According to the axiomatic literature on consensus methods, the best collective choice by one method of preference aggregation can easily be the worst by another. Are award committees, electorates, managers, online retailers, and web-based recommender systems stuck with an impossibility of rational preference aggregation? We investigate this social choice conundrum for seven social choice methods: Condorcet, Borda, Plurality, Antiplurality, the Single Transferable Vote, Coombs, and Plurality Runoff. We rely on Monte Carlo simulations for theoretical results and on twelve ballot datasets from American Psychological Association (APA) presidential elections for empirical results. Each of these elections provides partial rankings of five candidates from about 13,000 to about 20,000 voters. APA preferences are neither domain-restricted nor generated by an Impartial Culture. We find virtually no trace of a Condorcet paradox. In direct contrast with the classical social choice conundrum, competing consensus methods agree remarkably well, especially on the overall best and worst options. The agreement is also robust under perturbations of the preference prole via resampling, even in relatively small pseudosamples. We also explore prescriptive implications of our findings.