As London’s Metropolitan Police announce their intention to focus stop and search operations on young Asian men in an attempt to prevent suicide bombings, we take a look at some underlying assumptions about stop and search. Mathematics and reflections on the psychology of suicide bombing suggest that stop and search will make virtually no difference to the probability of a suicide bombing taking place.
No Stop and Search for ‘Old White Ladies’
This morning I listened to politicians from both the UK government and the main opposition party defending plans by London’s Metropolitan Police to focus stop and search operations on young Asian men. The politicians seemed very impressed with their argument that the obviously limited resources of police should be focused in areas where they would have the maximum impact; they suggested, for example, that one would be much more likely to find suicide bombers among a group of young Asian men than among a group of old white ladies. In the absence of any actual evidence that stopping and searching young Asian men would make any difference to the incidence of suicide bombings, we are being asked to accept a mathematical argument that this is a well thought-out policy.
So, I got to thinking about the mathematics of stop and search and the psychology of suicide bombing…
The Mathematical Magic of Random Sampling
To a mathematician, stop and search falls under the general heading of ‘random sampling’. If you have a large sample of something — say, widgets — and you’re interested in how many examples of a particular kind — say, blue widgets — are present in that sample, it turns out that you can often come up with a very good estimate just by randomly checking a small proportion of the whole sample. Randomly test 100 out of 1000 widgets, and if 50 of those 100 are blue, then probably 500 of the 1000 are also blue.
Manufacturers of things like widgets exploit this fact all the time to test the quality of their products. Although it might seem that a widget manufacturer would need to test every widget rolling off the assembly line in order to guarantee a certain level of widget quality — say, fewer than 5% faulty widgets — it turns out that they don’t have to do anywhere near that much work. The mathematical magic of random sampling means that they might only need to test 2% or 3% of each batch of widgets in order to believe, with a very high degree of confidence, that fewer than 5% of their total widgets are faulty.
This mathematical magic doesn’t come entirely for free: for example, the manufacturer needs already to have investigated empirically how faults occur in the product, and whether they tend to occur randomly or in bursts, etc. (Imagine how the example about blue widget sampling might work differently if we knew, for example, that blue widgets always occurred in clumps of 50, or if we knew that every set of 51 blue widgets was always accompanied by a red widget.) But if they know something about how these faults are distributed, there will be some level of random sampling which will be very likely to give them results that are just as good as sampling every single widget.
When Stop and Search Works Well
In some ways, people are like widgets.
Stop and search — i.e., random sampling of people — can work very well if you are faced with a large set of people and cannot directly search every one of them. By stopping and searching a relatively small percentage of the whole set of people, you can estimate with a high degree of confidence the probability that any of the others who have not been searched may still be carrying whatever it is you’re looking for.
But in other ways, people are not like widgets at all: it’s from psychology that stop and search derives its real power.
Stop and search works best as a law enforcement tool when people know (or believe) in advance that they risk being subjected to a random search; this awareness of risk provides an incentive to modify behaviour so as to reduce that risk. If you know, for example, that the 5 kgs of cocaine in your bag might be found as you go through airport security, you will probably take this into account when deciding whether to travel with 5 kgs of cocaine in your bag! The branch of mathematics called game theory can be used to examine the interrelationships between the costs to a person of being caught in a random search, the probability of being caught in the random search, and the payoff for them of succeeding in not being caught by a random search. Mathematical models of this type are almost certainly used by large criminal organizations to evaluate options for transporting illegal substances, just as they are used by ordinary businesses to evaluate the impact of other types of random risks apart from police searches. For an individual pondering whether to engage in some variety of criminal activity in the face of a risk of detection through random search, a rational assessment of the potential costs of being caught may well make the difference between carrying out that criminal activity and doing something else that day.
When Stop and Search is Irrelevant
The psychological contributions to the effectiveness of stop and search disappear, however, when people don’t know in advance that they face a risk of being stopped and searched, or when they know about those risks but do not care. Moreover, the non-psychological contributions to the effectiveness of stop and search — the mathematical magic I referred to above — don’t disappear, but they do become much smaller, when the underlying distribution of whatever it is that is being searched for becomes strongly non-random.
The practice of stopping and searching young Asian men in an attempt to reduce the incidence of suicide bombings suffers from both these problems.
It lacks psychological effectiveness, because suicide bombers do not experience the same risk from a random search that ordinary criminals do. The only risk to a suicide bomber of being caught in a random police search is that they might be forced to kill a different set of people than they’d planned to, as a result of having to detonate their explosive device earlier than planned. In other words, since suicide bombers are planning to die very shortly anyway, and since they have it within their power to bring that about at any time by simply detonating their explosives, they face essentially zero risk of arrest, or of spending time in jail, or of being embarrassed in front of peers, or of any of the other risks which might play a role in the mind of some other type of criminal pondering the dangers of being stopped and searched. In the absence of such risk, there is no incentive to alter behaviour.
What’s more, the distribution of suicide bombers in the general population is highly non-random: as the police themselves would no doubt agree, it is simply false that any given person on the street, or any given young Asian man on the street, has equal probability of being a suicide bomber. Suicide bombing is not only highly non-random, but also extremely low in probability. To catch such a highly non-random and low-probability occurrence via random sampling (even random sampling of a racially-defined sub-population) would require a comparatively very high rate of sampling — i.e., vast police resources — to achieve any significant degree of confidence in the outcome. The bottom line: little mathematical magic is available to you if you are trying to reduce or eliminate the incidence of such a non-random, low probability occurrence as a suicide bombing.
Real Security, or Just Faking It?
So, what can we conclude?
From the utter lack of psychological deterrence (given that a suicide bomber faces virtually zero risk as a result of being stopped and searched), and the severely limited mathematical power (given that suicide bombing is an extremely non-random, low probability event), I would suggest that stopping and searching young Asian men — or old white ladies, for that matter — will make virtually no difference to the probability of a suicide bombing taking place.
At best, stop and search appears to me to be an exercise in psychological engineering or simple public relations, an attempt to make people believe that they are safer without any actual evidence that they are.
At worst, stop and search appears to me to be a pointless violation of the civil liberties of innocent people, and a waste of police resources that could better be deployed in ways that really would make an actual difference to the incidence of suicide bombings.
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