Given a directed graph where each vertex has preferences over its in-neighbors, we consider the problem of finding a popular arborescence in this digraph. Popular arborescences have applications in liquid democracy or collective decision making; however, they need not exist in every input instance. We characterize popular arborescences in terms of dual certificates---this leads to an efficient combinatorial algorithm to decide if a given digraph admits a popular arborescence or not and if so, to find one. (Joint work with Kazuhisa Makino, Ildiko Schlotter, and Yu Yokoi.)