Cultural Consensus Theory (CCT) consists of cognitive models for aggregating the responses of informants to test items about some domain of their shared cultural knowledge. This paper proposes variants of CCT for pooling undirected, signed graphs collected from error-prone and biased informants. Informants provide dichotomous ’plus’ or ’minus’ responses to judgments on all possible ties among a fixed set of named nodes. The primary goal is to achieve a single pooled signed graph that better reflects the ”wisdom of the crowd” for small datasets than simple marginal averaging of responses.

These models break the typical CCT assumption of conditional independence of question items in two ways. First, the models attribute the quality of a response to properties of the pair of nodes in question. Both continuous and discrete nodal properties add dependencies between responses by the same informant. Second, a hard constraint on the aggregate graph imposes dependencies among the values of the aggregate graph ties.

We show that graph elicitations of different kinds warrant the use of new CCT models and that the models discussed here illuminate aspects of the underlying graph structure that are otherwise hidden using standard CCT methods.

A large component of the work involves novel estimation algorithms that operate under hard constraints on discrete parameters, something that has not been done before with CCT. Question ordering for undirected graphs and an incomplete design are discussed as well as possible extensions and related work.