  We explore a model of non-Bayesian information aggregation in networks.
Agents non-cooperatively choose among Friedkin-Johnsen type aggregation rules
to maximize payoffs. The DeGroot rule is chosen in equilibrium if and only if
there is noiseless information transmission, leading to consensus. With noisy
transmission, while some disagreement is inevitable, the optimal choice of rule
amplifies the disagreement: even with little noise, individuals place
substantial weight on their own initial opinion in every period, exacerbating
the disagreement. We use this framework to think about equilibrium versus
socially efficient choice of rules and its connection to polarization of
opinions across groups.
