Many Americans have strong opinions about policy issues shaping the presidential campaign, from immigration to Social Security. But their grasp of numbers that underlie those issues can be tenuous.

Americans vastly overestimate the percentage of fellow residents who are foreign-born, by more than a factor of two, and the percentage who are in the country illegally, by a factor of six or seven. They overestimate spending on foreign aid by a factor of 25, according to a 2010 survey. And more than two-thirds of those who responded to a 2010 Zogby online poll underestimated the part of the federal budget that goes to Social Security or Medicare and Medicaid.

“It’s pretty apparent that Americans routinely don’t know objective facts about the government,” says Joshua Clinton, a political scientist at Vanderbilt University.

Americans’ numerical misapprehension can be traced to a range of factors, including where they live, the news they consume, the political rhetoric they hear and even the challenges of numbers themselves. And it isn’t even clear how much this matters: Telling people the right numbers often doesn’t change their views.

This isn’t exclusively an American problem. Estimates by people in the U.K., Italy and France of immigrant populations in their nation miss by a bigger percentage than do Americans’ estimates, and Britons overstated the magnitude of U.K. net contributions to the European Union by more than 100 times in a 2010 survey.

Some of these findings may show simply that people don’t have a good grasp on very small or large numbers. Take a poll last year that found Americans overestimated federal spending on the Corporation for Public Broadcasting by a factor of at least 100. Arthur Lupia, a political scientist at the University of Michigan, says while Americans were far off the mark, the average response of 1% to 5% signals “that lots of people know that the amount spent is a small number.” CPB was budgeted $430 million last year, 0.01% of federal outlays.

“Numbers are hard,” says Ellen Peters, a psychologist at Ohio State University. “They’re difficult to evaluate and remember because they’re abstract symbols,” and their meaning shifts depending on the context. And absorbing policy numbers may not be worth the effort: “People are more likely to remember numbers accurately when that information is more valuable to them,” Ms. Peters says.

Pollsters and political scientists say people, when asked to estimate national figures, can place undue weight on their immediate surroundings. Someone who lives near many foreign-born people might exaggerate the national foreign-born population.

Even when polls have a narrower scope, respondents aren’t necessarily on firmer ground. A telephone poll last year of 2,004 Californians by the Public Policy Institute of California found that they didn’t know much about how their state government was spending its money.

Nearly half of respondents named prisons and corrections as the top state expenditure among four available choices, while just 16% named education. In fact, education was the leading state expenditure, with prisons getting about a quarter the funds that education does.

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H/T: eWallStreeter