I hate the polling question "What percentage of the US budget goes to foreign aid?" Or, more precisely, I hate the way the results are interpreted.

The way these polls are reported is essentially guaranteed to produce a wild overestimate, which inevitably leads experts to write "how wrong Americans are" pieces, like this Brookings article claiming that "Americans believe foreign aid is in the range of 25 percent of the federal budget," or KFF[1]reporting that the "average perceived amount spent on foreign aid was 26%."

But this isn't just ignorance. The real problem is a failure of measurement and the statistics used to summarize it. The story isn't "Americans are clueless" (though that may also be true), it's "pollsters are using the wrong math."

The Real Problem: Arithmetic Mean + Small Numbers

The problem is that pollsters ask for a percentage, then take the arithmetic mean to represent the data. For small true values, this approach is structurally doomed, and it has nothing to do with foreign aid specifically. It has to do with how we summarize guesses about small numbers.