If a group of individuals subject to some rule face an enforcement mechanism that is limited in its capacity, their rates of rule-violation will be interdependent.
Imagine a classroom of well-behaved children. When Johnnie throws a spitball at Suzie, Ms. Jones can give him her full attention, and Johnnie learns (and the others learn vicariously) that he can’t get away with throwing spitballs in Ms. Jones’s class.
Now imagine a classroom full of unruly children. When Johnnie throws a spitball at Suzie, Ms. Jones is too distracted by the need to break up the fight between Dick and Fred to have time to rebuke Johnnie, let alone the six others who are acting out at the same time. Johnnie and the others learn that they can get away with almost anything in Ms. Jones’s class.
Thus both the well-behaved and the ill-behaved classroom are self-sustaining situations. Indeed, they can be two equilibria of the same system: the very same children with the very same teacher may wind up either well-behaved or ill-behaved as the result of random accidents at the beginning of the period. This is an instance of the classic “tipping” model introduced by Thomas Schelling and popularized by Malcolm Gladwell.
In such a situation, the following statements can be rigorously demonstrated using fairly minimal behavioral assumptions, as Beau Kilmer and I show in a paper called “The Dynamics of Deterrence” (published in the Proceedings of the National Academy of Sciences, and adapted as Chapter 4 of When Brute Force Fails):
- Increasing enforcement capacity can lower not only violation rates but the volume of punishment actually administered.
- A temporary increment to enforcement capacity can have a lasting impact on violation rates if it succeeds in “tipping” the system from its high-violation to its low-violation equilibrium.
- Even if increased enforcement capacity cannot be obtained, the same effect can be created by “dynamic concentration”: focusing enforcement effort on a subset of offenders until their behavior comes under control, and then using the enforcement capacity freed up by reduced violation rates among that initial focus group to expand the size of the group.
The logic of these claims can be illustrated in a simple two-person game. Let Al and Bob by rational, risk-neutral actors, both be subject to some rule, and let the cost of complying with the rule be $10 while the penalty for non-compliance is $15. Assume that Al and Bob are not conscientious about the rule: each treats a penalty dollar and a compliance-cost dollar as of equal value.
Let Al have the first move: he either complies or violates, and then Bob chooses whether to comply or violate.
Assume that the enforcement system is constrained to be able to punish only one violation each round. Thus if Al alone violates, he is punished with certainty; if Bob alone violates, Bob is punished with certainty. But if both violate, each is punished with probability ½.
What should Al do? If he complies, he pays $10. If he violates, he pays $15 with certaintyif Bob complies, but pays $15 with probability ½ if Bob also violates. Since Al is risk-neutral, he values that ½ chance of a $15 penalty at $7.50. So Al wants to do whatever Bob does: he would prefer to violate, if Bob also violates, but would prefer to comply, if he thinks Bob will comply.
Under the standard “common knowledge” assumptions of game theory, Al can predict Bob’s behavior by assuming that Bob will act rationally. If Al violates, then Bob’s choice is between violating also, paying an expected cost of $7.50, or complying, paying a cost of $10. Thus Bob ought rationally to violate in that situation, and Al can be confident that he will do so.
Since Al prefers to violate if Bob violates also, and since Al knows that Bob will violate if Al violates, Al will indeed violate, as will Bob. Thus the score for each round is: violations 2, sanctions 1.
If the sanctions capacity constraint is relaxed so that two punishments per round can be given, then both Al and Bob know that violation will lead to certain punishment. Therefore, they both comply, and neither is punished: violations 0, sanctions 0. This illustrates the claim that greater sanctions capacity can lead not just to lower violation rates but to less actual punishment: a convincing threat never has to be carried out.
But – and this is the key point – it is not necessary to relax the constraint. A strategic enforcement authority can bring both Al and Bob in to compliance by establishing a priority order for punishment.
Say the enforcer announces that, if both Al and Bob violate, it is Al who will be punished. In that case, Al will certainly comply. But once Al has complied, Bob will also face certain punishment if he violates, so Bob will comply as well. Violations 0, sanctions zero. (The same is true if Bob is given priority; Al knows that Bob will comply, and therefore that if Al violates he will be punished.)
And the system can be extended to Charlie and Dan and Edgar: in theory to countably many potential violators. If no one wants to be the first violator, then no one will violate at all.
That, in a nutshell, is the key to having less crime and less punishment. The trick is making it work in practice. The HOPE probation-enforcement experience and the High Point low-arrest drug crackdown illustrate the feasibility of building actual enforcement programs on this basic principle.
