Aggregative Efficiency of Bayesian Learning in Networks

When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are log-linear functions of observations and admit a signal-counting interpretation of accuracy. Networks where agents observe multiple neighbors but not their common predecessors confound information, and even a small amount of confounding can lead to much lower accuracy. In a class of networks where agents move in generations and observe the previous generations, we quantify the information loss with an aggregative efficiency index. Aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Later generations contribute little additional information, even when generations are arbitrarily large and agents observe arbitrarily far into the past.