Emergent numeracy : how the Crowd Wisdom of non-rounding 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, contradicts the wisdom-of-crowds effect, which suggests that large samples of individuals should, as a collectivity, be good at estimating such figures. This article demonstrates that differentiating between rounding and non-rounding respondents allows to resolve this seeming contradiction. It argues that rounding is associated with uncertainty, resulting in less reliable estimates. Based on German and European survey data, it shows 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 substantial—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, suggesting more informed guesses. Second, simulations show that the coarse-grained nature of round numbers itself can contribute to inaccurate estimates. The emergence of crowd wisdom among non-rounding respondents qualifies the extent of immigration innumeracy and reveals hitherto hidden mechanisms behind a phenomenon that is often seen as a root cause of xenophobia.