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A wealth of empirical evidence shows that people display opposite behaviors when deciding whether to rely on an algorithm, even if it is inexpensive to do so and using the algorithm should enhance their own performance. This paper develops a formal theory to explain some of these conflicting facts and submit new testable predictions. Drawing from decision analysis, I invoke two key notions: the 'value of information' and the 'value of control'. The value of information matters to users of algorithms like recommender systems and prediction machines, which essentially provide information. I find that ambiguity aversion or a subjective cost of employing an algorithm will tend to decrease the value of algorithmic information, while repeated exposure to an algorithm might not always increase this value. The value of control matters to users who may delegate decision making to an algorithm. I model how, under partial delegation, imperfect understanding of what the algorithm actually does (so the algorithm is in fact a black box) can cause algorithm aversion. Some possible remedies are formulated and discussed. • This paper initiates a formal decision-theoretic approach to make sense of the empirical evidence concerning people's attitudes towards algorithms. • This approach exploits two fundamental notions: the value of information and the value of control. • Ambiguity aversion will tend to decrease the value of algorithmic information; repeated exposure to algorithms may not increase it. • A first model of 'black box' algorithms is developed to analyze the value of keeping versus delegating control. [ABSTRACT FROM AUTHOR]

Multiple-choice and continuous-response tasks pose a number of challenges for models of the decision process, from empirical challenges like context effects to computational demands imposed by choice sets with a large number of outcomes. This paper develops a general framework for constructing models of the cognitive processes underlying both inferential and preferential choice among any arbitrarily large number of alternatives. This geometric approach represents the alternatives in a choice set along with a decision maker's beliefs or preferences in a "decision space," simultaneously capturing the support for different alternatives along with the similarity relations between the alternatives in the choice set. Support for the alternatives (represented as vectors) shifts over time according to the dynamics of the belief / preference state (represented as a point) until a stopping rule is met (state crosses a hyperplane) and the corresponding selection is made. This paper presents stopping rules that guarantee optimality in multi-alternative inferential choice, minimizing response time for a desired level of accuracy, as well as methods for constructing the decision space, which can result in context effects when applied to preferential choice. [ABSTRACT FROM AUTHOR]

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions respectively. Our construction unifies the two different situations (compatible versus incompatible mental observables), by means of a single Hilbert space and of a deformation parameter which can be tuned to describe these opposite cases. One of the main foundational consequences of this paper for cognitive psychology is formalization of the mutual uncertainty about incompatible questions with the aid of Heisenberg’s uncertainty principle implying the mental state dependence of (in)compatibility of questions. [ABSTRACT FROM AUTHOR]

Arbitrage is a key concept in the theory of asset pricing and it plays a crucial role in financial decision making. The concept of the curvature of so-called ‘fibre bundles’ can be used to define arbitrage. The concept of ‘action’ can play an important role in the definition of arbitrage. In this paper, we connect the probabilities emerging from a (non) zero linear action with so-called risk neutral probabilities. The paper also shows how arbitrage/non arbitrage can be well defined within a quantum-like paradigm. We also discuss briefly the behavioural dimension of arbitrage. [ABSTRACT FROM AUTHOR]

Abstract We describe the properties of a constraint satisfaction network that is able to reason and decide rationally in strategic games. We use the structure of Bidirectional Associative Memory (BAM), a minimal two-layer recurrent neural network, and assume that network layers represent self and other strategies, whereas connection weights encode best responses. We apply BAM to finite-strategy two-player games, and show that network activation in the long run is restricted to the set of rationalizable strategies. The network is not guaranteed to reach a stable activation state, but any pure strategy profile that constitutes a stable state in the network must be a pure strategy Nash equilibrium. We illustrate the properties of the network using the traveler's dilemma, the rock–paper–scissors game, and coordination games. The network's behavior also depends on starting activation states, and we show how biases in these starting states can resolve equilibrium selection problems. Strategic decision making is a key part of complex social behavior, and our results illustrate how bidirectional constraint satisfaction networks can perform rational computations in this domain. Highlights • Bidirectional associative memory is used to study game theoretic decision making. • The network makes decisions through constraint satisfaction. • Long run activation is restricted to the set of rationalizable strategies. • Any pure strategy profile in a stable state must be a pure strategy Nash equilibrium. [ABSTRACT FROM AUTHOR]

