The rise of Donald Trump proves that a lot of Americans are really worried about the influence immigrants are having on their society. Ditto the recent surge of far-right parties and anti-refugee sentiment in Europe.

There are many reasons why these fears are inflated. But one of them is deceptively simple: People in these countries think there are way more immigrants than there actually are.

How do we know? Political scientists John Sides and Jack Citrin looked at big surveys in the US, Europe, and Australia, and then compared two sets of responses: the percentage of people in that country who are immigrants, and the percentage of the population that people in that country say are immigrants in polls.

This chart, from the indispensable data blog Our World in Data, plots the results. It turns out that in every single country in the sample, people overestimated the number of immigrants — often dramatically (accurate results would be on the red line):

Why do they do this? To find out, Sides and Citrin did a study where they gave people correct information about the immigrant population and examined whether that changed their attitude toward immigrants in general (either for good or for ill). Interestingly, they found no real effect.

What did they conclude from this? Basically, that native attitudes about immigration stem from deeply ingrained beliefs and suspicions. People have strong views about immigration rooted in their most fundamental social and political attitudes (e.g., racism). As a result, instead of reasoning to facts about the number of immigrants, they will only believe facts that fit their preferred narrative — which is often that immigration is a major threat to the American or European way of life.

"Factual knowledge or beliefs are secondary in attitude formation," Sides and Citrin write. "Symbolic predispositions such as national identity or a generalized tolerance for difference, predispositions that are developed early in life and durable over time, may be more potent than an encyclopedia’s worth of facts about immigration."

In short, then, the overestimation of the immigrant population may not be so much a cause of fears about immigrants as a symptom. People think there are a ton of immigrants in their country because that's what they're afraid of.