Cultural Consensus Theory: Comparing different concepts of cultural truth

Abstract

Cultural Consensus Theory (CCT) is a model-based approach to aggregating the responses of informants (respondents) to questions (items) about some domain of their shared cultural knowledge. The purpose of CCT is to allow a researcher to discover consensus knowledge in cultural groups. This paper compares and contrasts two CCT models for items requiring a dichotomous, true/false answer. The first model is the General Condorcet Model (GCM). A special case of the GCM is already in wide use, especially in cultural anthropology, and this paper generalizes that version and provides new mathematical and statistical results for it. The character of the GCM is that of a general signal detection model, where the item-trial type (signal or noise) as well as the respondents’ hit and false alarm rates, are latent rather than observable. The second model, the Latent Truth Model (LTM), is a new model that allows cultural truth to assume continuous values in the unit interval rather than the two-valued truth assumption of the GCM. Both models are compared analytically, and hierarchical Bayesian inference for each is developed. A posterior predictive model check is established for both models that bears directly on the assumption that there is a single consensus truth. In addition, the similarities and differences between the models are illustrated both with mathematical and statistical results, as well as by analyzing real and simulated data sets, and a second posterior predictive check that tends to differentiate the models is also provided.