Sequential sampling models are widely used in modeling the empirical data obtained from different decision making experiments. Since 1960s, several instantiations of these models have been proposed. A common assumption among these models is that the subject accumulates noisy information during the time course of a decision. The decision is made when the accumulated information favoring one of the responses reaches a decision boundary. Different models, however, make different assumptions about the information accumulation process and the implementation of the decision boundaries. Comparison among these models has proven to be challenging. In this paper we investigate the relationship between several of these models using a theoretical framework called the inverse first passage time problem. This framework has been used in the literature of applied probability theory in investigating the range of the first passage time distributions that can be produced by a stochastic process. In this paper, we use this framework to prove that any Wiener process model with two time-constant boundaries can be mimicked by an independent race model with time-varying boundaries. We also examine the numerical computation of the mimicking boundaries. We show that the mimicking boundaries of the race model are not symmetric. We then propose an equivalent race model in which the boundaries are symmetric and time-constant but the drift coefficients are time-varying. [ABSTRACT FROM AUTHOR]

This paper is devoted to a justification of quantum-like models of the process of decision making based on the theory of open quantum systems, i.e. decision making is considered as decoherence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment R surrounding her. Such an interaction generates “dissipation of uncertainty” from Alice’s belief-state ρ ( t ) into R and asymptotic stabilization of ρ ( t ) to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on R guaranteeing such stabilization. We found a partial solution of this problem (in the form of sufficient conditions). We present the corresponding decision making analysis for one class of mental environments, the so-called “almost homogeneous environments”, with the illustrative examples: (a) behavior of electorate interacting with the mass-media “reservoir”; (b) consumers’ persuasion. We also comment on other classes of mental environments. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory. [ABSTRACT FROM AUTHOR]

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common assumption of these models is that decision parameters, e.g., the rate of accumulation (drift rate), remain fixed over the course of a decision, allowing the derivation of analytic formulas for the probabilities of hitting the upper or lower decision threshold, and the mean decision time. There is reason to believe, however, that many types of behavior would be better described by a model in which the parameters were allowed to vary over the course of the decision process. In this paper, we use martingale theory to derive formulas for the mean decision time, hitting probabilities, and first passage time (FPT) densities of a Wiener process with time-varying drift between two time-varying absorbing boundaries. This model was first studied by Ratcliff (1980) in the two-stage form, and here we consider the same model for an arbitrary number of stages (i.e. intervals of time during which parameters are constant). Our calculations enable direct computation of mean decision times and hitting probabilities for the associated multistage process. We also provide a review of how martingale theory may be used to analyze similar models employing Wiener processes by re-deriving some classical results. In concert with a variety of numerical tools already available, the current derivations should encourage mathematical analysis of more complex models of decision making with time-varying evidence. [ABSTRACT FROM AUTHOR]

The Leaky Competitive Accumulator (LCA) model for perceptual discrimination is rapidly growing in popularity due to its neural plausibility. The model assumes that perceptual choices and associated response times are the consequence of the accrual of evidence for the various response alternatives up to a certain predetermined threshold. In addition, accrual of evidence is influenced by temporal leakage of information and mutual inhibition between the accumulators. In this paper we provide an overview of fitting routines that may be used to identify the parameter values used for generating data under the LCA assumptions. We find that because (a) there is no closed-form solution to the likelihood function of the LCA model, and (b) there are strong trade-offs between accumulation rate, leakage, and inhibition, it is extremely difficult to faithfully recover the parameters of the LCA model. To minimize these problems, we recommend to use DE-MCMC sampling, collect very large amounts of data, and constrain the parameter space where possible. [ABSTRACT FROM AUTHOR]

