Italians and Americans score worst when it comes to correctly assessing basic facts of modern life, such as what proportion of the population are immigrants or Muslims and what percentage of teenage girls get pregnant.
Swedes and Germans do best, although even they consistently get things wrong, according to a survey of 14 industrialised countries released on Wednesday.
The analysis by market research organisation Ipsos MORI shows how far perceptions stray from reality across a range of issues as people struggle to get a precise handle on aspects of society that are seen as risks or worries.
Levels of immigration — a hot-button topic in many developed countries — are overestimated everywhere but the United States veers further from reality than most, with an average guess that 32 percent of the population are immigrants when the reality is 13 percent.
Italy fares even worse, with an average guess of 30 percent against a real figure of only seven percent.
Italians are also spectacularly bad at estimating the number of old people in the country, believing that 48 percent are over 65 years old. In reality, the over-65s make up a fifth of the population — a relatively high figure but no higher than in Germany and considerably lower than in Japan.
Teenage pregnancy is another issue where people everywhere get the sums badly wrong, reflecting the difficulty of assessing occurrences that are relatively rare.
Americans think 24 percent of girls aged 15 to 19 give birth each year, when the real figure is just 3 percent, and even the sensible Swedes are badly out, believing the annual teenage pregnancy rate is 8 percent compared to the actual 0.7 percent.
“People are just not very good at maths and they find it particularly hard to make estimates about very large numbers or very small numbers,” said Bobby Duffy, global director of the Ipsos Social Research Institute.
“It seems people remember vivid anecdotes about things, regardless of whether they are describing something very rare.”
Health experts have bemoaned similar perception problems in the current Ebola outbreak, where public alarm over a handful of cases in the United States is at odds with the real risks. This topic was not covered in the survey, which was conducted in August among more than 11,000 people across the 14 countries.
Estimating religious groupings in society is another area where perception is seriously out of kilter with reality. Like other controversial topics, it is a subject where media coverage is likely to play a role in exaggerating misconceptions.
People hugely overestimate the proportion of Muslims living in their country, with the French putting the figure at 31 percent, when the real figure is 8 percent. The British guess at 21 percent (real figure 5 percent) and Americans estimate 15 percent (real figure 1 percent).
Even in countries such as Hungary, Poland, South Korea and Japan, where fewer than one percent of the population is Muslim, people put the figure at four to seven percent.
By contrast, majority-Christian countries tend to underestimate how many people count themselves as Christian.
The ramifications of widespread ignorance about basic measures of what is happening in society are unclear but they could potentially influence behaviour and undermine rational political debate.
If, as the survey found, people routinely underestimate the proportion of the population that votes in elections, there may be a persistent downward drift in voter turnout.
Similarly, if people are not accurately assessing the impact of policies in areas such as immigration, then action by governments may not influence the political debate as expected.
Much of the disconnect may be down to “emotional innumeracy” when answering, according to Duffy, who believes people may be sending a message about what is worrying them as much as trying to reply to the questions correctly.
“Cause and effect can run both ways, with our concern leading to our misperceptions as much as our misperceptions creating our concern,” he said.