models formalize the computations underlying this process [1-3], explain human perceptual discrimination behavior [4-9], and correspond to neuronal responses elicited by discrimination tasks [10-14]. These findings suggest that evidence integration is key to understanding the neural basis of decision making [15-18]. But while evidence integration has most often been studied with simple tasks that limit deliberation to relatively brief periods, many natural decisions unfold over much longer durations. Neural network models imply acute limitations on the timescale of evidence integration [19-23], and it is currently unknown whether existing computational insights can generalize beyond rapid judgments. Here, we introduce a new psychophysical task and report model-based analyses of human behavior that demonstrate evidence integration at long timescales. Our task requires probabilistic inference using brief samples of visual evidence that are separated in time by long and unpredictable gaps. We show through several quantitative assays how decision making can approximate a normative integration process that extends over tens of seconds without accruing significant memory leak or noise. These results support the generalization of evidence integration models to a broader class of behaviors while posing new challenges for models of how these computations are implemented in biological networks.

Attentional Selection Mediates Framing and Risk-Bias Effects

Humans display a number of puzzling choice patterns that contradict basic principles of rationality. For example, they show preferences that change as a result of task framing or of adding irrelevant alternatives into the choice set. A recent theory has proposed that such choice and risk biases arise from an attentional mechanism that increases the relative weighting of goal-consistent information and protects the decision from noise after the sensory stage. Here, using a divided-attention method based on the dot-probe technique, we showed that attentional selection toward values congruent with the task goal takes place while participants make choices between alternatives that consist of payoff sequences. Moreover, we demonstrated that the magnitude of this attentional selection predicts risk attitudes, indicating a common underlying cognitive process. The results highlight the dynamic interplay between attention and choice mechanisms in producing framing effects and risk biases.

Value-based attentional capture affects multi-alternative decision making

Humans and other animals often violate economic principles when choosing between multiple alternatives, but the underlying neurocognitive mechanisms remain elusive. A robust finding is that adding a third option can alter the relative preference for the original alternatives, but studies disagree on whether the third option's value decreases or increases accuracy. To shed light on this controversy, we used and extended the paradigm of one study reporting a positive effect. However, our four experiments with 147 human participants and a reanalysis of the original data revealed that the positive effect is neither replicable nor reproducible. In contrast, our behavioral and eye-tracking results are best explained by assuming that the third option's value captures attention and thereby impedes accuracy. We propose a computational model that accounts for the complex interplay of value, attention, and choice. Our theory explains how choice sets and environments influence the neurocognitive processes of multi-alternative decision making.

Confirmation Bias through Selective Overweighting of Choice-Consistent Evidence

People's assessments of the state of the world often deviate systematically from the information available to them [1]. Such biases can originate from people's own decisions: committing to a categorical proposition, or a course of action, biases subsequent judgment and decision-making. This phenomenon, called confirmation bias [2], has been explained as suppression of post-decisional dissonance [3, 4]. Here, we provide insights into the underlying mechanism. It is commonly held that decisions result from the accumulation of samples of evidence informing about the state of the world [5-8]. We hypothesized that choices bias the accumulation process by selectively altering the weighting (gain) of subsequent evidence, akin to selective attention. We developed a novel psychophysical task to test this idea. Participants viewed two successive random dot motion stimuli and made two motion-direction judgments: a categorical discrimination after the first stimulus and a continuous estimation of the overall direction across both stimuli after the second stimulus. Participants' sensitivity for the second stimulus was selectively enhanced when that stimulus was consistent with the initial choice (compared to both, first stimuli and choice-inconsistent second stimuli). A model entailing choice-dependent selective gain modulation explained this effect better than several alternative mechanisms. Choice-dependent gain modulation was also established in another task entailing averaging of numerical values instead of motion directions. We conclude that intermittent choices direct selective attention during the evaluation of subsequent evidence, possibly due to decision-related feedback in the brain [9]. Our results point to a recurrent interplay between decision-making and selective attention.