This paper recommends using mosaics, rather than ( σ -)algebras, as collections of events in decision under uncertainty. We show how mosaics solve the main problem of Savage’s (1954) uncertainty model, a problem pointed out by Duncan Luce. Using mosaics, we can connect Luce’s modeling of uncertainty with Savage’s. Thus, the results and techniques developed by Luce and his co-authors become available to currently popular theories of decision making under uncertainty and ambiguity. [ABSTRACT FROM AUTHOR]

This paper uses the tool of the logarithmic derivative function (LD) to ascertain the functional form of the risky weighting function for probabilistic outcomes. The LD function of a continuous function g ( x ) is defined as the ratio of the derivative of a function at x to the function itself. The LD is particularly sensitive to changes in the slope of a function thus making it an effective way of distinguishing functions with similar forms. The present study replicates earlier analyses of the LD candidates for the risky weighting function for positive binary gambles and extends the program of study to include negative binary gambles. Empirical estimates for LD values were elicited in an experiment in which participants matched gambles with positive outcomes or with negative outcomes. The risky weighting function for positive and negative gambles differed significantly only in the low range of probability values where p ≤ 0.15 . Several candidate models were shown to be incompatible with the observed LD pattern across both types of gambles. Other candidates had a functional form that was similar to the observed LD pattern, but systematically misfit the observed data in one or more regions of the curve. Of the models that predicted the right shape, only one–the Exponential Odds function ω ( p ) = exp ( − s ( 1 − p ) b p a ) –showed a random error pattern. The Exponential Odds function was also the only candidate function with best-fitting parameters that differed between positive and negative gambles and thereby picking up on an important difference between the two gamble types. [ABSTRACT FROM AUTHOR]

The paper starts with an introduction to the basic mathematical model of classical probability (CP), i.e. the Kolmogorov (1933) measure-theoretic model. Its two basic interpretations are discussed: statistical and subjective. We then present the probabilistic structure of quantum mechanics (QM) and discuss the problem of interpretation of a quantum state and the corresponding probability given by Born’s rule. Applications of quantum probability (QP) to modeling of cognition and decision making (DM) suffer from the same interpretational problems as QM. Here the situation is even more complicated than in physics. We analyze advantages and disadvantages of the use of subjective and statistical interpretations of QP. The subjective approach to QP was formalized in the framework of Quantum Bayesianism (QBism) as the result of efforts from C. Fuchs and his collaborators. The statistical approach to QP was presented in a variety of interpretations of QM, both in nonrealistic interpretations, e.g., the Copenhagen interpretation (with the latest version due to A. Plotnitsky), and in realistic interpretations (e.g., the recent Växjö interpretation). At present, we cannot make a definite choice in favor of any of the interpretations. Thus, quantum-like DM confronts the same interpretational problem as quantum physics does. [ABSTRACT FROM AUTHOR]

Abstract: argue that the coefficient of variation (CV) fails as a normative criterion for risk taking in risky choice because it predicts violations of dominance. They suggest that it fails also on descriptive grounds because such violations are not observed in a study they conducted and because people’s choices in two other situations were not predicted by the CV. This paper counters the normative argument by suggesting that occasional violations of dominance might be the price that organisms with only limited processing capacity pay to achieve a broad set of goals. The consistency axioms of rational choice theory have a long history of falling short of accounting for such tradeoffs. The paper then addresses the three instances of descriptive failures of the CV to predict risk taking provided by Cox and Sadiraj, showing them to be inappropriate or inconclusive arguments against the use of the CV as a measure of risk in risk-return models of human and animal risk taking. Finally, the paper reviews new behavioral and neuroscience evidence in support of the CV as a predictor of risk taking, especially in decisions from experience, for which the model was developed. [ABSTRACT FROM AUTHOR]

