Mathematical models allow for deep analysis of observed phenomena by providing a framework to simulate reasonable outcomes when designing appropriately scaled experiments is not feasible. In our work, we develop several models to study the decision-making processes and overall success of individuals on a structured network when given a task and asked to come to consensus. Based on experiments, we investigate four cases: two different network structures (homogeneously mixed and spatially embedded) and two tasks of varying complexity. Importantly, we focus on effectively modeling the use of both contextual information (i.e., learning gained by interacting with others directly about a topic) and background information (i.e., personal biases about a topic brought into a learning situation) to make selections. A robust model for these experiments can give us insight into the ways that people combine social information and past experience to make decisions in groups. Implications of modeling these scenarios are a deeper understanding of how information is exchanged in online spaces and how regulations may be targeted directly at harmful discourse.