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

Abstract

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.