Abstract: The Ornstein–Uhlenbeck (O–U) model has been successfully applied to describe the response accuracy and response time in 2-alternative choice tasks. This paper analyses properties and performance of variants of the O–U model with absorbing and reflecting boundary conditions that limit the range of possible values of the integration variable. The paper focuses on choice tasks with pre-determined response time. The type of boundary and the growth/decay parameter of the O–U model jointly determine how the choice is influenced by the sensory input presented at different times throughout the trial. It is shown that the O–U models with two types of boundary are closely related and can achieve the same performance under certain parameter values. The value of the growth/decay parameter that maximizes the accuracy of the model has been identified. It is shown that when the boundaries are introduced, the O–U model may achieve higher accuracy than the diffusion model. This suggests that given the limited range of the firing rates of integrator neurons, the neural decision circuits could achieve higher accuracy employing leaky rather than linear integration in certain tasks. We also propose experiments that could distinguish between different models of choice in tasks with pre-determined response time. [Copyright &y& Elsevier]

Abstract: An important reason why people deviate from expected utility is reference-dependence of preferences, implying loss aversion. Bleichrodt [Bleichrodt H. (2007). Reference-dependent utility with shifting reference points and incomplete preferences. Journal of Mathematical Psychology, 51, 266–276] argued that in the empirically realistic case where the reference point is always an element of the decision maker’s opportunity set, reference-dependent preferences have to be taken as incomplete. This incompleteness is a consequence of reference-dependence and is different in nature from the type of incompleteness usually considered in the literature. It cannot be handled by existing characterizations of reference-dependence, which all assume complete preferences. This paper presents new preference foundations that extend reference-dependent expected utility to cover this case of incompleteness caused by reference-dependence. The paper uses intuitive axioms that are easy to test. Two special cases of reference-dependent expected utility are also characterized: one model in which utility is decomposed into a normative and a psychological component and one model in which loss aversion is constant. The latter model has been frequently used in empirical research on reference-dependence. [Copyright &y& Elsevier]

Abstract: Many empirical studies have shown that people''s preferences are reference-dependent. Previous theoretical studies of reference-dependence assumed that the reference point was fixed and then imposed the usual assumptions of decision theory, in particular completeness of preferences. This paper gives preference foundations for additive reference-dependent utility when the reference point varies across decisions and is one of the options in the decision maker''s opportunity set. This decision situation is common, for example because usually the retention of the status quo is an available option, but is difficult to handle axiomatically because it implies incompleteness of preferences. The results of this paper provide tools to extend existing theories of reference-dependent preferences, such as prospect theory, to new and empirically important decision contexts. [Copyright &y& Elsevier]

This paper studies two important explanations of why people violate procedure invariance: loss aversion and scale compatibility. The paper extends previous research by studying loss aversion and scale compatibility simultaneously and in a quantitative manner, by looking at a new decision domain, medical decision making, and by using an experimental design that is less conducive to violations of procedure invariance. We find significant evidence both of loss aversion and of scale compatibility. The effects of loss aversion and scale compatibility are not constant but vary over trade-offs and most participants do not behave consistently according to loss aversion or scale compatibility. In particular, the effect of loss aversion in medical trade-offs decreases with life duration. The rejection of constant loss aversion and constant scale compatibility is discouraging for attempts to model loss aversion and scale compatibility. The findings are encouraging for utility measurement and prescriptive decision analysis that seeks to avoid the effects of loss aversion and scale compatibility. The data suggest that there exist decision contexts in which the effects of loss aversion and scale compatibility can be minimized and that utilities can be measured that are unaffected by their impact. [Copyright &y& Elsevier]

Computational models of reinforcement learning have played an important role in understanding learning and decision making behavior, as well as the neural mechanisms underlying these behaviors. However, fitting the parameters of these models can be challenging: the parameters are not identifiable, estimates are unreliable, and the fitted models may not have good predictive validity. Prior distributions on the parameters can help regularize estimates and to some extent deal with these challenges, but picking a good prior is itself challenging. This paper presents empirical priors for reinforcement learning models, showing that priors estimated from a relatively large dataset are more identifiable, more reliable, and have better predictive validity compared to model-fitting with uniform priors. [ABSTRACT FROM AUTHOR]

