Modeling 2-alternative forced-choice tasks: Accounting for both magnitude and difference effects

Efficiency in redundancy

In engineering, redundancy is the duplication of vital systems for use in the event of failure. In studies of human cognition, redundancy often refers to the duplication of the signal. Scores of studies have shown the salutary effects of a combined auditory and visual signal over single modality, the advantage of processing complete faces over facial features, and more recently the advantage of two observers over one. But what if the signal (or the number of observers) is fixed and cannot be altered or augmented? Can people improve the efficiency of information processing by recruiting an additional, redundant system? Here we demonstrate that recruiting a second redundant system can, under reasonable assumptions about human capacity, result in improved performance. Recruiting a second redundant system may come with a higher energy cost, but may be worthwhile in high-stakes situations where processing information accurately is crucial.

Neural correlates of confidence during decision formation in a perceptual judgment task

When we make a decision, we also estimate the probability that our choice is correct or accurate. This probability estimate is termed our degree of decision confidence. Recent work has reported event-related potential (ERP) correlates of confidence both during decision formation (the centro-parietal positivity component; CPP) and after a decision has been made (the error positivity component; Pe). However, there are several measurement confounds that complicate the interpretation of these findings. More recent studies that overcome these issues have so far produced conflicting results. To better characterise the ERP correlates of confidence we presented participants with a comparative brightness judgment task while recording electroencephalography. Participants judged which of two flickering squares (varying in luminance over time) was brighter on average. Participants then gave confidence ratings ranging from "surely incorrect" to "surely correct". To elicit a range of confidence ratings we manipulated both the mean luminance difference between the brighter and darker squares (relative evidence) and the overall luminance of both squares (absolute evidence). We found larger CPP amplitudes in trials with higher confidence ratings. This association was not simply a by-product of differences in relative evidence (which covaries with confidence) across trials. We did not identify postdecisional ERP correlates of confidence, except when they were artificially produced by pre-response ERP baselines. These results provide further evidence for neural correlates of processes that inform confidence judgments during decision formation.

"Reliable organisms from unreliable components" revisited: the linear drift, linear infinitesimal variance model of decision making

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann's (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann's problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann's problem do not address the main theoretical question that historically motivated research in this area.

Quantifying aberrant approach-avoidance conflict in psychopathology: A review of computational approaches

Making effective decisions during approach-avoidance conflict is critical in daily life. Aberrant decision-making during approach-avoidance conflict is evident in a range of psychological disorders, including anxiety, depression, trauma-related disorders, substance use disorders, and alcohol use disorders. To help clarify etiological pathways and reveal novel intervention targets, clinical research into decision-making is increasingly adopting a computational psychopathology approach. This approach uses mathematical models that can identify specific decision-making related processes that are altered in mental health disorders. In our review, we highlight foundational approach-avoidance conflict research, followed by more in-depth discussion of computational approaches that have been used to model behavior in these tasks. Specifically, we describe the computational models that have been applied to approach-avoidance conflict (e.g., drift-diffusion, active inference, and reinforcement learning models), and provide resources to guide clinical researchers who may be interested in applying computational modeling. Finally, we identify notable gaps in the current literature and potential future directions for computational approaches aimed at identifying mechanisms of approach-avoidance conflict in psychopathology.

Assessing evidence accumulation and rule learning in humans with an online game

Evidence accumulation, an essential component of perception and decision making, is frequently studied with psychophysical tasks involving noisy or ambiguous stimuli. In these tasks, participants typically receive verbal or written instructions that describe the strategy that should be used to guide decisions. Although convenient and effective, explicit instructions can influence learning and decision making strategies and can limit comparisons with animal models, in which behaviors are reinforced through feedback. Here, we developed an online video game and nonverbal training pipeline, inspired by pulse-based tasks for rodents, as an alternative to traditional psychophysical tasks used to study evidence accumulation. Using this game, we collected behavioral data from hundreds of participants trained with an explicit description of the decision rule or with experiential feedback. Participants trained with feedback alone learned the game rules rapidly and used strategies and displayed biases similar to those who received explicit instructions. Finally, by leveraging data across hundreds of participants, we show that perceptual judgments were well described by an accumulation process in which noise scaled nonlinearly with evidence, consistent with previous animal studies but inconsistent with diffusion models widely used to describe perceptual decisions in humans. These results challenge the conventional description of the accumulation process and suggest that online games provide a valuable platform to examine perceptual decision making and learning in humans. In addition, the feedback-based training pipeline developed for this game may be useful for evaluating perceptual decision making in human populations with difficulty following verbal instructions.NEW & NOTEWORTHY Perceptual uncertainty sets critical constraints on our ability to accumulate evidence and make decisions; however, its sources remain unclear. We developed a video game, and feedback-based training pipeline, to study uncertainty during decision making. Leveraging choices from hundreds of subjects, we demonstrate that human choices are inconsistent with popular diffusion models of human decision making and instead are best fit by models in which perceptual uncertainty scales nonlinearly with the strength of sensory evidence.

Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making

Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity.

Analysis of decisions based on option value (e.g. which pile of coins would you like?) suggests that the optimal rules correspond to simple mechanisms also known to be optimal for perceptual decisions (e.g. which light is brighter?) But, crucially, these analyses assume that the cost of time is linear—when the more usual assumption is made that time discounts multiplicatively (e.g. ‘a bird in the hand is worth two in the bush (and so two in the hand are worth four in the bush)’) then optimal decision-making looks quite different—in particular, the theory predicts that decision-making should be sensitive to the absolute magnitude of the opportunities, such as coin pile sizes, under consideration, in a way that the optimal perceptual mechanisms are not. As well as the theory, we present novel experimental evidence from human decision-making experiments, and foraging slime mould, of precisely such magnitude-sensitivity. This is a rare example of theory in behaviour making a falsifiable prediction that is confirmed in two, highly divergent, species, one with a brain and one without.

Winner Takes All! What Are Race Models, and Why and How Should Psychologists Use Them?

Interest in the processes that mediate between stimuli and responses is at the heart of most modern psychology and neuroscience. These processes cannot be directly measured but instead must be inferred from observed responses. Race models, through their ability to account for both response choices and response times, have been a key enabler of such inferences. Examples of such models appeared contemporaneously with the cognitive revolution, and since then have become increasingly prominent and elaborated, so that psychologists now have a powerful array of race models at their disposal. We showcase the state of the art for race models and describe why and how they are used.

Divergent effects of absolute evidence magnitude on decision accuracy and confidence in perceptual judgements

Whether people change their mind after making a perceptual judgement may depend on how confident they are in their decision. Recently, it was shown that, when making perceptual judgements about stimuli containing high levels of 'absolute evidence' (i.e., the overall magnitude of sensory evidence across choice options), people make less accurate decisions and are also slower to change their mind and correct their mistakes. Here we report two studies that investigated whether high levels of absolute evidence also lead to increased decision confidence. We used a luminance judgment task in which participants decided which of two dynamic, flickering stimuli was brighter. After making a decision, participants rated their confidence. We manipulated relative evidence (i.e., the mean luminance difference between the two stimuli) and absolute evidence (i.e., the summed luminance of the two stimuli). In the first experiment, we found that higher absolute evidence was associated with decreased decision accuracy but increased decision confidence. In the second experiment, we additionally manipulated the degree of luminance variability to assess whether the observed effects were due to differences in perceived evidence variability. We replicated the results of the first experiment but did not find substantial effects of luminance variability on confidence ratings. Our findings support the view that decisions and confidence judgements are based on partly dissociable sources of information, and suggest that decisions initially made with higher confidence may be more resistant to subsequent changes of mind.

Modeling evidence accumulation decision processes using integral equations: Urgency-gating and collapsing boundaries

