Where's Waldo, Ohio? Using Cognitive Models to Improve the Aggregation of Spatial Knowledge

We apply cognitive modeling to improve the wisdom of the crowd in a spatial knowledge task. Participants provided point estimates for where 48 US cities are located and then, using the point estimate as a center point, chose a radius large enough that they believed the resulting circle was certain to contain the city's location. Simple and radius-weighted arithmetic averages of the individuals' point estimates produced more accurate group answers than the majority of individuals. These statistical aggregates, however, assume there are no differences in individual expertise nor in the difficulty of locating different cities. Accordingly, we develop a set of cognitive models to infer group estimates that make various assumptions about individual expertise and differences in city difficulty. The model-based estimates generally outperform the statistical averages. The models are especially accurate if they allow for individual differences in expertise that can vary city by city. We replicate this finding by applying the same cognitive models to data reported by Mayer and Heck (2023) in which participants provided point estimates for the locations of European cities.