[graf staring “What should Al do?” edited to fix error]
Russ says:
Excellent post; applications to both domestic and world politics are quite interesting.
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October 27, 2009, 1:24 amDove says:
An extreme real-world example: everyone speeds because everyone speeds.
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October 27, 2009, 1:25 amintermeddler says:
Thanks for the interesting post Mark. The High Point crackdown seems to show a way to shift from a high-crime equilibrium to a low-crime equilibrium by using a coordinated crackdown to remove a large percentage of a neighborhood’s criminals from the picture. But couldn’t this shift also have been accomplished by charging and imprisoning the dealers? Or do you think that warning rather than arresting them somehow helped reduce crime going forward? I view the reduced punishment applied by the High Point project as a benefit unto itself, but I’m curious how you would answer the retributivist who argues for the coordinated imprisonment, rather than coordinated warning, of drug dealers?
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October 27, 2009, 2:17 amAssistant Village Idiot says:
It is a principle of behaviorism that immediate reward or punishment, however small, is more effective than great reward or punishment delivered long after one’s neurology can make the association. Appealing to the moral reasoning of not only criminals, but most of us, is less effective than consequences. Creating an atmosphere of swift justice (both reward and punishment) is better than other “preventive” measures.
The key in the HOPE project was that there was someone on board who could make sensible things happen because he had the clout. That is the situation you are going to find it hard to replicate. It is not simply a matter of society deciding to do things differently — institutional forces array against such changes, for good reasons and bad.
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October 27, 2009, 8:43 amTweets that mention The Volokh Conspiracy » Blog Archive » Positive feedback and strategic enforcement -- Topsy.com says:
[...] This post was mentioned on Twitter by Jan Olsen, scott joy. scott joy said: The Volokh Conspiracy » Blog Archive » Positive feedback and ...: Mark Kleiman, guest-blogging • October 27, 20.. http://bit.ly/8CxEq [...]
Plastic says:
No, that’s how to reduce crime amongst a rational and perfectly informed population. People are often not rational actors, and usually do not know the penalty or probability of being caught.
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October 27, 2009, 11:31 amdirc says:
Mr. Kleiman’s argument is completely undermined by the sexism with which it is presented. All violators are male: Johnnie, Dick, Fred, Al, Bob, Charlie, Dan and Edgar. The sole victim, Suzie, is female, as is the regime enforcer, Ms. Jones.
Clearly, Johnnie, et. al. are rebelling against the matriarchy and its oppression.
</tongue-in-cheek>
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October 27, 2009, 12:14 pmDerHahn says:
Shorter Klieman
If we stop calling the people who enforce laws “police”, the people who assign punishment “courts”, and the place you go when you’re punished “prison”, then we’ll have less “crime” and liberals will be happy!
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October 27, 2009, 12:32 pmBrett Bellmore says:
Everyone speeds because governments almost always set speed limits irrationally low in order to enhance revenues. If the speed limits were set rationally, most people wouldn’t speed.
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October 27, 2009, 12:48 pmBen says:
Interesting post. The WSJ article (from 2006) indicates that Kansas City was going to try to shut down some of its drug markets using the same strategies used in High Point, North Carolina. Is there any information or data out there on whether Kansas City’s efforts have been successful?
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October 27, 2009, 1:00 pmAllan Walstad says:
I read through the HOPE and High Point articles. They didn’t have anything to do with the silly game theory example. What appeared to work was simply swift and certain consequences–no surprise there. As for High Point, am I to assume that all the users who were buying drugs in the one cleaned-up area are now drug-free? Or are they just buying somewhere else? Factoring out the gross imposition of drug laws on personal autonomy, the genuine crime problem is the violence, and don’t you know, we’re still looking for dangerous person X who presumably will not be impressed by enlisting his mother’s good offices. Jail that person and others will step forward to make the huge profits available from illegal drugs. So maybe there’s a couple of useful around-the-edges ideas here. That’s about all I see.
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October 27, 2009, 1:13 pmyankee says:
How is this in any way related to anything Kleinman said?
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October 27, 2009, 1:16 pmyankee says:
Kleiman is apparently a deterrentist who sees locking up large numbers of people as a problem to be remedied. I don’t think there’s any way for someone with that perspective to answer a retributionist who sees punishment as an end in itself. Kleiman’s problem is the retributionist’s goal.
I’m a deterrentist who cares about cost control, so I see warnings as vastly superior to locking people up, assuming both work equally well.
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October 27, 2009, 1:25 pmRowerinVA says:
The real world has a problem with Kleinman’s thesis. Virtually 100% of bank robbers are caught, yet bank robbing still occurs. In most areas of the country, 90% or more of people who commit murders in public places are caught, yet the murders continue.
