Cultural consensus theory for multiple consensus truths

Cultural Consensus Theory (CCT) is a popular information pooling methodology used in the social and behavioral sciences. CCT consists of cognitive models designed to determine a consensus truth shared by a group of informants (respondents), and to better understand the cognitive characteristics of the informants (e.g. level knowledge, response biases). However prior to this paper, no CCT models have been developed that allow the possibility of the informant responses to come from a mixture of two or more consensus answer patterns. The major advance in the current paper is to endow one of the popular CCT models, the General Condorcet Model (GCM) for dichotomous responses, with the possibility of having several latent consensus answer patterns, each corresponding to a different, latent subgroup of informants. In addition, we augment the model to allow the possibility of questions having differential difficulty (cultural saliency). This is the first CCT finite-mixture model, and it is named the Multi-Culture GCM (MC-GCM). The model is developed axiomatically and a notable property is derived that can suggest the appropriate number of mixtures for a given data set. The model is extended in a hierarchical Bayesian framework and its application is successfully demonstrated on both simulated and real data, including a new experimental data set on political viewpoints.