Hidden Order: The Economics of Everyday Life
LinkSuppose one little old lady in ten carries a gun. Suppose that one in ten of those, if attacked by a mugger, succeeds in killing the mugger instead of being killed by him--or shooting herself in the foot. On average, the mugger is much more likely to win the encounter than the little old lady. But--also on average--every hundred muggings produce one dead mugger. At those odds, mugging is an unprofitable business--not many little old ladies carry enough money to justify one chance in a hundred of being killed getting it. The number of muggers declines drastically, not because they have all been killed but because they have, rationally, sought safer professions.
When, as children, we learn about different sorts of animals, we imagine them in a strict hierarchy, with the stronger and more ferocious preying on everything below them. That is not how it works. A lion could, no doubt, be fairly confident of defeating a leopard, or a wolf of killing a fox. But a lion that made a habit of preying on leopards would not survive very long; a small chance of being killed and a substantial risk of being injured is too high a price for one dinner. That is why lions hunt zebras instead.
In analyzing conflict, whether between two animals, criminal and victim, competing firms, or warring nations, our natural tendency is to imagine an all-out battle in which all that matters is victory or defeat. That is rarely if ever the case. In the conflict between the mugger and the little old lady, the mugger, on average, wins. But the cost of the conflict--one chance in a hundred of being killed--is high enough so that the mugger prefers to avoid it. In this case as in many others, the problem faced by the potential victim is not how to defeat the aggressor but only how to make aggression unprofitable.
Economics Joke #3: Two men encountered a hungry bear. One turned to run. "It's hopeless," the other told him, "you can't outrun a bear." "No," he replied "But I might be able to outrun you."
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Suppose one little old lady in ten carries a gun. Suppose that one in ten of those, if attacked by a mugger, succeeds in killing the mugger instead of being killed by him--or shooting herself in the foot. On average, the mugger is much more likely to win the encounter than the little old lady. But--also on average--every hundred muggings produce one dead mugger. At those odds, mugging is an unprofitable business--not many little old ladies carry enough money to justify one chance in a hundred of being killed getting it. The number of muggers declines drastically, not because they have all been killed but because they have, rationally, sought safer professions.

check out The Undercover Economist -Tim Harford.
Its similar in style and substance to the both Levitt and Friedman
Sounds like an interesting book, although one that perhaps assumes a higher level of intelligence that the average criminal possesses. :)
Yeah, but is this idea backed up by evidence? There are a lot of places, Iraq for example, where everyone is armed and the crime rate is still high. What about that?