An appropriate lead-in to this post is the quote attributed to Stalin: “A single death is a tragedy; a million deaths is a statistic.” This fits very nicely into the structure of information theory, as formulated by Claude Shannon sixty years ago. His measure of information is equivalent to the reciprocal of the probability of occurrence of an event (specifically, the logarithm of this number). That is, if the probability of an occurrence is 100% (1.0), that is, if it’s certain to occur, then its information content is the logarithm[1] of 1, or 0; if the probability is 10%, its information content is 1; if its probability is .001, its information content is 3. In other words, the less likely the event is to occur, the higher the information content of its occurrence. That’s why it’s also called a measure of “surprise,” because the occurrence of a highly unlikely event is more surprising than one that is highly likely to occur.

What, pray tell, does this have to do with fear of crime? A lot, it turns out. As Steven Pinker has shown, violence and violent death has declined markedly over the past few centuries, and we are much, much less likely than our ancestors to die at the hands of others, either through wars or by crimes of violence. But this very fact means that (per the quote at the top of this post) each violent death nowadays *has a greater surprise value* than it did in the past. And that greater surprise value translates directly into greater fear – fear that oneself or one’s family is going to be harmed by others.

So we have this paradox: the safer we make ourselves, the more fear we have – of the unknown, of “them” (any outsider), of MS-13, of the person walking toward you (“Quick, get out your gun before he gets his out”). And of course, it is all so easy to stir up fear in a population, especially when those in power, whom we expect to be responsible adults, are the ones stirring it up.

‘Nuff said.

[1] To make it easy to follow, I’m using logs to the base 10. For those who slept through math class, the logarithm of a number goes up much more slowly than the number itself, so in the examples above the log of 1 is 0, of 10 (the reciprocal of 1/10) is 1, and of 1000 is 3. End of lesson.

chetmurthy says

Mike,

I’m not disagreeing with you about the “surprise” value of rare crimes. Rather, I feel like this ignores the “social” nature of the way we -ascribe- crimes to various -groups- (and, heck, how we construct those groups in your imaginations). I’ll just give two examples, b/c too tiresome …

(1) Sikhs, b/c they wear turbans, and we all know that “ragheads” are terrorists, don’t we?

(2) Good old boys from my hometown of Weatherford TX, where it was clear, clear, clear that a brown-skinned boy like me, ought not to display any sign of a sexual drive, or bad things might happen. Sufficiently clear that one day this brown-skinned boy got attacked by his whole P.E. class …. b/c (wait for it … wait for it) he was gay.

Yes, that’s RIGHT! I got attacked by my PE class, for doing my best to NOT GET LYNCHED!!!!!

It’s a complex thing, who gets blamed for various crimes. Sometimes, nobody gets blamed, but instead, people like Donnie Smallhands get *acclaimed*, b/c after all, accounting control fraud is just a sign that somebody is *smart*, and worthy of being Predisent. That’s not a crime, is it? NoOoOoo.

byomtov says

I’m not sure I buy the model here.

What about the frequency of events? High probability events have high frequency. If crime is high we may have two events, each with a probability of .002. Then the surprise value is about 5.4 > 3.