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Comment by HillaryBriss | Hacker News Reader

a retired police officer once told me that the quantity of officers citywide goes through a repeated cycle from low to high to low again.

when the number of officers is too low and there's too much crime, the people demand that the government hire more.

so government does that. and crime goes down.

then the public notices all these police officers "doing nothing" and complains about wasted government resources.

so, naturally, they demand a reduction in the number of officers.

and so it goes...

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This is a common phenomena, and I'm not sure if there's a general term for it. E.g. people prematurely stop taking antibiotics because they feel better, or people go off their meds because they feel fine, etc.

Not finishing the course of antibiotics is the spicy-hot take:

https://www.bmj.com/content/358/bmj.j3418

Also a common pattern in biological ecosystems. Great weather one year leads to lots of fresh grass around, so more rabbits than usual survive to adulthood. An abundance of rabbits leads to more foxes than usual surviving. But the next year the increased fox population over-hunts the rabbits, crashing their population, and the next winter the underfed fox population crashes in turn, allowing more rabbits to survive to adulthood... etc. etc.

The Lotka-Volterra equations are a simple and popular mathematical model of this kind of dynamics:

https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equatio...

It strikes me as some type of attribution error. Not the FAE we all know, but a different or more general one. As in, results are not attributed to the cause.

But in the antibiotics example, it's the other way around. The results are ignored in spite of the cause ("I feel better, therefore I'm done"). That one could also just be regular old ignorance, but that's a boring topic of discussion.

I'd say this is best described by the concepts from control theory. In this case it really reminds me of bang-bang control: https://en.wikipedia.org/wiki/Bang%E2%80%93bang_control and in particular, the failure state that it can result in when applied in the real world: "depending on the width of the hysteresis gap and inertia in the process, there will be an oscillating error signal around the desired set point value (e.g., temperature), often saw-tooth shaped." In this case, there is a ton of hysteresis and inertia in the process, and by golly, the sawtooth is what you get... more officers this year, more officers next year, more officers after that, maybe it tops out a bit, and then BANG big cut.

It doesn't perfectly apply because technically, the system does not merely have two states, but the failure state is still very reminiscent of what is described here.

As kcorbitt points out in a sibling comment, differential equations are also a very powerful mechanism for understanding these phenomena, even when they are continuously approximating a discrete function like "number of police officers". Unfortunately, the standard treatment of this incredibly practical and important topic in college is terrible, and people come out with no understanding of how important it is to understanding the real world. As a really simple example, anywhere you can find a -dx^2/dt^2 term, you are almost certain to experience oscillations; they can be drowned out but it takes a lot, to put it in intuitive terms. With so many such terms in the world, there's a lot of oscillations that you simply can't avoid. I tend to believe our economy oscillations more than it absolutely has to for various reasons, for instance, but the idea I've sometimes seen proposed that it shouldn't oscillate at all is impractical. Too many terms like that in the world.

We should use a PID controller to set the number of cops. Where number of cops is the control variable, and crime rate is the process variable ;)

It is really painful sometimes to navigate life and witness the complete lack of understanding of control systems shown by the designers of many essential pieces of basic infrastructure from roads and parking all the way up to the banking/financial system.

Another common lack of understanding that is particularly prevalent within middle management is the trade-off between efficiency and resilience, the application of this to the finacial system is discussed at length in [0].

[0]http://www.lietaer.com/images/Sapiens_text_final.pdf

In biology this would be the red queen phenomenon. Wolves bring down the rabbit numbers, wolves starve, rabbits flourish, wolves flourish, wolves devour rabbits, and so on.

I assume you're getting downvoted because the Red Queen hypothesis actually applies to a scenario where neither wolves nor rabbits change their numbers significantly. Perhaps a better description would be along the lines of: Wolves get better eye sight, so rabbits get better at camouflage, so the wolves get better smell, so rabbits get better at hiding in inaccessible areas, so wolves get thicker coats to dig into the briar patch, etc. This year's model of wolf or rabbit is more fit than last year's model, but is never able to gain a lasting advantage over the wolves.

As the Red Queen said to Alice in Through the Looking Glass, "Now, here, you see, it takes all the running you can do, to keep in the same place."

predator–prey https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equatio...

in control theory this is called stable equilibrium

https://en.wikipedia.org/wiki/Stability_theory

Because crime is directly caused by the lack of police officers there to "prevent" it. &eyeroll&

here's a little supporting evidence, but, I freely admit, it's from a mostly rural country many people consider barbaric: http://www.cbc.ca/archives/entry/1969-montreals-night-of-ter...

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