Diffusion models are widely-used and successful accounts of the time course of two-choice decision making. Most diffusion models assume constant boundaries, which are the threshold levels of evidence that must be sampled from a stimulus to reach a decision. We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries. We then develop a computational method for finding time-varying boundaries from empirical data, and apply our new method to two problems. The (...) first problem involves finding the time-varying boundaries that make diffusion models equivalent to the alternative sequential sampling class of accumulator models. The second problem involves finding the time-varying boundaries, at the individual level, that best fit empirical data for perceptual stimuli that provide equal evidence for both decision alternatives. We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference. (shrink)

The semantic fluency task is commonly used as a measure of one’s ability to retrieve semantic concepts. While performance is typically scored by counting the total number of responses, the ordering of responses can be used to estimate how individuals or groups organize semantic concepts within a category. I provide an overview of this methodology, using Alzheimer’s disease as a case study for how the approach can help advance theoretical questions about the nature of semantic representation. However, many open questions (...) surrounding the validity and reliability of this approach remain unresolved. (shrink)

The medial prefrontal cortex (mPFC) has been the subject of intense interest as a locus of cognitive control. Several computational models have been proposed to account for a range of effects, including error detection, conflict monitoring, error likelihood prediction, and numerous other effects observed with single-unit neurophysiology, fMRI, and lesion studies. Here, we review the state of computational models of cognitive control and offer a new theoretical synthesis of the mPFC as signaling response–outcome predictions. This new synthesis has two interacting (...) components. The first component learns to predict the various possible outcomes of a planned action, and the second component detects discrepancies between the actual and intended responses; the detected discrepancies in turn update the outcome predictions. This single construct is consistent with a wide array of performance monitoring effects in mPFC and suggests a unifying account of the cognitive role of medial PFC in performance monitoring. (shrink)

After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in futility. The complex-systems (...) approach can be informative and innovative, but only if it is implemented as a formal model that allows concrete prediction, falsification, and comparison against more traditional approaches. (shrink)

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian (...) inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)

The speed‐accuracy trade‐off (SAT) effect refers to the behavioral trade‐off between fast yet error‐prone respones and accurate but slow responses. Multiple theories on the cognitive mechanisms behind SAT exist. One theory assumes that SAT is a consequence of strategically adjusting the amount of evidence required for overt behaviors, such as perceptual choices. Another theory hypothesizes that SAT is the consequence of the mixture of multiple categorically different cognitive processes. In this paper, these theories are disambiguated by assessing whether the fixed‐point (...) property of mixture distributions holds, in both simulations and data. I conclude that, at least for perceptual decision making, there is no evidence for a mixture of different cognitive processes to trade off accuracy of responding for speed. (shrink)

Piéron's Law describes the relationship between stimulus intensity and reaction time. Previously (Stafford & Gurney, 2004), we have shown that Piéron's Law is a necessary consequence of rise-to-threshold decision making and thus will arise from optimal simple decision-making algorithms (e.g., Bogacz, Brown, Moehlis, Holmes, & Cohen, 2006). Here, we manipulate the color saturation of a Stroop stimulus. Our results show that Piéron's Law holds for color intensity and color-naming reaction time, extending the domain of this law, in line with our (...) suggestion of the generality of the processes that can give rise to Piéron's Law. In addition, we find that Stroop condition does not interact with the effect of color saturation; Stroop interference and facilitation remain constant at all levels of color saturation. An analysis demonstrates that this result cannot be accounted for by single-stage decision-making algorithms which combine all the evidence pertaining to a decision into a common metric. This shows that human decision making is not information-optimal and suggests that the generalization of current models of simple perceptual decision making to more complex decisions is not straightforward. (shrink)

