Sources of imprecision in integrated value comparisons

Many everyday decisions involve integrating multiple attributes rather than comparing a single value. While normative and stochastic choice theories assume that each option is evaluated independently, evidence shows that choices can instead depend on attribute-wise comparisons between options. To investigate the source of imprecision in such comparisons, we introduce a paradigm in which participants compare two sequences of numbers and decide which sequence has the larger sum. Across three conditions, which only differ in how numbers from the two sequences are paired, we observe systematic differences in accuracy: participants perform best when paired values are closer in magnitude. This finding indicates that judgments depend on framewise comparisons of values presented simultaneously, rather than on independent processing of each option. To account for these results, we fit several models of noisy judgment based on cumulative integration of framewise comparisons. We consider both models based on nonlinear integration of framewise comparisons and models in which comparison noise variance depends on size of the framewise differences, and find that these mechanisms are of differing importance for different subjects. Clustering analyses confirm this heterogeneity, identifying one subgroup best characterized by models with value-dependent noise and another for whom nonlinear transformation of the framewise-differences is more important. Finally, we introduce hybrid models integrating both mechanisms, and find that these best explain behavior across clusters, and predict participants' performance more accurately than single-mechanism models. Our findings demonstrate that attribute-wise comparisons play a central role in multi-attribute decision-making, even in tasks that do not involve subjective preferences. They further highlight the need for models that combine distorted value encoding with value-dependent noise to explain heterogeneity in human choice behavior.