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.

Our scientific knowledge of human behavior has taken great leaps with the formalization of quantitative psychology. This dissertation is an amalgamation of mathematical models in the field of psychology, specifically as it pertains to higher order cognition. The goal is to provide a variety of useful contributions to psychology in three unique areas of the field. The first focuses on Signal Processing Models in recognition memory. I begin by outlining the two most popular models and describing their mathematical properties. This is done to promote both models usefulness as measurement tools, regardless of their mathematical differences. I continue by developing a novel extension for each model to further elucidate their usefulness in psychology. The second area of research discussed in this dissertation moves away from purely theoretical applications of mathematical models towards real-world applications of a stochastic system. Here, we develop and explore a Hidden Markov Model for memory deficits, with the goal of understanding dementia. Since clinical trials contain a variety of memory tests, a second paper devoted to further understanding memory decay in Alzheimers is provided. Finally, the last two chapters of this dissertation focus on decision making as it applies to information pooling techniques. We utilize the mathematical concepts developed throughout the dissertation in order to identify an area of improvement for models in current use, and offer an innovative new interpretation of existing theory. The final paper explores a natural extension to the theory for continuous-type responses, and outlines further opportunities for additional research in this area.