IF I had to guess, I'd say that 90% of the time, when you ask people to estimate quantities in the population, over 50% pick numbers that are off by more than 25%. But I could be wrong. Because the press tends to over-report surveys in which large numbers of people make spectacularly inaccurate guesses, my impression of the percentage of people who tend to wildly exaggerate statistics may be wildly exaggerated.

Like Kevin Drum, I think this kind of media-driven process is key to what's happening in the Gallup pollKarl Smith cites, in which 52% of Americans estimated that at least 20% of Americans are gay. As Mr Smith says, these people "can't be experiencing anything like: 1 out of every 5 people I know is gay," since only 3.5% of Americans identify as gay, lesbian, bisexual or transgender. But gay issues have been very prominent in the news for decades, there are lots of gay celebrities, and gay characters are ubiquitous in fiction, film and TV. In 1995 "My So-Called Life" was pushing the envelope by including a gay best-friend character; by the time of "Glee", even a semi-parodic high-school show has to have a semi-parodic gay character who goes through a semi-parodic coming-out drama with his dad. In terms of how people constitute their mental pictures of society, these things drive the impression that gays are a normal and substantial portion of the population.

Unfortunately Gallup doesn't seem to have polled this question far enough back, but things were definitely different in the 1980s. I graduated from a gay-rights-friendly high school, with several out teachers, but still had the ludicrous impression that the gay-rights movement's population stats must be grossly inflated since, after all, none of the students in my high school were gay. Duh! That closet took about a decade to get fully sorted out. I imagine that back then, most people had ridiculously exaggerated senses of how few Americans are gay, rather than how many, and I think the gradual destigmatisation of homosexuality at the high-school level means that fortunately a lot fewer kids these days are as dumb as I was on this subject.

The overestimates of the percentage of gay Americans are clearly related to the Gallup poll's finding that 56% of Americans now find gay relations morally acceptable, versus 39% who think they're morally wrong. In 2001 that was close to flipped, with 40% accepting and 53% thinking them morally wrong. Jonathan Rauch thinks this shift means the "superstructure" of discrimination against gays is about to melt away. I think the experience of European countries that saw the same shift in attitudes a decade or two earlier suggests he's right. Of course Adam Serwer and Andrew Sullivan are also right that in the short term, this might instead drive a redoubling of anti-gay political exploitation by the culture-war wing of the conservative movement. But once you consider the Miley Cyrus factor, the outcome really isn't in doubt.