Evidence accumulation has been the core component in recent development of perceptual and value-based decision-making theories. Most studies have focused on the evaluation of evidence between alternative options. What remains largely unknown is the process that prepares evidence: how may the decision-maker sample different sources of information sequentially, if they can only sample one source at a time? Here we propose a normative framework in prescribing how different sources of information should be sampled proactively to facilitate the decision process: beliefs (...) for different noisy sources are updated in a Bayesian manner and participants can proactively allocate resource for sampling (i.e. saccades) among different sources to maximize the information gain in such process. We show that our framework can account for human participants’ actual choice and saccade behaviors in a two-alternative value-based decision-making task. Moreover, our framework makes novel predictions about the empirical eye movement patterns. (shrink)

Researchers studying complex cognition have grown increasingly interested in mapping symbolic cognitive architectures onto subsymbolic brain models. Such a mapping seems essential for understanding cognition under all but the most extreme viewpoints (namely, that cognition consists exclusively of digitally implemented rules; or instead, involves no rules whatsoever). Making this mapping reduces to specifying an interface between symbolic and subsymbolic descriptions of brain activity. To that end, we propose parameterization techniques for building cognitive models as programmable, structured, recurrent neural networks. Feedback (...) strength in these models determines whether their components implement classically subsymbolic neural network functions (e.g., pattern recognition), or instead, logical rules and digital memory. These techniques support the implementation of limited production systems. Though inherently sequential and symbolic, these neural production systems can exploit principles of parallel, analog processing from decision-making models in psychology and neuroscience to explain the effects of brain damage on problem solving behavior. (shrink)

The speed-accuracy trade-off effect refers to the behavioral trade-off between fast yet error-prone respones and accurate but slow responses. Multiple theories on the cognitive mechanisms behind SAT exist. One theory assumes that SAT is a consequence of strategically adjusting the amount of evidence required for overt behaviors, such as perceptual choices. Another theory hypothesizes that SAT is the consequence of the mixture of multiple categorically different cognitive processes. In this paper, these theories are disambiguated by assessing whether the fixed-point property (...) of mixture distributions holds, in both simulations and data. I conclude that, at least for perceptual decision making, there is no evidence for a mixture of different cognitive processes to trade off accuracy of responding for speed. (shrink)

Past research suggests that people process verbal quantifiers differently from numerical ones, but this suggestion has yet to be formally tested. Drawing from traditional correlates of dual-process...

This study investigated the interaction between sampling behavior and preference formation underlying subjective decision making for like and dislike decisions. Two-alternative forced-choice tasks were used with closely-matched musical excerpts and the participants were free to listen and re-listen, i.e. to sample and resample each excerpt, until they reached a decision. We predicted that for decisions involving resampling, a sampling bias would be observed before the moment of conscious decision for the like decision only. The results indeed showed a gradually increasing (...) sampling bias favouring the choice before the moment of overt response for like decisions. Such a bias was absent for dislike decisions. Furthermore, the participants reported stronger relative preferences for like decisions as compared to dislike decisions. This study demonstrated distinct differences in preference formation between like and dislike decisions, both in the implicit orienting/sampling processes prior to the conscious decision and in the subjective evaluation afterwards. (shrink)

We explore the idea that eye-movement strategies in reading are precisely adapted to the joint constraints of task structure, task payoff, and processing architecture. We present a model of saccadic control that separates a parametric control policy space from a parametric machine architecture, the latter based on a small set of assumptions derived from research on eye movements in reading (Engbert, Nuthmann, Richter, & Kliegl, 2005; Reichle, Warren, & McConnell, 2009). The eye-control model is embedded in a decision architecture (a (...) machine and policy space) that is capable of performing a simple linguistic task integrating information across saccades. Model predictions are derived by jointly optimizing the control of eye movements and task decisions under payoffs that quantitatively express different desired speed-accuracy trade-offs. The model yields distinct eye-movement predictions for the same task under different payoffs, including single-fixation durations, frequency effects, accuracy effects, and list position effects, and their modulation by task payoff. The predictions are compared to—and found to accord with—eye-movement data obtained from human participants performing the same task under the same payoffs, but they are found not to accord as well when the assumptions concerning payoff optimization and processing architecture are varied. These results extend work on rational analysis of oculomotor control and adaptation of reading strategy (Bicknell & Levy, ; McConkie, Rayner, & Wilson, 1973; Norris, 2009; Wotschack, 2009) by providing evidence for adaptation at low levels of saccadic control that is shaped by quantitatively varying task demands and the dynamics of processing architecture. (shrink)

