A Perceptual-Like Population-Coding Mechanism of Approximate Numerical Averaging

Abstract

Humans possess a remarkable ability to rapidly form coarse estimations of numerical averages. This ability is important for making decisions that are based on streams of numerical or value-based information, as well as for preference formation. Nonetheless, the mechanism underlying rapid approximate numerical averaging remains unknown, and several competing mechanism may account for it. Here, we tested the hypothesis that approximate numerical averaging relies on perceptual-like processes, instantiated by population coding. Participants were presented with rapid sequences of numerical values (four items per second) and were asked to convey the sequence average. We manipulated the sequences' length, variance, and mean magnitude and found that similar to perceptual averaging, the precision of the estimations improves with the length and deteriorates with (higher) variance or (higher) magnitude. To account for the results, we developed a biologically plausible population-coding model and showed that it is mathematically equivalent to a population vector. Using both quantitative and qualitative model comparison methods, we compared the population-coding model to several competing models, such as a step-by-step running average (based on leaky integration) and a midrange model. We found that the data support the population-coding model. We conclude that humans' ability to rapidly form estimations of numerical averages has many properties of the perceptual (intuitive) system rather than the arithmetic, linguistic-based (analytic) system and that population coding is likely to be its underlying mechanism.