Schneier and Paulos on automated wiretapping
The problem is essentially the same one that makes it pointless to engage in programs of blanket drug-testing of grade school children or mandatory HIV testing in order to obtain a marriage license--the population being tested contains such a small number of people who meet the criteria being tested for, which means that even a highly accurate test returns vastly more false positives than true positives.
Paulos points out that a 99-percent-accurate sorting mechanism for detecting terrorist conversations, on a population of 300 million Americans that includes one-in-a-million with terrorist ties (300) will identify 297 of them, along with 3 million innocent Americans. That's 297 true positives and 3 million false positives, producing a new sample population that is .009% terrorists and 99.99% innocent Americans who may be wrongly investigated.
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