Diffusion models of evidence accumulation have successfully accounted for the distributions of response times and choice probabilities from many experimental tasks, but recently their assumption that evidence is accumulated at a constant rate to constant decision boundaries has been challenged. One model assumes that decision-makers seek to optimize their performance by using decision boundaries that collapse over time. Another model assumes that evidence does not accumulate and is represented by a stationary distribution that is gated by an urgency signal to make a response. We present explicit, integral-equation expressions for the first-passage time distributions of the urgency-gating and collapsing-bounds models and use them to identify conditions under which the models are equivalent. We combine these expressions with a dynamic model of stimulus encoding that allows the effects of perceptual and decisional integration to be distinguished. We compare the resulting models to the standard diffusion model with variability in drift rates on data from three experimental paradigms in which stimulus information was either constant or changed over time. The standard diffusion model was the best model for tasks with constant stimulus information; the models with time-varying urgency or decision bounds performed similarly to the standard diffusion model on tasks with changing stimulus information. We found little support for the claim that evidence does not accumulate and attribute the good performance of the time-varying models on changing-stimulus tasks to their increased flexibility and not to their ability to account for systematic experimental effects. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Neural Signature of Buying Decisions in Real-World Online Shopping Scenarios – An Exploratory Electroencephalography Study Series

The neural underpinnings of decision-making are critical to understanding and predicting human behavior. However, findings from decision neuroscience are limited in their practical applicability due to the gap between experimental decision-making paradigms and real-world choices. The present manuscript investigates the neural markers of buying decisions in a fully natural purchase setting: participants are asked to use their favorite online shopping applications to buy common goods they are currently in need of. Their electroencephalography (EEG) is recorded while they view the product page for each item. EEG responses to pages for products that are eventually bought are compared to those that are discarded. Study 1 repeats this procedure in three batches with different participants, product types, and time periods. In an explorative analysis, two neural markers for buying compared to no-buying decisions are discovered over all three batches: frontal alpha asymmetry peak and frontal theta power peak. Occipital alpha power at alpha asymmetry peaks differs in only one of the three batches. No further significant markers are found. Study 2 compares the natural product search to a design in which subjects are told which product pages to view. In both settings, the frontal alpha asymmetry peak is increased for buying decisions. Frontal theta peak increase is replicated only when subjects search through product pages by themselves. The present study series represents an attempt to find neural markers of real-world decisions in a fully natural environment and explore how those markers can change due to small adjustments for the sake of experimental control. Limitations and practical applicability of the real-world approach to studying decision-making are discussed.

High-value decisions are fast and accurate, inconsistent with diminishing value sensitivity

It is a widely held belief that people's choices are less sensitive to changes in value as value increases. For example, the subjective difference between $11 and $12 is believed to be smaller than between $1 and $2. This idea is consistent with applications of the Weber-Fechner Law and divisive normalization to value-based choice and with psychological interpretations of diminishing marginal utility. According to random utility theory in economics, smaller subjective differences predict less accurate choices. Meanwhile, in the context of sequential sampling models in psychology, smaller subjective differences also predict longer response times. Based on these models, we would predict decisions between high-value options to be slower and less accurate. In contrast, some have argued on normative grounds that choices between high-value options should be made with less caution, leading to faster and less accurate choices. Here, we model the dynamics of the choice process across three different choice domains, accounting for both discriminability and response caution. Contrary to predictions, we mostly observe faster and more accurate decisions (i.e., higher drift rates) between high-value options. We also observe that when participants are alerted about incoming high-value decisions, they exert more caution and not less. We rule out several explanations for these results, using tasks with both subjective and objective values. These results cast doubt on the notion that increasing value reduces discriminability.

An initial 'snapshot' of sensory information biases the likelihood and speed of subsequent changes of mind

We often need to rapidly change our mind about perceptual decisions in order to account for new information and correct mistakes. One fundamental, unresolved question is whether information processed prior to a decision being made ('pre-decisional information') has any influence on the likelihood and speed with which that decision is reversed. We investigated this using a luminance discrimination task in which participants indicated which of two flickering greyscale squares was brightest. Following an initial decision, the stimuli briefly remained on screen, and participants could change their response. Using psychophysical reverse correlation, we examined how moment-to-moment fluctuations in stimulus luminance affected participants' decisions. This revealed that the strength of even the very earliest (pre-decisional) evidence was associated with the likelihood and speed of later changes of mind. To account for this effect, we propose an extended diffusion model in which an initial 'snapshot' of sensory information biases ongoing evidence accumulation.