We continue to analyze basic constraints on the human decision making from the viewpoint of quantum measurement theory (QMT). As it has been found, the conventional QMT based on the projection postulate cannot account for the combination of the question order effect (QOE) and the response replicability effect (RRE). This was an alarming finding for quantum-like modeling of decision making. Recently, it was shown that this difficulty can be resolved by using of the general QMT based on quantum instruments. In the present paper we analyze the problem of the combination of QOE, RRE, and the well-known QQ-equality (QQE). This equality was derived by Busemeyer and Wang, and it was shown (in a joint paper with Solloway and Shiffrin) that statistical data from many social opinion polls satisfy it. Here we construct quantum instruments satisfying QOE, RRE and QQE. The general features of our approach are formalized with postulates that generalize (the Wang–Busemeyer) postulates for quantum-like modeling of decision making. Moreover, we show that our model closely reproduces the statistics of the well-known Clinton–Gore Poll data with a prior belief state independent of the question order. This model successfully corrects for the order effect in the data to determine the "genuine" distribution of the opinions in the Poll. The paper also provides an accessible introduction to the theory of quantum instruments — the most general mathematical framework for quantum measurements. • The question order effect and response replicability have been taken as in conflict. • A quantum model showing both effects and the QQ-equality as well is constructed. • This model reproduces the well-known Clinton–Gore Poll statistics almost faithfully. [ABSTRACT FROM AUTHOR]

Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex generative models, enabling simulation of a wide range of complex behaviours. Due to successive developments in active inference, it is often difficult to see how its underlying principle relates to process theories and practical implementation. In this paper, we try to bridge this gap by providing a complete mathematical synthesis of active inference on discrete state-space models. This technical summary provides an overview of the theory, derives neuronal dynamics from first principles and relates this dynamics to biological processes. Furthermore, this paper provides a fundamental building block needed to understand active inference for mixed generative models; allowing continuous sensations to inform discrete representations. This paper may be used as follows: to guide research towards outstanding challenges, a practical guide on how to implement active inference to simulate experimental behaviour, or a pointer towards various in-silico neurophysiological responses that may be used to make empirical predictions. • We review active inference on discrete state-spaces, a framework thought to underwrite perception, action, planning, decision-making and learning in biological and artificial agents. • We derive the associated process theory and discuss its biological plausibility. • We discuss outstanding challenges for the theory, its implementation and empirical validation. [ABSTRACT FROM AUTHOR]

Abstract: Consider a multi-trial game with the goal of maximizing a quantity . At each trial , the player doubles the accumulated quantity, unless the trial number is , in which case all is lost and the game ends. The expected quantity for the next trial will favor continuing play, as long as the probability that the next trial is is less than one half. is vaguely specified (e.g., someone is asked to fill a sheet of paper with digits, which are then permuted to produce ). Conditional on reaching trial , we argue that the probability that the next trial is is extremely small (much less than one half), and that this holds for any . Thus, single trial reasoning recommends one should always play, but this guarantees eventual ruin in the game. It is necessary to stop, but how can a decision to stop on be justified, and how can be chosen? The paradox and the conflict between what seem to be two equally plausible lines of reasoning are caused by the vagueness in the specification of the critical trial . Many everyday reasoning situations involve analogous situations of vagueness, in specifying probabilities, values, and/or alternatives, whether in the context of sequential decisions or single decisions. We present a computational scheme for addressing the problem of vagueness in the above game, based on quantum probability theory. The key aspect of our proposal is the idea that the range of stopping rules can be represented as a superposition state, in which the player cannot be assumed to believe in any specific stopping rule. This scheme reveals certain interesting properties, regarding the dynamics of when to stop to play. [Copyright &y& Elsevier]

Abstract: We study mathematical models of the collaborative solving of a two-choice discrimination task. We estimate the difference between the shared performance for a group of observers over a single person performance. Our paper is a theoretical extension of the recent work of Bahrami, Olsen, Latham, Roepstorff, and Frith (2010) from a dyad (a pair) to a group of interacting minds. We analyze several models of communication, decision-making and hierarchical information-aggregation. The maximal slope of psychometric function is a convenient parameter characterizing performance. For every model we investigated, the group performance turns out to be a product of two numbers: a scaling factor depending of the group size and an average performance. The scaling factor is a power function of the group size (with the exponent ranging from 0 to 1), whereas the average is arithmetic mean, quadratic mean, or maximum of the individual slopes. Moreover, voting can be almost as efficient as more elaborate communication models, given the participants have similar individual performances. [Copyright &y& Elsevier]

