How bad is forming your own opinion?

The question of how people form their opinion has fascinated economists and sociologists for long time. In many of the models, a group of people in a social network, each holding a numerical opinion, arrive at a shared opinion through repeated averaging with their neighbors in the network. Motivated by the observation that in reality consensus is rarely reached, we study a related sociological model in which individuals' intrinsic beliefs counterbalance the averaging process and yield a diversity of opinions.We interpret the repeated averaging process as best-response dynamics in an underlying game with natural payoffs and its limit as an equilibrium. This allows us to study the cost of disagreement by comparing between the cost at equilibrium and the social optimum. We also consider a natural network design problem in this setting: which links can we add to the underlying network to reduce the cost at equilibrium?.