File this one under “Economics vs Omerta” — or just a bit of Tuesday morning tomfoolery to make the week pass by a little easier.
Via Slate, here’s a trend we were unaware of related to the mob bust in the US last week (emphasis ours):
The last few years have seen a new kind of indictment—the superbust—that targets organized crime on a much larger scale. In February 2008, federal officials rounded up 62 reputed mobsters in the New York area, charging them with the usual slew of mob-related crimes, including murder, conspiracy, drug-trafficking, robbery, and extortion. Three months later, they indicted another 23 people, including one of the highest-ranking Gambinos. Then on the morning of Jan. 20, the FBI and local law enforcement arrested 127 suspected mafiosos.
By corralling so many people at once, investigators are more likely to get individuals to cooperate. Say the police arrested you and one other partner in crime: The odds of your partner turning informant in exchange for leniency would be relatively low. If they arrest 127 people, betrayal is almost assured. (Not all the alleged criminals arrested on Thursday worked together, of course.) A single turncoat can do a lot of damage to his family and others.
The reasoning appears straightforward enough. The more people you arrest, the better chance that you’ll find someone who is either squeamish or disloyal enough to spill his guts under pressure.
But there is another ridiculously geeky interesting aspect to this idea. Think back to economics 101: the original prisoner’s dilemma only has only two prisoners, and their inability to collaborate leads each to confess (or turning state’s evidence, in the parlance of our times) — thereby ratting out other and sub-optimally hitting the slammer.
But given the trend towards large-scale busts, the police and other authorities are clearly aware that the the fussy details of real life complicate the picture, as annoyingly they tend to do. So let’s change the rules a bit — not to perfectly imitate real life, but just to see why the outcome changes under different assumptions as we get a bit closer.
So assume instead that you:
– are one of two arrested prisoners
– know the other prisoner well
– have discussed in advance how you would each act if arrested
– can estimate, based on the above, only a 20 per cent chance that the other prisoner will rat you out
– are pretty tough yourself, and loyal, and the other prisoner knows this
– are confident he’ll calculate the same probability about your own silence.
In this example, keeping your mouth shut actually looks like a safe bet.
The classic prisoner’s dilemma assumes no collaboration. In our example, you and the other prisoner still can’t interact directly after you’ve been detained. But if you know something about each other or have discussed in advance how you would act if arrested, then that would still qualify as a kind of preemptive collaboration.
There are also likely to be powerful loyalty and identity issues that further influence the decision of whether to talk. And perhaps other reward mechanisms are involved — a bump in money or status for staying quiet, or the threat of getting whacked if you don’t. (For one of these to be a factor, the outcome for all prisoners denying the crime simultaneously would have to be even better than if you were to go free by ratting when the others didn’t.)
Reducing jail time, in other words, isn’t each prisoner’s sole motivation, and all of these “real-life” factors are working against confessing.
Now take the same assumptions as in the example above, but this time you’re just one of a hundred people arrested from your mob, and each of you has the power to bring down everyone else. You can still estimate just a 20 per cent the risk that any single one of them will rat you out, but because there are so many, it’s now mathematically likely that at least one of them will, in fact, send you to the pen.
We recognise that these new assumptions are themselves simplistic. But the point is that with so many more people arrested, each individual prisoner is more likely to estimate a higher aggregate probability that at least one of the other prisoners will rat him out — and is therefore more likely to accept a deal himself.
So even given the other behavioural factors involved, the cops are taking fewer chances the greater number of people they arrest. Of course, this is all intuitively obvious, even if we’ve just spent a lot of time struggling to explain it using mathematical jargon.
A Mafioso law of large numbers, if you will.
Related link:
Soccer, Game Theory, and Dives – FT Alphaville
Brains, guns, and automatons – FT Alphaville
Mafia still holding US ports at random – FT Alphaville