Abstract: The judgments of human beings can be biased; they can also be noisy. Across a wide range of settings, use of algorithms is likely to improve accuracy, because algorithms will reduce both bias and noise. Indeed, algorithms can help identify the role of human biases; they might even identify biases that have not been named before. As compared to algorithms, for example, human judges, deciding whether to give bail to criminal defendants, show Current Offense Bias and Mugshot Bias; as compared to algorithms, human doctors, deciding whether to test people for heart attacks, show Current Symptom Bias and Demographic Bias. These are cases in which large data sets are able to associate certain inputs with specific outcomes. But in important cases, algorithms struggle to make accurate predictions, not because they are algorithms but because they do not have enough data to answer the question at hand. Those cases often, though not always, involve complex systems. (1) Algorithms might not be able to foresee the effects of social interactions, which can depend on a large number of random or serendipitous factors, and which can lead in unanticipated and unpredictable directions. (2) Algorithms might not be able to foresee the effects of context, timing, or mood. (3) Algorithms might not be able to identify people’s preferences, which might be concealed or falsified, and which might be revealed at an unexpected time. (4) Algorithms might not be able to anticipate sudden or unprecedented leaps or shocks (a technological breakthrough, a successful terrorist attack, a pandemic, a black swan). (5) Algorithms might not have “local knowledge,” or private information, which human beings might have. Predictions about romantic attraction, about the success of cultural products, and about coming revolutions are cases in point. The limitations of algorithms are analogous to the limitations of planners, emphasized by Hayek in his famous critique of central planning. It is an unresolved question whether and to what extent some of the limitations of algorithms might be reduced or overcome over time, with more data or various improvements; calculations are improving in extraordinary ways, but some of the relevant challenges cannot be solved with ex ante calculations.