Cultural consensus theory for two-dimensional location judgments

Cultural consensus theory is a model-based approach for analyzing responses of informants when correct answers are unknown. The model provides aggregate estimates of the latent consensus knowledge at the group level while accounting for heterogeneity in informant competence and item difficulty. We develop a new version of cultural consensus theory for two-dimensional continuous judgments which are obtained when asking informants to locate a set of unknown sites on a geographic map. The new model is fitted using hierarchical Bayesian modeling. A simulation study shows satisfactory parameter recovery for realistic numbers of informants and items. We also assess the accuracy of the aggregate location estimates by comparing the new model against simply computing the unweighted average of the informants’ judgments. A simulation study shows that, due to weighing judgments by the inferred competence of the informants, cultural consensus theory provides more accurate location estimates than unweighted averaging. The new model also showed a higher accuracy in an empirical study in which individuals judged the location of 57 European cities on maps.