Horrific events, like the one mentioned in a post below where an 8 year-old girl was abducted, raped, and murdered on her way home from school, happen in real life. They're not a media fabrication. When people perceive their prevalence to be rising, as they did sometime in the later 1970s and in full force during the '80s, they begin to panic -- what is the world coming to?
Nerdy skeptics at the time, and eventually everyone once they have the benefit of hindsight, charge the panickers with over-reacting to a sensational event that is being blown out of proportion. Meanwhile, the panickers look back at the non-believers like they're at best clueless, and at worst complicit in allowing the problem to grow even more out of control.
Since the panickers' reaction to a perceived growing threat is so widespread across human groups and back through time, it is probably the correct reaction -- otherwise the individuals and/or groups who adopted it would have been weeded out long ago. Yet the educated classes always charge them with blowing things out of proportion, being driven by rare (and, so it is implied, irrelevant) sensationalistic stories. Let us see why the mob is right.
The elite mistakenly believe that the average panicker is trying to do epidemiological research and estimate the probability that a bad event will happen, for various levels of "bad" -- assault, burglary, rape, murder, and so on. So when one of the panickers' representatives starts to spread a suspicious estimate -- say, that 2 million children are abducted every year -- the nerd, who has been waiting to pounce, sends off a variety of reasons why this estimate is likely bogus, and so why no reasonable person should pay any attention to the panickers, if this moron's estimate is any guide to their collective brainpower.
But, strange as it may seem, real people making real decisions in real life are not trying to ape academics, who live in a sheltered and fake world. They are not trying to estimate how widespread a problem is at an isolated point in time -- rather, they are always talking about how some pattern of behavior is growing more common or dying out during one period compared to an earlier period, i.e. the rate of change or in what direction society appears to be moving.
Well, OK, the educated skeptic says, sure the rate of child abduction (or rape or murder) may have been increasing back when everyone was panicking about it. Still, because the hysterics had so exaggerated how common it was at the time, they wound up worrying about an extremely rare problem. There are problems far more common, and only somewhat less devastating, that it would have made more sense to panic about, like a parent who pushes their kid down the stairs or smacks them across the face for changing the channel without asking, as opposed to the far rarer cases of rape, murder, etc.
However, those less sensational cases are necessarily harder (more costly) to get good information about -- you'd have to do extensive interviews with a large chunk of the neighborhood to find out. Paying attention to the sensational solves that problem by pushing us to acquire only very cheap information -- when a little girl is abducted, raped, and killed, everyone will know very soon, with no research on their part required.
Ah, but the skeptic interrupts, that sensational info may be cheaper but it's of lower quality -- what does it really tell us about violence in general? It only tells us about some incredibly rare act of violence that, while lamentable, is too uncommon to be worth losing sleep for days over.
And yet the sensational does tell us about the overall distribution of violence. Such extreme cases serve as a convenient point along the continuum of violent acts for us to apply La Griffe du Lion's "method of thresholds." In brief, to compare how two distributions compare to each other on average, find a threshold value for the trait in question. Consider the example of trying to find out if people in the neighborhood are getting taller, shorter, or staying the same height. You could look at how many of the people can dunk on the basketball court. We don't know how tall you need to be in order to dunk -- we just know that it's tall enough that we won't mis-classify anyone (midgets cannot dunk, and very tall people can).
That, by the way, is the danger in the supposedly sophisticated approach of trying to measure the prevalence of less sensational cases. The kid who shows up to school with a bruised eye -- did he fall down, was it just rough-housing with his brother, did he miss a fly ball, did his stepdad beat him, or what? The more sensational the threshold, the less difficulty there is in classifying people correctly. If he shows up with bruises all over his body, he got beaten up by someone -- not ordinary rough-housing, not a dropped fly ball. If he's not only bruised up but also dead, then we're certain he was the victim of violence.
Back on the basketball court, say that we -- meaning lots of us -- notice that there seem to be a lot more people playing ball who can dunk, compared to when we were little kids ourselves. Not being interested at all in epidemiology, we don't bother estimating the probability that a kid can dunk now, and the probability that a kid could have dunked when we were little, as though this calculation were the basis for our hunch. We simply notice that, despite the population of kids staying more or less the same in size, a lot more of them are tall enough to dunk these days. We also hear complaints about kids having to duck to fit under doorways, that beds are no longer long enough in hotels, and so on. (This all happened for real in Holland as the Dutch people got incredibly taller during recent decades.)
When a greater fraction of the population meets or exceeds some threshold value, that either means that the average has increased -- i.e., that the distribution has shifted toward the right -- or that the variance has increased -- i.e., that the distribution has stretched out fatter in both directions, while staying the same on average. Here a quick glance at the other extreme tells us which reason it is -- do we also notice lots more midgets running around these days, in addition to all those dunkers on the basketball court? If so, then people are probably the same height on average as before, but for whatever reason the distribution is spreading out and there are more people at both extremes. If not, then that means people are getting taller on average (as in the Dutch case).
Returning to the distribution of violence, we began hearing lots more reports of strangers doing sick things to kids in the later '70s and '80s. Did we also hear reports of a growing trend of strangers passing out scholarship money on the playground, or other Mother Teresa behavior? Maybe a bit more than earlier, but not really -- and certainly not to the extent that there was a trend toward greater harm of children. Therefore, using the threshold of "kids are getting abducted (or raped or killed)," we infer that the entire distribution of violence was shifting in a more violent direction.
And that is what people panicked about -- not that the probability of some particular crime went from X to Y, but that the whole distribution of events was moving in a more violent direction. Sure, murder of children may have still been "rare" in some undefined and ultimately baseless sense, but it was more common -- and that was just the tip of the iceberg, so to speak. Every type of harm to kids had become more prevalent. But since the less extreme forms are harder for us to see without doing extensive investigation, it was the increase in more sensational forms that tipped us off to the overall rise in violence against children.
Without measuring it directly, we found out that the average encounter with a stranger had shifted in a more violent direction, just as ordinary observers lacking any statistical training or instruments outside their own mind deduced that Dutch people were getting taller on average, from paying attention to the sensational cases of beds, doorways, and seats that needed to be overhauled because a growing number complained that these things were too short.
So we see that our "obsession with the sensational" is highly efficient -- the information you get is very cheaply obtained, and it buys you a lot of additional highly reliable information about the rest of the distribution that you did not measure, which is what you really care about.
And because it can't be repeated enough times, the elite's whole notion of "over-reacting" to rare yet sensational events is bogus. The panickers are not worried over just that tiny slice of the spectrum of harm, but rather their correct appraisal that the entire distribution of people's behavior has shifted in a more dangerous direction. So even the less sensational, quotidian harms have become more common. Perhaps this shift will stop, maybe even reverse, but then again it may get worse. No one knows, so it's better to prepare for the worst: complacency here can kill (asymmetric costs of type I vs. type II error). Hence the atmosphere of panic.
Ultimately the charge of "over"-reaction can only be granted if the elite give us a solidly reasoned list of what the optimal range should be for various anxieties, like the ranges you see on your blood test. In this case, given the true prevalence of abduction, rape, murder, etc., of children, how many column inches should have been devoted to the topic in the local newspaper, how many minutes of local news coverage, how many minutes of word-of-mouth discussion, and so on?
Certainly a small, unrepresentative group that lasts for a fleeting moment could get the impression of reality wrong. But when a good chunk from a broad cross-section of the community has a persistent picture of things getting worse, we should trust their "over"-reaction more than the tongue-clucking of distant academics who pretend to know what the optimal levels of all sorts of behavior are.