Which rules should guide our reasoning? Human reasoners often use reasoning shortcuts, called heuristics, which function well in some contexts but lack the universality of reasoning rules like deductive implication or inference to the best explanation. Does it follow that human reasoning is hopelessly irrational? I argue: no. Heuristic reasoning often represents human reasoners reaching a local rational maximum, reasoning more accurately than if they try to implement more “ideal” rules of reasoning. I argue this is a genuine rational achievement. (...) Our ideal rational advisors would advise us to reason with heuristic rules, not more complicated ideal rules. I argue we do not need a radical new account of epistemic norms to make sense of the success of heuristic reasoning. (shrink)

This paper addresses a common challenge with computational cognitive models: identifying parameter values that are both theoretically plausible and generate predictions that match well with empirical data. While computational models can offer deep explanations of cognition, they are computationally complex and often out of reach of traditional parameter fitting methods. Weak methodology may lead to premature rejection of valid models or to acceptance of models that might otherwise be falsified. Mathematically robust fitting methods are, therefore, essential to the progress of (...) computational modeling in cognitive science. In this article, we investigate the capability and role of modern fitting methods—including Bayesian optimization and approximate Bayesian computation—and contrast them to some more commonly used methods: grid search and Nelder–Mead optimization. Our investigation consists of a reanalysis of the fitting of two previous computational models: an Adaptive Control of Thought—Rational model of skill acquisition and a computational rationality model of visual search. The results contrast the efficiency and informativeness of the methods. A key advantage of the Bayesian methods is the ability to estimate the uncertainty of fitted parameter values. We conclude that approximate Bayesian computation is (a) efficient, (b) informative, and (c) offers a path to reproducible results. (shrink)

Recently, psychological phenomena have been expanded to new domains, crisscrossing boundaries of organizational levels, with the emergence of areas such as social personality and ecosystem learning. In this contribution, we analyze the ascription of an individual-based concept (personality) to the social level. Although justified boundary crossings can boost new approaches and applications, the indiscriminate misuse of concepts refrains the growth of scientific areas. The concept of social personality is based mainly on the detection of repeated group differences across a population, (...) in a direct transposition of personality concepts from the individual to the social level. We show that this direct transposition is problematic for avowing the nonsensical ascription of personality even to simple electronic devices. To go beyond a metaphoric use of social personality, we apply the organizational approach to a review of social insect communication networks. Our conceptual analysis shows that socially self-organized systems, such as isolated ant trails and bee’s recruitment groups, are too simple to have social personality. The situation is more nuanced when measuring the collective choice between nest sites or foraging patches: some species show positive and negative feedbacks between two or more self-organized social structures so that these co-dependent structures are inter-related by second-order, social information systems, complying with a formal requirement for having social personality: the social closure of constraints. Other requirements include the decoupling between individual and social dynamics, and the self-regulation of collective decision processes. Social personality results to be sometimes a metaphorical transposition of a psychological concept to a social phenomenon. The application of this organizational approach to cases of learning ecosystems, or evolutionary learning, could help to ground theoretically the ascription of psychological properties to levels of analysis beyond the individual, up to meta-populations or ecological communities. (shrink)

This paper explains what’s wrong with a Hume-inspired argument for skepticism about induction. Hume’s argument takes as a premise that inductive reasoning presupposes that the future will resemble the past. I explain why that claim is not plausible. The most plausible premise in the vicinity is that inductive reasoning from E to H presupposes that if E then H. I formulate and then refute a skeptical argument based on that premise. Central to my response is a psychological explanation for how (...) people judge that if E then H without realizing that they thereby settled the matter rationally. (shrink)

