To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate tradeoffs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. (...) While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps. (shrink)

Visual working memory is a construct hypothesized to store a small amount of accurate perceptual information that can be brought to bear on a task. Much research concerns the construct's capacity and the precision of the information stored. Two prominent theories of VWM representation have emerged: slot-based and continuous-resource mechanisms. Prior modeling work suggests that a continuous resource that varies over trials with variable capacity and a potential to make localization errors best accounts for the empirical data. Questions remain regarding (...) the variability in VWM capacity and precision. Using a novel eye-tracking paradigm, we demonstrate that VWM facilitates search and exhibits effects of fixation frequency and recency, particularly for prior targets. Whereas slot-based memory models cannot account for the human data, a novel continuous-resource model does capture the behavioral and eye tracking data, and identifies the relevant resource as item activation. (shrink)

How can we study bounded rationality? We answer this question by proposing rational task analysis —a systematic approach that prevents experimental researchers from drawing premature conclusions regarding the rationality of agents. RTA is a methodology and perspective that is anchored in the notion of bounded rationality and aids in the unbiased interpretation of results and the design of more conclusive experimental paradigms. RTA focuses on concrete tasks as the primary interface between agents and environments and requires explicating essential task elements, (...) specifying rational norms, and bracketing the range of possible performance, before contrasting various benchmarks with actual performance. After describing RTA’s core components we illustrate its use in three case studies that examine human memory updating, multitasking behavior, and melioration. We discuss RTA’s characteristic elements and limitations by comparing it to related approaches. We conclude that RTA provides a useful tool to render the study of bounded rationality more transparent and less prone to theoretical confusion. (shrink)

Cognition is both empowered and limited by representations. The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such tasks, the model links several problems and semantic domains and provides a new perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems. The shared structural construct of a 2 × 2 matrix supports a set of generic tasks (...) and semantic mappings that provide a unifying framework for understanding problems and defining scientific measures. Our model's key explanatory mechanism is the adoption of particular perspectives on a 2 × 2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization. As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation. To demonstrate the explanatory scope of our model, we use it to clarify theoretical debates on biases and facilitation effects in Bayesian reasoning and to integrate the scientific measures from various semantic domains within a unifying framework. A better understanding of problem structures, representational transparency, and the role of perspectives in the scientific process yields both theoretical insights and practical applications. (shrink)