# Back of the envelope cost/benefit analysis of bag searches

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Let's try to do the cost/benefit analysis of the NYC subway search program. Say that you can search one passenger a minute. That seems like a reasonable compromise between a quick look in the bag (10 s) and a TSA-style dump everything out and check for explosives search (5 minutes). So, on a given working day, a single officer can check about 480 people. (At a commensurate cost to whatever other law enforcement activities they're engaging in, though since presumably a lot of that time is spent just being present and deterring crime, that's probably only partially lost.)

So, how well does this actually work? On a given day there are about 5 million passengers riding the NY subway. We're told that the Transit Bureau has about 3,000 officers, so in principle, then, they can check anywhere between zero and 33% of the subway passengers. So, what's the marginal value of tasking another officer to search passengers?

If searches are conducted randomly, then on average each additional officer devoted to searching will increase the chance of detecting a terrorist by 480/5 million, or about 10-4. If we assume charitably that when terrorists are detected they just walk away rather than blowing themselves up (a line of people waiting to be searched makes a rather nice target). If we assume that about 100 people a year will be killed by subway bombings (to date nobody has been killed in NYC subway bombings and the London bombing only killed 56 people), then each police offer saves .01 lives, at a cost per life of about \$10,000,000, near the top end of the standard estimates for statistical value of a human life.

Of course, this depends on some pretty charitable assumptions, namely:

1. The rate of attempted attacks will be substantially higher
2. People don't blow themselves up when detected.
3. That people who are detected don't just come back later try again.
4. That you can do a reasonable search in a minute. The TSA secondary screenings I've been on seem to take more like five.
5. That the terrorists won't shift to some new target. Railway stations are good, but so are airports (outside the security perimeter), shopping malls, etc.

I'm not sure I believe any of these. And if you do, then you should be in favor of searching nearly everyone, since the cost/benefit numbers look the same for nearly any search fraction up to the point where the probability of a successful attack is so low that the terrorists just choose another target. I'm not sure exactly where this point is, but I expect you need to get above 25%. I'm extremely skeptical that a percent or so will get the job done.

Surely the concept of "random" searches is just a politically correct fig leaf to cover, what in practice will actually be "racial profiling" based searches, using skin colour and "religous" clothing etc. ?

Obviously this will do nothing to detect determined terrorists either, but the figures in your cost benefit analysis will be very different.

Why assume that every terrorist attacking the public transport system will be a "suicide bomber" ? The bombs in Madrid last year, and the Tokyo sarin gas attack were not "suicide" attacks per se.

I don't assume that every future attack will necessarily be a suicide attack. However, if a significant fraction are suicide attacks or at least potential suicide attacks--willing to die in execution if necessary--than the value of searches declines dramatically.

I'm curious how the increased terror from a well-coordinated team attack might alter this analysis.

If there's some increased terror from ensuring that a bunch of bombs all go off within, say, 30 seconds throughout one main area, and then a second attack happens a few minutes later in the same zone -- maybe because you disrupt traffic and possibly hit the emergency responders -- then catching any one attacker might have value well beyond the one bomber deterred. The one you catch is both a signal that there may be others (and if you have to guess, you can guess they are most likely spreading out in a zone centered on the one you caught) and of course a potential source of other valuable information. This can trigger an immediate early response.

The problem is, you DON'T catch the attacker. All he does is say "No, bye", and walks out and in another enterance.

Likewise, if you profile, the suspects counter-profile: Baseball caps, a NYC sweat shirt, trim the beard really close (you can get clippers rather than a razor and you don't offend your god when you shave.) Hey, isn't that what the london bombers did?

Now if you are a cold Brazilian electrician (70 degrees is pretty cold if you are from Brazil), watch out: plainclothes cops will start chasing you and when you fall, shoot you in the head.

The news reports I heard said that you could refuse the search, but they'd turn you away from the subway station if you did. Kinda makes your whole analysis moot, eh?

Not really, no. See point (3) above.

Subay stations, especially in Manhattan, are VERY close together, and have multiple enterances with multiple people. There is NOTHING which prevents said bomber from saying "Bye" and then entering at another enterance or station.

Frankly, if the @#)\$(*@#)\$*s tried to search my bags in NYC, I'd do that myself. I hate stupid security.

Re: "The problem is, you DON'T catch the attacker. All he does is say 'No, bye', and walks out and in another enterance."

OK, yes. But if he or she is working as a part of a team, do you get some benefit out of throwing their timing off? Maybe not a lot, but also maybe better than nothing.

I suspect there's a short-term benefit to any new security measure, against an attacker that has carefully planned out the attack, and that has to be extremely careful about communications to keep the benefits of their cell structure. Anything that changes the defenses may delay an attack for awhile.

Now, this probably doesn't actually prevent many attacks, so I doubt it's worth all the cost. But I think this is a benefit.

--John