In both those situations, the chance of getting caught doesn’t seem to be the important variable. The punishment is the important variable. Perps for those crimes know that the “time” just isn’t that bad versus what they are likely to get out of the crime in terms of money or prestige.
Other examples: Carjacking. High-speed public car chases in California, one famous example of which was a repeat offender! The two Washington, DC residents who drove a truck through a Virginia gun store, stole and sold into the DC crime community more than a dozen handguns, and received sentences of 18 months! 18 months!
If Mr. Kleinman is in favor of harsh, long, meaningful sentences, then perhaps he’s onto something. Is he?
Otherwise, he’s missing the fact that the problem with current law enforcement isn’t the enforcement, it’s the ludicrously light penalties given for so many serious, community-damaging crimes.
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October 27, 2009, 1:40 pmTGGP says:
In a diavlog Kleinman stated that the open-air drug markets relocated to strip clubs. “No strippers have complained”.
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October 27, 2009, 1:41 pmAllan Walstad says:
TGGP: Thanks for the heads-up.
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October 27, 2009, 2:35 pmSteve Clay says:
I believe the evidence will show the idea still works for criminals who are “ill-informed”.
1. Only a tiny number of people are “irrational”, and no policy will “work” to keep them behaving as free adults. Criminals are rational but just more short-sighted and impulsive than most people (and alcohol makes both problems worse).
2. The beauty of HOPE is that an offender needs to know very little information to weigh consequences. “If I drink or break a parole rule I’ll be in jail tonight.”
Remember the current system tells him, “You’ve failed 2 drug tests, but if you keep failing them, at some point you may cross some legal boundary or a fed-up judge may decide to put you away.” That’s how small possession offenses slowly turn into real jail time, and why any drug warrior that tells you non-violent drug users don’t go to jail is a liar. The HOPE system doesn’t reform drug laws (we should still do that), but at least gives users a shot at treatment if they can’t quit on their own.
The most surprising thing about the data is that HOPE appears to be the most effective way of quitting meth; even our best voluntary treatment programs don’t work as well as having a credible threat of a night in jail looming overhead. This probably means that users of any legal drug that are desperate to quit could use a voluntary (private) HOPE-like program.
As I understand it most crime is not bank robbery, murder, and televised events. One reason why penalties are light for big offenses? Prisons have lots of small beans offenders who kept re-offending until a dumb law (3 strikes!) or a fed-up judge put them away. This is certainly the case in CA where federal judges are about to force 40K prisoners to be freed (and they can’t by law free the non-violent 3 strikes folks!)
The HOPE project is a solution for day-to-day crime, not murder.
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October 27, 2009, 2:52 pmLarryA says:
Now imagine a classroom of normal children. Johnny throws a spitball at Suzie. Ms. Jones is too busy searching everyone’s lockers for aspirin, writing up a report to the second vice principal for disciplinary affairs because David called Chuckie a doodoohead, and escorting Angle to the first vice principal for disciplinary affairs because she has a dress code violation, to see what Johnnie did.
Getting rid of a bunch of crimes would help a lot more than tweaking responses.
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October 27, 2009, 3:36 pmLeo Marvin says:
Don’t you mean the opposite, i.e., he pays $15 if Bob complies, but pays $15 with probability ½ if Bob also violates?
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October 27, 2009, 3:51 pmDisappointed Youngster says:
Right, he is a liberal, we had better hurry up and ignore him. Motivated reasoning as a term seems insufficient to describe the substance of what you have just said, which is essentially “he is a liberal, therefore his discussion of enforcement resource concentration is simply an attempt to name our way into a good feeling.”
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October 27, 2009, 3:54 pmyankee says:
That does not follow. It’s far from obvious that prospective bank robbers care much about whether the sentence is two years or twenty. Especially since they’re irrational enough to believe that they’re the exception and will be able to evade the law even though virtually everyone else gets caught.
Of course, it might be true, but we can’t say so a priori.
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October 27, 2009, 5:33 pmRowerinVA says:
Yankee and Steve Clay, you’ve accused me of attacking a straw man, but set up a straw figure of your own.
You didn’t hear me supporting the massive incarceration of small time nonviolent and nonrepeat offenders. And yes, Mr. Kleinman is talking about the HOPE project in this post, which may be directed to crime that most would consider small potato stuff, but he’s generalizing his lessons to serious, violent crime (see yesterday’s post). Accordingly, it’s fair to talk about whether it makes any sense to generalize in such a fashion. I could have been more clear about that, I concede. I’m not attacking the HOPE project by itself; rather, I’m asking, “so what?”