Magnitude-sensitivity: rethinking decision-making

Magnitude-sensitivity refers to the result that performance in decision-making, across domains and organisms, is affected by the total value of the possible alternatives. This simple result offers a window into fundamental issues in decision-making and has led to a reconsideration of ecological decision-making, prominent computational models of decision-making, and optimal decision-making. Moreover, magnitude-sensitivity has inspired the design of new robotic systems that exploit natural solutions and apply optimal decision-making policies. In this article, we review the key theoretical and empirical results about magnitude-sensitivity and highlight the importance that this phenomenon has for the understanding of decision-making. Furthermore, we discuss open questions and ideas for future research.

Input-dependent noise can explain magnitude-sensitivity in optimal value-based decision-making

Recent work has derived the optimal policy for two-alternative value-based decisions, in which decision-makers compare the subjective expected reward of two alternatives. Under specific task assumptions — such as linear utility, linear cost of time and constant processing noise — the optimal policy is implemented by a diffusion process in which parallel decision thresholds collapse over time as a function of prior knowledge about average reward across trials. This policy predicts that the decision dynamics of each trial are dominated by the difference in value between alternatives and are insensitive to the magnitude of the alternatives (i.e., their summed values). This prediction clashes with empirical evidence showing magnitude-sensitivity even in the case of equal alternatives, and with ecologically plausible accounts of decision making. Previous work has shown that relaxing assumptions about linear utility or linear time cost can give rise to optimal magnitude-sensitive policies. Here we question the assumption of constant processing noise, in favour of input-dependent noise. The neurally plausible assumption of input-dependent noise during evidence accumulation has received strong support from previous experimental and modelling work. We show that including input-dependent noise in the evidence accumulation process results in a magnitude-sensitive optimal policy for value-based decision-making, even in the case of a linear utility function and a linear cost of time, for both single (i.e., isolated) choices and sequences of choices in which decision-makers maximise reward rate. Compared to explanations that rely on non-linear utility functions and/or non-linear cost of time, our proposed account of magnitude-sensitive optimal decision-making provides a parsimonious explanation that bridges the gap between various task assumptions and between various types of decision making.

Multi-Odor Discrimination by Rat Sniffing for Potential Monitoring of Lung Cancer and Diabetes

The discrimination learning of multiple odors, in which multi-odor can be associated with different responses, is important for responding quickly and accurately to changes in the external environment. However, very few studies have been done on multi-odor discrimination by animal sniffing. Herein, we report a novel multi-odor discrimination system by detection rats based on the combination of 2-Choice and Go/No-Go (GNG) tasks into a single paradigm, in which the Go response of GNG was replaced by 2-Choice, for detection of toluene and acetone, which are odor indicators of lung cancer and diabetes, respectively. Three of six trained rats reached performance criterion, in 12 consecutive successful tests within a given set or over 12 sets with a success rate of over 90%. Through a total of 1300 tests, the trained animals (N = 3) showed multi-odor sensing performance with 88% accuracy, 87% sensitivity and 90% specificity. In addition, a dependence of behavior response time on odor concentrations under given concentration conditions was observed, suggesting that the system could be used for quantitative measurements. Furthermore, the animals’ multi-odor sensing performance has lasted for 45 days, indicating long-term stability of the learned multi-odor discrimination. These findings demonstrate that multi-odor discrimination can be achieved by rat sniffing, potentially providing insight into the rapid, accurate and cost-effective multi-odor monitoring in the lung cancer and diabetes.

Does Attention Increase the Value of Choice Alternatives?

A growing recognition of the role of attention in decision-making has been driven by both the technology of eye tracking and the development of models that explicitly incorporate attention. One result of this convergence is the arresting claim that attention, by itself, can increase the perceived value of a decision alternative. In this review, we cover the origins of that claim, its empirical foundation, and the reasoning that supports it. The conclusion is that, to date, there is not sufficient evidence to support the claim. Alternative explanations for the extant evidentiary base are discussed, as is the balance between the bottom-up influence of empirical evidence and the top-down commitment to a conceptual framework.

