From small committees to national elections, group decision-making can be complicated -- and it may not always settle on the best choice. That's partly because some members of the group do research on their own, and others take their cues from the people around them. A new mathematical framework predicts that decision-making groups have a critical threshold of people who get their information from others. Below that threshold, the group chooses the high-quality outcome. Above it, the group can end up choosing the better or worse option.