Systematic variation in proportion judgments: Spatial features impact adults' strategies and decisions

Proportional information is important for a range of everyday actions, from infants' and toddler's probabilistic inferences to adults' medical and financial decisions. Unfortunately, children and adults frequently make systematic errors in some proportional reasoning contexts. For example, people tend to focus more on the numerators, rather than the proportional relations, when proportions are discrete (i.e., with enumerable units) or when the subcomponents are spatially separated. Importantly, it is not that people cannot reason proportionally, as they do not make these same errors with continuous proportions presented as part of a single coherent whole. Although format-dependent variation has been shown across many studies with both children and adults, no work has systematically manipulated multiple aspects of visual, nonsymbolic proportional stimuli simultaneously to better understand which spatial factors impact proportional reasoning, and how. Here, we manipulate proportional stimuli in three ways: the availability of enumerable units (i.e., discreteness), predictability of the proportional information, and spatial separateness of the proportion subcomponents. We also formalize competing strategy explanations using mathematical models to infer people's strategies. Overall, we find that discreteness, predictability, and spatial separateness (as operationalized here) significantly impact adults' performance and strategies. Furthermore, all features interact with each other, and qualitative patterns suggest that spatial separateness and predictability may be particularly important, despite being less well-studied. By systematically varying the spatial features of proportions, we provide insight into the mechanisms that underlie proportional reasoning and highlight important interactions between spatial, numerical, and relational information. (PsycInfo Database Record (c) 2026 APA, all rights reserved).