A new model of decision processing in instrumental learning tasks

Learning and decision-making are interactive processes, yet cognitive modeling of error-driven learning and decision-making have largely evolved separately. Recently, evidence accumulation models (EAMs) of decision-making and reinforcement learning (RL) models of error-driven learning have been combined into joint RL-EAMs that can in principle address these interactions. However, we show that the most commonly used combination, based on the diffusion decision model (DDM) for binary choice, consistently fails to capture crucial aspects of response times observed during reinforcement learning. We propose a new RL-EAM based on an advantage racing diffusion (ARD) framework for choices among two or more options that not only addresses this problem but captures stimulus difficulty, speed-accuracy trade-off, and stimulus-response-mapping reversal effects. The RL-ARD avoids fundamental limitations imposed by the DDM on addressing effects of absolute values of choices, as well as extensions beyond binary choice, and provides a computationally tractable basis for wider applications.

Perceptual change-of-mind decisions are sensitive to absolute evidence magnitude

To navigate the world safely, we often need to rapidly 'change our mind' about decisions. Current models assume that initial decisions and change-of-mind decisions draw upon common sources of sensory evidence. In two-choice scenarios, this evidence may be 'relative' or 'absolute'. For example, when judging which of two objects is the brightest, the luminance difference and luminance ratio between the two objects are sources of 'relative' evidence, which are invariant across additive and multiplicative luminance changes. Conversely, the overall luminance of the two objects combined is a source of 'absolute' evidence, which necessarily varies across symmetric luminance manipulations. Previous studies have shown that initial decisions are sensitive to both relative and absolute evidence; however, it is unknown whether change-of-mind decisions are sensitive to absolute evidence. Here, we investigated this question across two experiments. In each experiment participants indicated which of two flickering greyscale squares was brightest. Following an initial decision, the stimuli remained on screen for a brief period and participants could change their response. To investigate the effect of absolute evidence, the overall luminance of the two squares was varied whilst either the luminance difference (Experiment 1) or luminance ratio (Experiment 2) was held constant. In both experiments we found that increases in absolute evidence led to faster, less accurate initial responses and slower changes of mind. Change-of-mind accuracy decreased when the luminance difference was held constant, but remained unchanged when the luminance ratio was fixed. We show that the three existing change-of-mind models cannot account for our findings. We then fit three alternative models, previously used to account for the effect of absolute evidence on one-off decisions, to the data. A leaky competing accumulator model best accounted for the changes in behaviour across absolute evidence conditions - suggesting an important role for input-dependent leak in explaining perceptual changes of mind.

Examining aging and numerosity using an integrated diffusion model

Two experiments are presented that use tasks common in research in numerical cognition with young adults and older adults as subjects. In these tasks, one or two arrays of dots are displayed, and subjects decide whether there are more or fewer dots of one kind than another. Results show that older adults, relative to young adults, tend to rely more on the perceptual feature, area, in making numerosity judgments when area is correlated with numerosity. Also, convex hull unexpectedly shows different effects depending on the task (being either correlated with numerosity or anticorrelated). Accuracy and response time (RT) data are interpreted with the integration of the diffusion decision model with models for the representation of numerosity. One model assumes that the representation of the difference depends on the difference between the numerosities and that standard deviations (SDs) increase linearly with numerosity, and the other model assumes a log representation with constant SDs. The representational models have coefficients that are applied to differences between two numerosities to produce drift rates and SDs in drift rates in the decision process. The two tasks produce qualitatively different patterns of RTs: One model fits results from one task, but the results are mixed for the other task. The effects of age on model parameters show a modest decrease in evidence driving the decision process, an increase in the duration of processes outside the decision process (nondecision time), and an increase in the amount of evidence needed to make a decision (boundary separation). (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Modeling the interaction of numerosity and perceptual variables with the diffusion model

Ratcliff and McKoon (2018) proposed integrated diffusion models for numerosity judgments in which a numerosity representation provides evidence used to drive the decision process. We extend this modeling framework to examine the interaction of non-numeric perceptual variables with numerosity by assuming that drift rate and non-decision time are functions of those variables. Four experiments were conducted with two different types of stimuli: a single array of intermingled blue and yellow dots in which both numerosity and dot area vary over trials and two side-by-side arrays of dots in which numerosity, dot area, and convex hull vary over trials. The tasks were to decide whether there were more blue or yellow dots (two experiments), more dots on which side, or which dots have a larger total area. Development of models started from the principled models in Ratcliff and McKoon (2018) and became somewhat ad hoc as we attempted to capture unexpected patterns induced by the conflict between numerosity and perceptual variables. In the three tasks involving numerosity judgments, the effects of the non-numeric variables were moderated by the number of dots. Under a high conflict, judgments were dominated by perceptual variables and produced an unexpected shift in the leading edge of the reaction time (RT) distributions. Although the resulting models were able to predict most of the accuracy and RT patterns, the models were not able to completely capture this shift in the RT distributions. However, when subjects judged area, numerosity affected perceptual judgments but there was no leading edge effect. Based on the results, it appears that the integrated diffusion models provide an effective framework to study the role of numerical and perceptual variables in numerosity tasks and their context-dependency.