A sensible epistemologist may not see how she could know that she is not a brain in a vat ; but she doesn’t panic. She sticks with her empirical beliefs, and as that requires, believes that she is not a BIV. (She does not inferentially base her belief that she is not a BIV on her empirical knowledge—she rejects that ‘Moorean’ response to skepticism.) Drawing on the psychological literature on metacognition, I describe a mechanism that’s plausibly responsible for a sensible (...) epistemologist coming to believe she is not a BIV. I propose she thereby knows that she is not a BIV. The particular belief-forming mechanism employed explains why she overlooks this account of how she knows she is not a BIV, making it seem that there is no way for her to know it. I argue this proposal satisfactorily resolves the skeptical puzzle. (shrink)

We review how leaky competing accumulators (LCAs) can be used to model decision making in two‐alternative, forced‐choice tasks, and we show how they reduce to drift diffusion (DD) processes in special cases. As continuum limits of the sequential probability ratio test, DD processes are optimal in producing decisions of specified accuracy in the shortest possible time. Furthermore, the DD model can be used to derive a speed–accuracy trade‐off that optimizes reward rate for a restricted class of two alternative forced‐choice decision (...) tasks. We review findings that compare human performance with this benchmark, and we reveal both approximations to and deviations from optimality. We then discuss three potential sources of deviations from optimality at the psychological level—avoidance of errors, poor time estimation, and minimization of the cost of control—and review recent theoretical and empirical findings that address these possibilities. We also discuss the role of cognitive control in changing environments and in modulating exploitation and exploration. Finally, we consider physiological factors in which nonlinear dynamics may also contribute to deviations from optimality. (shrink)

For decisions between many alternatives, the benchmark result is Hick's Law: that response time increases log-linearly with the number of choice alternatives. Even when Hick's Law is observed for response times, divergent results have been observed for error rates—sometimes error rates increase with the number of choice alternatives, and sometimes they are constant. We provide evidence from two experiments that error rates are mostly independent of the number of choice alternatives, unless context effects induce participants to trade speed for accuracy (...) across conditions. Error rate data have previously been used to discriminate between competing theoretical accounts of Hick's Law, and our results question the validity of those conclusions. We show that a previously dismissed optimal observer model might provide a parsimonious account of both response time and error rate data. The model suggests that people approximate Bayesian inference in multi-alternative choice, except for some perceptual limitations. (shrink)

In approaching the question of whether groups of people can have cognitive capacities that are fundamentally different than the cognitive capacities of the individuals within the group, we lay out a Multiple, Interactive Levels of Cognitive Systems (MILCS) framework. The goal of MILCS is to explain the kinds of cognitive processes typically studied by cognitive scientists, such as perception, attention, memory, categorization, decision making, problem solving, and judgment. Rather than focusing on high-level constructs such as modules in an information processing (...) flow diagram or internal representations, MILCS focuses on mechanisms that allow systems to engage in flexible, adaptive behavior. Examples of these mechanisms are network structure-process pairs that: combine data from perception with top-down theories, achieve consistency and consensus through information exchange, selectively attend to information globally assessed as relevant, and develop specialized units from originally homogeneous networks through competition among the units. Two such systems are considered in some detail -- lateral inhibition within a network for selecting from a candidate set the option that is most attractive, and a diffusion process for accumulating evidence to reach a generally rapid and accurate decision. These system descriptions are aptly applied at multiple levels, including within and across people. These systems provide accounts that unify cognitive processes across multiple levels, can be expressed in a common vocabulary provided by network science, are inductively powerful yet appropriately constrained, and are applicable to a large number of superficially diverse cognitive systems. Given that people are typically highly motivated to participate in strong groups, cognitively resourceful people will tend to form groups that effectively employ cognitive systems at higher levels than the individuals. The impressive cognitive capacities of individual people do not eliminate the need to talk about group cognition. Instead, smart people generally form smart groups. (shrink)

