We introduce the class of virtually additive non-Bayesian learning heuristics to aggregating beliefs in social networks. A virtually additive heuristic is characterized by a single function that maps a belief to a real number that represents the virtual belief. To aggregate beliefs, an agent simply sums up all the virtual beliefs of his neighbors to obtain his new virtual belief.
This class of heuristics determines whether robust learning, by any naive heuristic, is possible. That is, we show that in a canonical setting with a binary state and conditionally i.i.d. signals whenever it is possible to naively learn the state robustly it is also possible to do so with a virtually additive heuristic.
We also extend our results to achieve network-robust learning with dynamics that are based on local weights adjustments that agents assigned to each other in the network. These adjustments are based on the famous Sinkhorn-Knopp matrix scaling algorithm.