Despite the mapping between objective and subjective magnitudes being central to psychology’s foundational discipline of psychophysics, quantitative characterisations that are stable across different individuals and contexts have remained elusive. We address this problem through a theoretical framework defining subjective magnitudes as the inputs to a dynamic model of perceptual two-alternative forced choice. Three observer-specific parameters—their sensitivity to subjective magnitudes, and differences between magnitudes, and their decision urgency, along with the psychophysical function mapping objective to subjective magnitudes—determine the rate at which evidence for each choice accrues. Responses and response times are a function of the evidence rate, additive stochastic noise, the threshold amount of evidence required to make a choice, and the time for non-decision processes. We develop both non-parametric and parametric methodologies within this framework to measure the psychometric function and apply them to judgements about which of two rectangles has a greater area of one of two colours. In almost every participant over several experiments varying the decision context (sets of stimuli spanning different ranges), both methodologies converge on an identity mapping between the objective proportional area and the subjective input to the decision process. Further experiments, looking at broader stimulus ranges and different decision tasks explored the limits of this unanimity.
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Gronau, Q. F., Matzke, D., &