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Ensemble perception is a process by which we summarize complex scenes. Despite the importance of ensemble perception to everyday cognition, there are few computational models that provide a formal account of this process. Here we develop and test a model in which ensemble representations reflect the global sum of activation signals across all individual items. We leverage this set of minimal assumptions to formally connect a model of memory for individual items to ensembles. We compare our ensemble model against a set of alternative models in five experiments. Our approach uses performance on a visual memory task for individual items to generate zero-free-parameter predictions of interindividual and intraindividual differences in performance on an ensemble continuous-report task. Our top-down modelling approach formally unifies models of memory for individual items and ensembles and opens a venue for building and comparing models of distinct memory processes and representations. 

In many decision tasks, we have a set of alternative choices and are faced with the problem of how to use our latent beliefs and preferences about each alternative to make a single choice. Cognitive and decision models typically presume that beliefs and preferences are distilled to a scalar latent strength for each alternative, but it is also critical to model how people use these latent strengths to choose a single alternative. Most models follow one of two traditions to establish this link. Modern psychophysics and memory researchers make use of signal detection theory, assuming that latent strengths are perturbed by noise, and the highest resulting signal is selected. By contrast, many modern decision theoretic modeling and machine learning approaches use the softmax function (which is based on Luce’s choice axiom; Luce, 1959) to give some weight to non-maximal-strength alternatives. Despite the prominence of these two theories of choice, current approaches rarely address the connection between them, and the choice of one or the other appears more motivated by the tradition in the relevant literature than by theoretical or empirical reasons to prefer one theory to the other. The goal of the current work is to revisit this topic by elucidating which of these two models provides a better characterization of latent processes in -alternative decision tasks, with a particular focus on memory tasks. In a set of visual memory experiments, we show that, within the same experimental design, the softmax parameter varies across -alternatives, whereas the parameter of the signal-detection model is stable. Together, our findings indicate that replacing softmax with signal-detection link models would yield more generalizable predictions across changes in task structure. More ambitiously, the invariance of signal detection model parameters across different tasks suggests that the parametric assumptions of these models may be more than just a mathematical convenience, but reflect something real about human decision-making. 

Abstract Visual working memory is highly limited, and its capacity is tied to many indices of cognitive function. For this reason, there is much interest in understanding its architecture and the sources of its limited capacity. As part of this research effort, researchers often attempt to decompose visual working memory errors into different kinds of errors, with different origins. One of the most common kinds of memory error is referred to as a “swap,” where people report a value that closely resembles an item that was not probed (e.g., an incorrect, non-target item). This is typically assumed to reflect confusions, like location binding errors, which result in the wrong item being reported. Capturing swap rates reliably and validly is of great importance because it permits researchers to accurately decompose different sources of memory errors and elucidate the processes that give rise to them. Here, we ask whether different visual working memory models yield robust and consistent estimates of swap rates. This is a major gap in the literature because in both empirical and modeling work, researchers measure swaps without motivating their choice of swap model. Therefore, we use extensive parameter recovery simulations with three mainstream swap models to demonstrate how the choice of measurement model can result in very large differences in estimated swap rates. We find that these choices can have major implications for how swap rates are estimated to change across conditions. In particular, each of the three models we consider can lead to differential quantitative and qualitative interpretations of the data. Our work serves as a cautionary note to researchers as well as a guide for model-based measurement of visual working memory processes. 

Scholars heavily rely on theoretical scope as a tool to challenge existing theory. We advocate that scientific discovery could be accelerated if far more effort were invested into also overtly specifying and painstakingly delineating the intended purview of any proposed new theory at the time of its inception. As a case study, we consider Tversky and Kahneman (1992). They motivated their Nobel-Prize-winning cumulative prospect theory with evidence that in each of two studies, roughly half of the participants violated independence, a property required by expected utility theory (EUT). Yet even at the time of inception, new theories may reveal signs of their own limited scope. For example, we show that Tversky and Kahneman’s findings in their own test of loss aversion provide evidence that at least half of their participants violated their theory, in turn, in that study. We highlight a combination of conflicting findings in the original article that make it ambiguous to evaluate both cumulative prospect theory’s scope and its parsimony on the authors’ own evidence. The Tversky and Kahneman article is illustrative of a social and behavioral research culture in which theoretical scope plays an extremely asymmetric role: to call existing theory into question and motivate surrogate proposals.