There are various security-critical decisions routinely made, on the basis of information provided by peers: routing messages, user reports, sensor data, navigational information, blockchain updates, etc. Jury theorems were proposed in sociology to make decisions based on information from peers, which assume peers may be mistaken with some probability. We focus on attackers in a system, which manifest as peers that strategically report fake information to manipulate decision making. We define the property of robustness: a lower bound probability of deciding correctly, regardless of what information attackers provide. When peers are independently selected, we propose an optimal, robust decision mechanism called Most Probable Realisation (MPR). When peer collusion affects source selection, we prove that generally it is NP-hard to find an optimal decision scheme. We propose multiple heuristic decision schemes that can achieve optimality for some collusion scenarios
