  Decision-making often involves ranking and selection. For example, to
assemble a team of political forecasters, we might begin by narrowing our
choice set to the candidates we are confident rank among the top 10% in
forecasting ability. Unfortunately, we do not know each candidate's true
ability but observe a noisy estimate of it. This paper develops new Bayesian
algorithms to rank and select candidates based on noisy estimates. Using
simulations based on empirical data, we show that our algorithms often
outperform frequentist ranking and selection algorithms. Our Bayesian ranking
algorithms yield shorter rank confidence intervals while maintaining
approximately correct coverage. Our Bayesian selection algorithms select more
candidates while maintaining correct error rates. We apply our ranking and
selection procedures to field experiments, economic mobility, forecasting, and
similar problems. Finally, we implement our ranking and selection techniques in
a user-friendly Python package documented here:
https://dsbowen-conditional-inference.readthedocs.io/en/latest/.
