When more is not more: evidence for bounded perceptual-relational integration in non-symbolic proportion judgments

Non-symbolic proportion judgments require relational information to be extracted from perceptual input, yet the computational principles governing the contribution of continuous visual magnitude remain unclear. The present study examined whether perceptual influences on proportion judgments vary with relational context and whether their contribution increases linearly with cue strength or is subject to functional constraints. Across four experiments, participants compared non-symbolic proportions while continuous perceptual magnitude was manipulated through area scaling without altering the underlying proportional relationships. Experiments 1 and 2 showed that unilateral enlargement and contraction both influenced proportion judgments, indicating that perceptual effects were not specific to a single direction of physical scaling. Experiment 3 further showed that performance varied according to the alignment between perceptual and relational information, with perceptually congruent conditions generally facilitating performance and incongruent conditions producing interference. Experiment 4 manipulated perceptual cue strength at two scaling levels and found that increasing cue magnitude did not produce proportional increases in behavioral influence; this constraint was more evident in response-time dynamics than in categorical accuracy. Hierarchical drift-diffusion modeling provided converging computational evidence: a model incorporating a bounded transformation of perceptual input showed better predictive performance than a purely linear integration model. Together, these findings indicate that non-symbolic proportion judgments are not fully insulated from continuous perceptual variation. Instead, perceptual information contributes to decision formation in a context-sensitive manner, and its influence is better characterized by a constrained computational framework than by unrestricted linear cue accumulation.