Abstract: Sequential sampling process models provide promising approaches to characterizing human judgment and decision making. In this paper, we study one class of sequential sampling process models referred to as Decision Field Theory (DFT). These models not only provide qualitative explanations of empirical findings, but also provide quantitative predictions of real time performance. We analyze major DFT models in the literature, and demonstrate that models which are seemingly similar can behave very differently, depending upon the cognitive basis for model parameters. Based on this analysis, we propose a mathematical framework which attempts to unify DFT models. [Copyright &y& Elsevier]

Abstract: In this paper we develop a general quantum-like model of decision making. Here updating of probability is based on linear algebra, the von Neumann–Lüders projection postulate, Born’s rule, and the quantum representation of the state space of a composite system by the tensor product. This quantum-like model generalizes the classical Bayesian inference in a natural way. In our approach the latter appears as a special case corresponding to the absence of relative phases in the mental state. By taking into account a possibility of the existence of correlations which are encoded in relative phases we developed a more general scheme of decision making. We discuss natural situations inducing deviations from the classical Bayesian scheme in the process of decision making by cognitive systems: in situations that can be characterized as objective and subjective mental uncertainties. Further, we discuss the problem of base rate fallacy. In our formalism, these “irrational” (non-Bayesian) inferences are represented by quantum-like bias operations acting on the mental state. [Copyright &y& Elsevier]

Abstract: Choice confidence is a central measure in psychological decision research, often being reported on a probabilistic scale. Simple mechanisms that describe the psychological processes underlying choice confidence, including those based on error and confirmation biases, have typically received support via fits to data averaged over subjects. While averaged data ease model development, they can also destroy important aspects of the confidence data distribution. In this paper, we develop a hierarchical model of raw confidence judgments using the beta distribution, and we implement two simple confidence mechanisms within it. We use Bayesian methods to fit the hierarchical model to data from a two-alternative confidence experiment, and we use a variety of Bayesian tools to diagnose shortcomings of the simple mechanisms that are overlooked when applied to averaged data. Bugs code for estimating the models is also supplied. [Copyright &y& Elsevier]

Abstract: Adaptive learning games should provide opportunities for the student to learn as well as motivate playing until goals have been reached. In this paper, we give a mathematically rigorous treatment of the problem in the framework of Bayesian decision theory. To quantify the opportunities for learning, we assume that the learning tasks that yield the most information about the current skills of the student, while being desirable for measurement in their own right, would also be among those that are efficient for learning. Indeed, optimization of the expected information gain appears to naturally avoid tasks that are exceedingly demanding or exceedingly easy as their results are predictable and thus uninformative. Still, tasks that are efficient for learning may be experienced as too challenging, and the resulting failures can lower motivation. Therefore, in addition to quantifying the expected informational benefit for learning of any prospective task to be presented next, we also model the expected motivational cost of its presentation, measured simply as the estimated probability of failure in our example model. We propose a “learner-friendly” adaptation algorithm that chooses the learning tasks by optimizing the expected benefit divided by the expected cost. We apply this algorithm to a Rasch-like student model implemented within a real-world application and present initial results of a pilot experiment. [Copyright &y& Elsevier]

Abstract: In engineering systems, noise is a curse, obscuring important signals and increasing the uncertainty associated with measurement. However, the negative effects of noise are not universal. In this paper, we examine how people learn sequential control strategies given different sources and amounts of feedback variability. In particular, we consider people’s behavior in a task where short- and long-term rewards are placed in conflict (i.e., the best option in the short-term is worst in the long-term). Consistent with a model based on reinforcement learning principles [Gureckis, T., & Love, B.C. Short term gains, long term pains: How cues about state aid learning in dynamic environments. Cognition (in press)], we find that learners differentially weight information predictive of the current task state. In particular, when cues that signal state are noisy, we find that participants’ ability to identify an optimal strategy is strongly impaired relative to equivalent amounts of noise that obscure the rewards/valuations of those states. In other situations, we find that noise and noise in reward signals may paradoxically improve performance by encouraging exploration. Our results demonstrate how experimentally-manipulated task variability can be used to test predictions about the mechanisms that learners engage in dynamic decision making tasks. [Copyright &y& Elsevier]

