Tuesday, September 02, 2008

The myth of sexual predators: a positive feedback model   posted by agnostic @ 9/02/2008 10:36:00 PM

As a special case of the downward trend in homicide and forcible rape beginning in the early 1990s, from 1990 to 2004, sexual abuse of minors steadily declined by 49%, reversing an upward trend from the 15 years before 1990; and from 1993 to 2004, sexual assaults against 12 to 17 year-olds steadily declined by 67%. See Finkelhor & Jones (2006) (free PDF here) for a review of the data, why they are real declines, and some proposed explanations. Also see Wolak et al. (2008) (free PDF here) for a review of the fact and fiction about internet sexual predators -- in particular, it appears that most sexual relationships involving teenage females that began with internet contact are voluntary (although still statutory rape if the female is under the age of consent), often repeated, and that the males rarely use deception. Unwholesome, but not what you see on To Catch a Predator.

Not to put too fine a point on it, but the recent panic that the mass media have been fueling about "sexual predators" is horseshit. For the same methodological reasons as in this post on the rape hysterias, I look at data on the popularity of the "sexual predator" theme in the New York Times. It is the opposite of the prediction from a "following the beat" view of journalistic practice, instead fitting a "spreading an unfounded rumor" view. I propose a simple model and estimate the annual growth rate of the rumor. First, let's see how many articles were written in the NYT in a given year that contained "sexual predator," "sex predator," or the plural forms of these two terms.

Here is a graph:

Right away we observe that the coverage is completely outta whack with the crime statistics on the ground: the phrases first appear in 1966, but there is essentially no coverage up through 1980, a moderate increase until 1990, and an explosion of articles starting around 1990. Because the increase in coverage cannot be explained by a rational response to easily discovered crime statistics, we conclude that it is an irrational "moral panic" -- if the sexual predator did not exist, it would be necessary to invent him.

Going further, let's look at the data from 1981 to 2007. I start with 1981 because that is the first year when at least 2 articles appear -- 1 article every 5 or 10 years you could write off as flukes -- and I drop 2008 since the year is not done yet:

Of the typical curves used to fit data, here the exponential does the best: r^2 = 0.8772, and there is a theoretical reason to expect exponential growth. Actually, a quadratic curve improves r^2 by 0.0037, but that's not very much, and it doesn't illuminate what's going on. By setting 1981 equal to t = 1, and calling the number of articles N, the curve above is:

N(t) = 0.8896*exp(0.1665*t) - 1

So, the estimated annual growth rate is 0.1665.

An exponential function solves a differential equation of the form:

dN/dt = r*N

In words, the rate of increase in the number of articles is directly proportional to the current number of articles, where r is the growth rate we just estimated above. This says that somehow each article begets more articles which beget more articles. This is how a rumor spreads, although "articles written" are technically not the same thing as "people who have heard the rumor." Perhaps in the future the number of articles will saturate at some level, and we will have to re-model it using logistic growth. Or the meme could become unfashionable and the number will plummet to 0, in which case we'd use a boom-and-bust model. These two more realistic models are variations on the S-I-R model of the spread of contagious diseases, the only difference being whether the "infected" people can lose their infectivity or stay infected forever.

Clearly the unlimited exponential growth model is inadequate because the total number of articles in all of the NYT is bounded, so the articles written on "sexual predators" cannot increase without bound. But since their number has not saturated yet (logistic model) or crashed downward (boom-and-bust model), we can't decide between the two more plausible models, let alone estimate the related parameters (like the steady-state number of articles in the logistic model). What is important here is that we have shown that the popularity of the "sexual predator" idea behaves like a rumor and takes on a life of its own or fuels its own growth.

To wrap up, the panic over "sexual predators" is a lot like the Early Modern witch-hunts, which could not have succeeded without mass communication to spread the rumors of well-to-do worry-warts. Because it's easier to swallow rumors than to investigate them, there's a clear incentive for most reporters to do just that. And most of the blogosphere too, for that matter. The desire to know is just not uniformly distributed among the population, even among the affluent sectors. That's something to consider any time you find yourself parroting the hype -- if it were based on good work, then it would pay to buy into it. But most journalists are too stupid, lazy, credulous, or moralistic to figure out what's going on. And most of the blogosphere too, for that matter.

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