Decision making in numeracy tasks with spatially continuous scales

A diffusion model of decision making on continuous response scales is applied to three numeracy tasks. The goal is to explain the distributions of responses on the continuous response scale and the time taken to make decisions. In the model, information from a stimulus is spatially continuously distributed, the response is made by accumulating information to a criterion, which is a 1D line, and the noise in the accumulation process is continuous Gaussian process noise over spatial position. The model is fit to the data from three experiments. In one experiment, a one or two digit number is displayed and the task is to point to its location on a number line ranging from 1 to 100. This task is used extensively in research in education but there has been no model for it that accounts for both decision times and decision choices. In the second task, an array of dots is displayed and the task is to point to the position of the number of dots on an arc ranging from 11 to 90. In a third task, an array of dots is displayed and the task is to speak aloud the number of dots. The model we propose accounts for both accuracy and response time variables, including the full distributions of response times. It also provides estimates of the acuity of decisions (standard deviations in the evidence distributions) and it shows how representations of numeracy information are task-dependent. We discuss how our model relates to research on numeracy and the neuroscience of numeracy, and how it can produce more comprehensive measures of individual differences in numeracy skills in tasks with continuous response scales than have hitherto been available.

Feeling free: External influences on endogenous behaviour

When we are presented with two equally appealing options, how does the brain break the symmetry between them and make a choice? Recent research has proposed that when no clear information can guide decisions, we use irrelevant noise to tip the scale in favour of one alternative and decide how to act. In the present study, we investigated this issue exploring how human decisions were influenced by noise in a visual signal that cued instructed or free choice. Participants were presented with random-dot kinematograms, moving unidirectionally either upwards or downwards (in instructed trials) or both upwards and downwards simultaneously (free-choice trials). By varying the coherence of dot motion, we were able to test how moment-to-moment fluctuations in motion energy could influence action selection processes. We also measured participants' awareness of such influence. Our results revealed three novel findings: Participants' choices tended to follow fluctuations in dot motion, showing that sensory noise biased "free" selection between actions, irrespective of the clarity of the free cue. However, participants appeared to remain unaware of that influence, because subjective ratings of freedom did not correlate with the degree of sensory biasing. In one exception to this general rule, we found that, when participants resisted the bias and made a choice opposite to the one suggested by the stimulus, they reported strong subjective sense of having chosen independently of the stimulation. This result suggests that inhibitory control is tightly linked to the sense of freedom of choice.

Theoretical models of reaction times arising from simple-choice tasks

In this work we present a group of theoretical models for reaction times arising from simple-choice task tests. In particular, we argue for the inclusion of a shifted version of the Gamma distribution as a theoretical model based on a mathematical result on first hitting times. We contrast the goodness-of-fit of those models with the Ex-Gaussian distribution, using data from recently published experiments. The evidence of the results obtained highlights the convenience of proposing theoretical models for reaction times instead of models acting exclusively as quantitative distribution measurements.

Gaze Amplifies Value in Decision Making

When making decisions, people tend to choose the option they have looked at more. An unanswered question is how attention influences the choice process: whether it amplifies the subjective value of the looked-at option or instead adds a constant, value-independent bias. To address this, we examined choice data from six eye-tracking studies ( Ns = 39, 44, 44, 36, 20, and 45, respectively) to characterize the interaction between value and gaze in the choice process. We found that the summed values of the options influenced response times in every data set and the gaze-choice correlation in most data sets, in line with an amplifying role of attention in the choice process. Our results suggest that this amplifying effect is more pronounced in tasks using large sets of familiar stimuli, compared with tasks using small sets of learned stimuli.