Signal detection theory (SDT) and the sequential probability ratio test (SPRT) are two leading models for binary perceptual decision-making in psychology and neuroscience. For initiates in this research area, the foundational relationship between SDT and the SPRT, or between statistical inference models and their mechanistic counterparts, can be unclear because many decision-making models in use today are much extended versions of the original, simpler models that contain the essence of these models' claims to optimality. For those familiar with the models, it would be useful to have a quantitative comparison between their performance as multi-sample hypothesis tests. In this tutorial review of SDT and the SPRT, we emphasize that SDT and the SPRT differ only in their sampling procedures and so can be viewed as static and dynamic variants from the same family of hypothesis tests. Furthermore, we map the sample efficiency gains of using the SPRT over a multi-sample version of SDT by a novel construction of ROC curves. The goal of this paper is to provide a compact treatise on the statistical underpinnings of SDT and the SPRT, how they relate to the drift–diffusion model (DDM), and what these models imply for the physical implementation of evidence gathering and optimal decision making in biological systems. • Relating signal detection theory and the sequential probability ratio test. • Comparative ROC curve analysis for signal detection theory and sequential analysis. • Analytic and simulated decision threshold and relation to sample efficiencies. • Visualization of map between decision costs and optimal decision thresholds. [ABSTRACT FROM AUTHOR]

Modelling plays a key role in explaining data in psychology and neuroscience and helps elucidate neural computations. Recent observations of magnitude-sensitivity (i.e. sensitivity to overall magnitudes and magnitude differences) in both humans engaged in perceptual decision making and monkeys engaged in value-based decisions have shown that new assumptions (such as the inclusion of noise that is proportional to magnitudes of external stimuli) in routinely-used sequential sampling models need to be considered to fit this type of magnitude-sensitive data. In this paper, we studied different variants of diffusion-type models and a leaky-competing accumulator model, and compared their behaviour in response to varying input magnitudes as well as their ability to resemble each other. We evaluated the extent to which these models can give good fits to simulated reaction time distributions for choices between unequal and equal alternatives. As a result, in some cases we obtained good fits of model and data, even when the underlying model used for data generation was different compared to the model used to fit these data. Our results underpin the importance of both overall magnitude and magnitude difference effects in models describing the sequential integration of evidence, and contribute to the debate over possible model candidate explanations. We discuss how magnitude-dependent input noise and lateral inhibition may be used to regulate different magnitude-sensitive effects and the implications for quantitative analyses of experimental data. • DDM and OU processes with input magnitude-dependent noise may mimic each other. • DDM and OU processes with input magnitude-dependent noise may be resembled by the LCA. • Non-reciprocity is observed between LCA fits to DDM and OU data and vice versa. • Multiplicative noise strength and inhibition strength may modulate magnitude effects. [ABSTRACT FROM AUTHOR]

In a recent paper, Andraszewicz and Rieskamp (2014) proposed the standardized covariance as a measure of association, similarity and co-riskiness. Budescu and Bo (2017) wrote a comment on the proposed measure, in which they interpret the standardized covariance as a measure of additive association, or a “measure of disparity between the ranges of outcomes offered by two lotteries” (Budescu and Bo, 2017). In the reply to this comment, we point out that the statistical interpretation of the standardized covariance provided by Budescu and Bo (2017) is strongly linked with its cognitive interpretation. Also, in this comment, we give a cognitive interpretation to the Budescu and Bo’s (2017) analytical findings of the similarity measure for statistically independent gambles proposed by Andraszewicz and Rieskamp (2014). [ABSTRACT FROM AUTHOR]