IT IS not the “unknown unknowns” that catch people out, but the truths they hold to be self-evident that turn out to be completely wrong. On many issues, the gap between public perceptions and reality is very wide. The polling company Ipsos Mori found that Americans think 33% of the population are immigrants, for example, when the actual number is 14%. A 2013 poll found that Britons thought 24% of the population was Muslim—almost five times the correct figure of 5%.

Misperceptions about economic policy are common, too. Asked to name the top two or three areas of government spending, 26% of Britons cited foreign aid, more than picked pensions or education. In fact, aid spending is a small fraction of the other two and only 1% of the total.

Some of this is to do with innumeracy. Only a quarter of Britons could work out that the odds of throwing two consecutive heads in a coin toss was 25%. People are also heavily influenced by anecdotal evidence and by fears for themselves or their families—hence the tendency to overestimate the prevalence of crime or teenage pregnancy. (Asked how many teenage girls get pregnant each year, Americans plumped for 24%; the actual figure is 3%.)

More worrying is the possibility that people simply do not trust the official numbers. When Britons were asked why they overestimated the percentage of immigrants within the population, two answers dominated. One camp said that the government undercounted the numbers because of illegal immigration; a second group simply insisted their own answer was right, regardless of the evidence.

This points to the difficulty facing mainstream politicians who are trying to halt the rise of populists like Donald Trump. Reasoned presentation of the facts may not help since the source of the information, whether it is the government or the mainstream media, will always be suspect. Those advocating that Britons vote to leave the European Union in next month’s referendum, for example, dismiss warnings about the economic impact from the IMF, OECD and Bank of England on the grounds that, “They would say that, wouldn’t they?”

If public misperceptions can distort economic debate, they are also a problem when it comes to financial markets. Financial products are often complex and buyers can be confused by the terminology. One survey found that only half of Americans knew that mutual funds did not offer a guaranteed return. A lack of mathematical knowledge is a further difficulty. Another survey asked 50-somethings questions that related to financial literacy; asked to calculate how much each of five prize-winners would get from a lottery jackpot of $2m, only 56% of respondents could answer the question. More than two-fifths did not know the difference between simple and compound interest.

The trend has been for individuals to shoulder more responsibility for their financial well-being than they did in the past. This is particularly true in the case of pensions, where companies are retreating from the paternalistic approach of offering pensions linked to a worker’s final salary. In the brave new world of defined-contribution schemes, workers get a pot at retirement which they must eke out for the rest of their lives.

These are difficult calculations to make. A survey by the Society of Actuaries found that around 40% of Americans underestimated the average life expectancy of retired people by five years or more. Around 77% of Americans are very or somewhat confident that they are well prepared for retirement but only 63% say they have saved any money towards it, according to the Employee Benefit Research Institute.

These misapprehensions illustrate the problem with the idea of caveat emptor, or buyer beware, when it comes to retail customers of financial services. Investment products are not the same as other goods. First, the price is not immediately obvious, given the impact of annual charges and fees on a customer’s long-term return. Second, the usefulness of the product may only become apparent after several years. A mutual fund is not like a corked wine that people can hand back to the waiter right away. By the time customers find out things have gone wrong, their financial future may be badly damaged. Third, there is an asymmetry of information between the seller and the buyer.

Educating children and adults to be financially literate might help in the long term. Until then regulators, just like politicians, must deal with the public as they are, not how they might like them to be.

Economist.com/blogs/buttonwood