A unified theory of discrete and continuous responding.

Kvam, Peter D.; Marley, A. A. J.; Heathcote, Andrew · 2022 · Psychological Review

DOI: 10.1037/rev0000378

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Summary

This paper addresses the challenge of developing a unified cognitive model that explains how internal stimulus representations are mapped onto both discrete (choice) and continuous response scales. The authors argue that while discrete and continuous measures are widely used in psychological assessment, existing models often treat them as distinct processes or fail to account for the joint distributions of responses and response times. To resolve this, the study proposes the Multiple Anchored Accumulation Theory (MAAT), which posits that a common evidence accumulation process underlies both response types. This process is driven by multiple reference points, or "anchors," which correspond to exemplars of stimuli at the extremes or key points of the stimulus range. The authors tested MAAT using data from two experiments involving absolute judgment tasks. In the first study, participants responded to unidimensional line length stimuli using either discrete choices or continuous scales. The design manipulated the number of response options and the similarity among stimuli to examine "bow" effects (accuracy variations across the stimulus range) and "set-size" effects (performance changes with the number of options). The second study utilized color stimuli varying in hue, modeled with three anchors (red, green, and blue), to investigate how similarity among response options affects decision-making. The experimental design allowed for a direct comparison of performance metrics, including accuracy and response time, across discrete and continuous conditions. The results demonstrated that MAAT successfully accounts for several key phenomena observed in both discrete and continuous responding. Specifically, the model explained why responses near the ends of a scale are more accurate, faster, and more skewed. It also captured the decline in accuracy and increase in response time as the number of discrete choice options increases. Crucially, the study found a "near-competitor effect," where responses were slower and less accurate when alternative options were similar to the target response. This finding contradicts assumptions in some continuous models that stopping rules (thresholds) are invariant across options. Instead, MAAT suggests that decision thresholds are sensitive to the perceived similarity among response options, with participants effectively raising thresholds for options with similar competitors to maintain accuracy. The significance of these findings lies in the demonstration that discrete and continuous response tasks can share a common underlying evidence representation. The study concludes that the decision process is fundamentally sensitive to the structure of the response space, particularly the similarity among options. By unifying these paradigms, MAAT provides a more comprehensive framework for understanding cognitive mapping processes, offering insights into how humans translate perceptual inputs into varied output formats. This approach resolves inconsistencies in previous models and highlights the importance of anchor-based reference points in shaping both the speed and accuracy of psychological responses.

Key finding

The Multiple Anchored Accumulation Theory demonstrates that discrete and continuous response tasks share a common evidence accumulation process where decision thresholds are dynamically adjusted based on the similarity of response options.

Methodology

mixed_methods

Provenance

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Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.

Topics

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• dual task multitasking