As algorithms are increasingly applied to screen applicants for high-stakes decisions in employment, education, lending, and other domains, concerns have been raised about the effects of "algorithmic monoculture", in which many decision-makers all rely on the same algorithm. This concern invokes analogies to agriculture, where a monocultural system runs the risk of severe harm from unexpected shocks. We present a set of basic models characterizing the potential risks from algorithmic monoculture, showing that monocultural convergence on a single algorithm by a group of decision-making agents, even when the algorithm is more accurate for any one agent in isolation, can reduce the overall quality of the decisions being made by the full collection of agents. Our results rely on minimal assumptions, and involve a combination of game-theoretic arguments about competing decision-makers with the development of a probabilistic framework for analyzing systems that use multiple noisy estimates of a set of alternatives. The talk is based on joint work with Manish Raghavan.