Emergent numeracy: How the crowd wisdom of non-rounding survey respondents generates accurate immigration estimates

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Survey respondents overestimate, on average, the number of immigrants living in their country. This phenomenon, known as immigration innumeracy, seems incompatible with the wisdom-of-crowds effect, which suggests that large samples of individuals should, as a collectivity, be good at estimating such figures. However, this article reveals that crowd wisdom does emerge in a previously overlooked subgroup: non-rounding respondents. Drawing on German and European survey data, it is shown that when round estimates (5, 10, 15, …) are excluded, a subset of “wise” non-rounding respondents remains, who collectively estimate the share of foreigners in their country with astounding precision. Thus, a relevant—and easily identifiable—part of the population is actually collectively immigration numerate. Two potential mechanisms behind this emergent phenomenon are explored. First, regression models reveal that non-rounders are more educated and politically interested than rounders, indicating more informed guesses. Second, simulations show that the coarse-grained nature of round numbers itself can contribute to inaccurate estimates. Using round numbers is thus associated with uncertainty, resulting in biased estimates. Taking the crowd wisdom of non-rounding respondents into account qualifies the extent of immigration innumeracy and improves our understanding of a phenomenon that is often seen as a root cause of xenophobia.