Cognitive science continues to make a compelling case for having a coherent, unique, and fundamental subject of inquiry: What is the nature of minds, where do they come from, and how do they work? Central to this inquiry is the notion of agents that have goals, one of which is their own persistence, who use dynamically constructed knowledge to act in the world to achieve those goals. An agentive perspective explains why a special class of systems have a cluster of (...) co‐occurring capacities that enable them to exhibit adaptive behavior in a complex environment: perception, attention, memory, representation, planning, and communication. As an intellectual endeavor, cognitive science may not have achieved a hard core of uncontested assumptions that Lakatos (1978) identifies as emblematic of a successful research program, but there are alternative conceptions according to which cognitive science has been successful. First, challenges of the early, core tenet of “Mind as Computation” have helped put cognitive science on a stronger foundation—one that incorporates relations between minds and their environments. Second, even if a full cross‐disciplinary theoretic consensus is elusive, cognitive science can inspire distant, deep, and transformative connections between pairs of fields. To be intellectually vital, cognitive science need not resemble a traditional discipline with its associated insularity and unchallenged assumptions. Instead, there is strength and resilience in the diverse perspectives and methods that cognitive science assembles together. This interdisciplinary enterprise is fragile and perhaps inherently unstable, as the looming absorption of cognitive science into psychology shows. Still, for many researchers, the excitement and benefits of triangulating on the nature of minds by integrating diverse cases cannot be secured by a stable discipline with an uncontested core of assumptions. (shrink)

I present a computational-level model of semantic interference effects in online word production within a rate–distortion framework. I consider a bounded-rational agent trying to produce words. The agent's action policy is determined by maximizing accuracy in production subject to computational constraints. These computational constraints are formalized using mutual information. I show that semantic similarity-based interference among words falls out naturally from this setup, and I present a series of simulations showing that the model captures some of the key empirical patterns (...) observed in Stroop and Picture–Word Interference paradigms, including comparisons to human data from previous experiments. (shrink)

If our choices make us who we are, then what does that mean when these choices are made in the human-machine interface? Developing a clear understanding of how human decision making is influenced by automated systems in the environment is critical because, as human-machine interfaces and assistive robotics become even more ubiquitous in everyday life, many daily decisions will be an emergent result of the interactions between the human and the machine – not stemming solely from the human. For example, (...) choices can be influenced by the relative locations and motor costs of the response options, as well as by the timing of the response prompts. In drift diffusion model simulations of response-prompt timing manipulations, we find that it is only relatively equibiased choices that will be successfully influenced by this kind of perturbation. However, with drift diffusion model simulations of motor cost manipulations, we find that even relatively biased choices can still show some influence of the perturbation. We report the results of a two-alternative forced-choice experiment with a computer mouse modified to have a subtle velocity bias in a pre-determined direction for each trial, inducing an increased motor cost to move the cursor away from the pre-designated target direction. With queries that have each been normed in advance to be equibiased in people’s preferences, the participant will often begin their mouse movement before their cognitive choice has been finalized, and the directional bias in the mouse velocity exerts a small but significant influence on their final choice. With queries that are not equibiased, a similar influence is observed. By exploring the synergies that are developed between humans and machines and tracking their temporal dynamics, this work aims to provide insight into our evolving decisions. (shrink)

Cognitive science has been traditionally organized around the individual as the basic unit of cognition. Despite developments in areas such as communication, human–machine interaction, group behavior, and community organization, the individual-centric approach heavily dominates both cognitive research and its application. A promising direction for cognitive science is the study of augmented intelligence, or the way social and technological systems interact with and extend individual cognition. The cognitive science of augmented intelligence holds promise in helping society tackle major real-world challenges that (...) can only be discovered and solved by teams made of individuals and machines with complementary skills who can productively collaborate with each other. (shrink)