Applying Becker's Economic Analysis of Crime and Punishment

If criminals behave as if they are rational maximizers, then increasing the expected cost of committing a crime should lead to less crime. One way to do this is to increase the size of the punishment if the criminal is caught. A second way is to increase the probability that the criminal will be detected, caught, and punished.

It is this second method that underlies the NYC searches of backpacks. See this article by Heidi Singer and Leonard Greene [registration required]:

Even if cops never touched a backpack or briefcase, the mere possibility of searches is enough to improve security in the subways, experts said yesterday.

... "There are no silver bullets," said Daniel Prieto, a Harvard University professor who is a security consultant to the federal government. "So you have to increase the costs to terrorists."

Former Police Commissioner Howard Safir agreed.

"I think it's a great idea," Safir said. "No one is going to stop terrorism, but the more probabilities you put in place that somebody's going to get caught, the more effective you'll be."

These views are consistent with results that John Henderson and I derived several years ago.