Yankee, fair enough, it’s not a mathmetical proof that “if being caught is nearly certain, the amount of punishment must be the important thing.” But it’s a testable hypothesis. Where tested — for example, in the Project Exile tests where illegals guns resulted in automatic 5 year sentences — the hypothesis has tested true. Criminals who see other convicts back on the street five, three, or even fewer years after being sent away for homicide (common, in Washington, D.C.) might rationally think, “well, the downside isn’t so great.” Raise that to some figure such as a 15 or 25 year minimum and rational (or even partially rational) criminals are likely to react. More importantly to Mr. Kleinman’s approach, raise the illegal weapon penalties to 5 or 10 years, and perhaps the homicides won’t even be under consideration.
A frustration that I have is that the same people who reasonably propose reducing sentences for small potato crimes are also generally for incorrectly defining major crimes such as assault and felony gun possession as small potato, or keeping the ridiculously low de facto penalties for assault and murder.
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October 27, 2009, 6:01 pmSuperSkeptic says:
Thank you LarryA for your point as well as your real-world-ish example and insight. My first reaction to this post (as well as the former) was how unrealistic it is:
The logic of these claims can be illustrated in a simple two-person game. Let Al and Bob by rational, risk-neutral actors, both be subject to some rule, and let the cost of complying with the rule be $10 while the penalty for non-compliance is $15. Assume that Al and Bob are not conscientious about the rule: each treats a penalty dollar and a compliance-cost dollar as of equal value.
Sure, let’s assume the world is populated by perfectly rational, fully informed people who are either total criminals or total angels, subject to “some rule,” with a determinable cost of compliance or non-comliance, and also assume they have no moral feelings about the “rightness” or “wrongness” of the rule... I tried, and I see your logic game, but it’s so devoid of reality it’s not worth it. Any conclusions you reach from such hypothetical games (pun intended) will be incompatible with the real world if implemented and need adjustment, so you might as well adjust ahead of time.
I’m reminded of these prescient comments from the last thread:
If you’re not willing to address the folly of the War on Drugs while you advocate we lower the crime and incarceration rates, your position is about as sensible as an anti-nuclear proliferation activist who is okay with every country on earth having nukes.
“End the drug war” should be the opening statement of anybody that wants to see any significant diminution of the crime and incarceration rates, and, when it isn’t, they almost always are not being serious about what they are saying.
and
Based on the post I have to say I am not encouraged. I am not much in favor of large-scale incarceration, but I am even less in favor of letting violent criminals out on to the streets.
That said, I have to say that our drug laws are responsible for much needless incarceration. Are you going to go there? Bravo if so, but again it does not sound like it. My own preference would be reserving criminal penalties for those who offend against another. Merely doing that would slash our incarceration rate
and
And put me down as another person who believes that the monumentally stupid, counterproductive, and (IMHO, IANAL) unconstitutional “War on Drugs” has been the cause of our astonishing crime and incarceration rates.
and
War on Drugs: This has our country in quite a pickle.
and
My solution is easier and cheaper. Legalize victimless crimes.
and
Interesting to see that most commenters across the political spectrum agree on the solution: decriminalize victimless crimes. Because it’s such an easy and reasonable solution, of course, it will never happen.
(these are all before 9AM, btw — but they go on and on)
and yet, they, like reality, remain unaddressed by our new friend...
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October 27, 2009, 6:09 pmyankee says:
Well, if raising the minimum sentences works as a deterrent, I’m all for it. My impression had been that this wasn’t a particularly effective strategy, but I’m not familiar with the research on this issue so I don’t really have an informed opinion. The “smart policing” strategies Kleiman seems to be advocating are hardly inconsistent with this either.
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October 27, 2009, 6:52 pmEinhverfr says:
Interesting. I guess defeat in detail works as a policing strategy too....
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October 27, 2009, 7:56 pmSuperSkeptic says:
This comment is more relevant than it may initially seem.
Let’s assume, for the sake of argument, that the motives of governments (and people who advise them, like Mr. Kleiman) are pure. I know, I know, I just criticized him for being unrealistic. Nevertheless.
Re-phrased altruistically the comment reads:
Everyone speeds because governments almost always set speed limits irrationally low in order to
enhance revenuesmake us all safe. If the speed limits were set rationally, most people wouldn’t speed.Brett posits that if the speed limits were set more rationally (assuming he doesn’t quite mean purely free, where there are no speed limits and only negligence standards would apply), then less people would be in violation of them, precisely because they would be set at a higher speed. Either way, people are naturally inclined to go the speed they will or that they feel comfortable with, and thus do, often in violation of the speed limit. So, with a higher speed limit we’d have less infractions (i.e. solving the complained of problem of incarceration).
