Before revision:  We provide a simple linear formula characterizing agents' actions in terms of paths in the network and use this formula to determine when society learns correctly in the long-run. Because early agents are disproportionately influential, standard network structures can lead to herding on incorrect beliefs .
After revision:  We provide a simple linear formula characterizing agents' actions in terms of paths in the network and use this formula to determine when society eventually learns correctly. Disproportionately influential early agents can cause herding on incorrect beliefs .