In a broad range of classification and decision-making problems, one is given the advice or predictions of several classifiers, of unknown reliability, over multiple questions or queries. This scenario is different from the standard supervised setting, where each classifier's accuracy can be assessed using available labeled data, and raises two questions: Given only the predictions of several classifiers over a large set of unlabeled test data, is it possible to (i) reliably rank them and (ii) construct a metaclassifier more accurate than most classifiers in the ensemble? Here we present a spectral approach to address these questions. First, assuming conditional independence between classifiers, we show that the offdiagonal entries of their covariance matrix correspond to a rank-one matrix. Moreover, the classifiers can be ranked using the leading eigenvector of this covariance matrix, because its entries are proportional to their balanced accuracies. Second, via a linear approximation to the maximum likelihood estimator, we derive the Spectral Meta-Learner (SML), an unsupervised ensemble classifier whose weights are equal to these eigenvector entries. On both simulated and real data, SML typically achieves a higher accuracy than most classifiers in the ensemble and can provide a better starting point than majority voting for estimating the maximum likelihood solution. Furthermore, SML is robust to the presence of small malicious groups of classifiers designed to veer the ensemble prediction away from the (unknown) ground truth.spectral analysis | classifier balanced accuracy | unsupervised learning | cartels | crowdsourcing E very day, multiple decisions are made based on input and suggestions from several sources, either algorithms or advisers, of unknown reliability. Investment companies handle their portfolios by combining reports from several analysts, each providing recommendations on buying, selling, or holding multiple stocks (1, 2). Central banks combine surveys of several professional forecasters to monitor rates of inflation, real gross domestic product growth, and unemployment (3-6). Biologists study the genomic binding locations of proteins by combining or ranking the predictions of several peak detection algorithms applied to large-scale genomics data (7). Physician tumor boards convene a number of experts from different disciplines to discuss patients whose diseases pose diagnostic and therapeutic challenges (8). Peer-review panels discuss multiple grant applications and make recommendations to fund or reject them (9). The examples above describe scenarios in which several human advisers or algorithms provide their predictions or answers to a list of queries or questions. A key challenge is to improve decision making by combining these multiple predictions of unknown reliability. Automating this process of combining multiple predictors is an active field of research in decision science (cci.mit.edu/research), medicine (10), business (refs. 11 and 12 and www.kaggle.com/competitions), and government...