But, some would protest, that means there would be more accidents, defeating the whole purpose of to “make us all safe.”
But, does a 65mph speed limit on a highway really make you feel safe? Are you ever really safe on a highway? Is that even possible, or is that feeling an illusion? Would we create a social norm of say, 75 or 85 mph for cruising naturally? (the observant drivers among you would note that we already have, although it’s tethered about 5–10 mph too low because of our awareness that at any given moment, we may have to slow down for smokey — without pushing the brakes of course.)
But my real point is this: Isn’t this the same as re-characterizing the action as non-criminal — in the very same sense that (although he’d like to avoid it here) ending drug prohibition laws, for example, is a re-characterization of actions as non-criminal would be? This is the whole point, drugs aren’t going away, speeding isn’t going away. This guy has been researching and studying policy (and advising the government on it) for some 20+ years since he’s gotten his credentials from great schools that study how to mold the public for our own benefit, and he doesn’t know any more than you or I do. It’s the top-down imposition of such “public policy” that creates the problems the “public policy” scholars themselves then turn around and try to “solve.” — and they are usually best solved by abstention.
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October 27, 2009, 8:26 pmTGGP says:
One suggestion I heard Kleiman give for non-drug crime is the use of GPS ankle bracelets for parolees and those on probation. If a crook knows his location is being tracked and he will be placed at the scene of a crime right when it occurred (with irrefutable evidence), he’ll be less likely to commit it. It won’t do as much for those who have never been caught, but perhaps shifting to a lower crime equilibrium will also discourage that. I’ll also note that a whole lot of murders are connected to the drug trade, which is yet another argument for legalizing them. Kleiman has also endorsed a compromise on guns. Registration, but decentralized with gun dealers. I find that acceptable.
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October 27, 2009, 11:48 pmMatthew Yglesias » Dynamic-Concentration and Parenting says:
[...] to commit crimes. Which makes it even harder to enforce the law. Mark Kleiman’s idea of dynamic-concentration is a way around the [...]
disconnect says:
“...Johnnie learns (and the others learn vicariously) that he can’t get away with throwing spitballs in Ms. Jones’s class.”
Wrong. Johnnie learns to throw a spitball at Suzie when Ms. Jones’ back is turned, then Suzie learns that relating the events of this particular assault is “tattling”, and the power dynamic is shifted in favor of the bully. And the rest of the class learns that (a) in order to get attention, you need to misbehave, and (b) the consequences of misbehaving are probably not that bad. And this situation degenerates to the “unruly” class.
What is needed here is (a) constant vigilance and/or (b) a schoolyard culture that encourages individual freedom from tyranny, so that when the assault happens, the offender is appropriately punished. Which is another matter; even if Johnnie is caught in the act, NOTHING BAD HAPPENS TO HIM. He gets admonished, he gets a note put in his permanent file, he spends time talking to the principal, AND THAT’S IT. Tomorrow, another spitball, another talking-to, and life goes on. Meanwhile, Suzie’s freedom to pursue happiness is slowly eroded, she starts liking school less and less, and she develops a small seed of hatred for school, boys, authority figures, whatever.
Draw your own extensions to the current topic.
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October 28, 2009, 2:10 pmDavidS says:
I made this comment jokingly on Matt Yglesias’s site, but it seems like it is actually serious here: You have to worry about the possibility that Bob pays Al $7 to violate the rule.
Al will take this deal. He gets 7 and pays a penalty of 15, for a net loss of 8, less than the cost of compliance. Bob spends 7, also less than the cost of compliance.
Now, this won’t be a problem for simple street crime. I would imagine that criminals would find it hard to make deals with each other and even harder to commit to them — If Bob pays first, he has to fear that Al will cheat by complying with the rule; if Al violates the rule first, he has to fear that he won’t be repaid.
But if you are dealing with large gangs, who have reputations that they care about, or are dealing with corporations who can be sued, it seems to me that your solution will only be stable for as long as it takes Bob to think of this strategy. (Obviously, the courts would not enforce a bare contract like this. But imagine, for example, an insurance company that sells liability insurance and is known to turn a blind eye to customers who deliberately fail to maintain their property safely.)
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October 29, 2009, 8:13 amSearch engine says:
The key in the HOPE project was that there was someone on board who could make sensible things happen because he had the power. That is the situation you are going to find it hard to replicate. It is not simply a matter of society deciding to do things differently.
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February 3, 2010, 8:41 am