  Being able to correctly aggregate the beliefs of many people into a single
belief is a problem fundamental to many important social, economic and
political processes such as policy making, market pricing and voting. Although
there exist many models and mechanisms for aggregation, there is a lack of
methods and literature regarding the aggregation of opinions when influence and
learning between individuals exist. This is in part because there are not many
models of how people update their belief when exposed to the beliefs of others,
and so it is hard to quantify the dependencies between people's mental models
which is essential to minimizing redundancies in the aggregation. In this
paper, we explore many models of how users influence and learn from each other,
and we benchmark our models against the well-known DeGroot model. Our main
contributions are: 1) we collect a new dataset of unprecedented size and detail
to be posted online; 2) we develop a new Social Bayesian model of how people
update their mental models, 3) we compare of our model to other well-known
social learning models. Specifically, we show that our new Social Bayesian
model is superior to the other models tested.
