Survey Respondents *Can* Collectively Produce Accurate Immigration Estimates: Here’s how

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What do you think is the percentage of foreign-born people in your country? Please take a moment to think of an answer!

If you are like most people, you may have guessed something like 10 percent, 20 percent, or perhaps 25 percent. Most people use round numbers such as these when guessing (a sign of uncertainty!) – and they collectively overestimate the share of migrants in their country. However, some people use non-round numbers (8 percent, 12 percent, 17 percent, etc.) and they – as a group – produce surprisingly accurate immigration estimates, as a new MPC working paper reveals.

Immigration Innumeracy vs. Crowd Wisdom

Past research has shown that survey respondents consistently overestimate, on average, the share of immigrants in their country. This phenomenon, known as immigration innumeracy, is important, because it offers an explanation for the prevalence of anti-immigrant sentiment and the success of right-wing populism: People feel threatened because they perceive the outgroup of foreigners in their society as larger than it actually is.

So far, however, it has not been considered that the existence of immigration innumeracy is puzzling in that it contradicts the wisdom-of-crowds effect, which suggests that large samples of individuals should actually be good, on average, at estimating such figures.

The classic example for the emergence of crowd wisdom is a competition that took place at a fair in Plymouth in 1906 where people had to guess the weight of an ox. Francis Galton, who visited the fair, was skeptical of the abilities of the masses and surprised when he found in his statistical analyses of the 787 guesses by the local population that on average, they estimated the weight of the Ox correctly.

The reason behind this fascinating phenomenon of “collective intelligence” is that while individual guesses can be off to either side, these deviations cancel each other out when the quantity of estimates is large enough.

Crowd wisdom can emerge—and be used to derive better judgements—in many different contexts from political and economic forecasting to the evaluation of nuclear safety or the rise of sea levels. Why then should crowd wisdom not also occur in the case of immigration estimates?

The Crowd Wisdom of Non-Rounding Survey Respondents

In a new working paper, I show that actually, a substantial share of respondents collectively estimates the share of foreigners in their country correctly, in line with the wisdom-of-crowds effect. This crowd wisdom becomes visible when rounding and non-rounding respondents are looked at separately.

I show, based on ALLBUS survey data that is representative of the German population (and European Social Survey data), that when respondents who round (i.e., who use numbers that end with the digit “0” or “5”) are excluded from the analysis, the remaining sample of non-rounding respondents is collectively capable of estimating the share of foreigners in their country with astounding precision.

For example, in Western Germany, the official share of foreigners across the three years under study was 10.9 percent. All survey respondents who made a guess estimated the share of foreigners to be 20.0 percent on average – a clear case of immigration innumeracy. The overestimation was even bigger among rounding respondents. The group of non-rounders, by contrast, deviated from the official value by a mere 0.19 percentage points – far less than one percentage point, which is used in the literature as the most rigorous threshold for a correct estimate.

This shows that there is actually a “wise crowd” of non-rounders that remains hidden among the overall sample as long as rounding respondents are not excluded.

Reversely, those respondents who do collectively overestimate the share of foreigners all have in common that they round. This suggests that immigration innumeracy could be driven by uncertainty about the correct answer rather than a conviction that the share of foreigners is really higher than it actually is.

This finding has meaningful implications: If a lack of certainty generates the overestimation, then targeted information about the actual situation might have a better chance of being accepted. This is in contrast to a situation where individuals have strong conviction that the share of foreigners is overly high. The role of the rounding bias in creating immigration innumeracy should thus be considered by actors interested in educational measures against xenophobia.

In future research, I aim to explore whether the collective numeracy of non-rounders also emerges in other estimation and prediction tasks. After all, people are today regularly confronted with such tasks in their everyday lives. For example, faced with a viral threat, they have to estimate health risks when engaging in social interaction. In light of the climate crisis, they need to estimate the environmental costs of their behavior. Ever more often, this requires handling numbers, from COVID-19 incidence rates to CO2 footprints.


Emanuel Deutschmann is an Assistant Professor of Sociological Theory at Europa-Universität Flensburg in Germany and an Associate at the European University Institute’s Migration Policy Centre.

Read Emanuel’s new working paper here