If you just send everybody who was in contact with a positively tested person into testing (they give samples, send them in, get tested, get the results back), but they keep going about their normal lives, they will statistically infect more people before the tests come back.
So the false positive rate is quite important, as it potentially means sending thousands of people into home-quarantine.
Of course it's important and of the course the lower the false positive rate the better. But the argument remains: even with a high false positive rate, what's the net result? Maybe overall it's worth putting thousands of false positive in quarantine now than a whole city of millions two months later.
There are so many variables and known unknowns in this approach. I argue that even with all the well reasoned arguments against, at this scale and with this stakes they stay theoretical until we actually do it. Let's try at least once, and if it fails it's still knowledge gained.
If everyone of those has the app installed and has, on average, 100 registered contacts (so that’s about 98 false positives, if we assume that on average two of those lead to infections) that’s about 30,000 people being told to isolate every day.
If they are told to isolate for one week (should be sufficient, on balance) that’s around 200,000 people isolated at any one point in time.
If only 50% have the app installed that’s down to 100,000 people.
Sounds high but ok to me. Given how active the infection currently is in Germany I wouldn’t want false positives be higher than that – but somewhere in that high ballpark sounds fine to me.
Maybe at most a couple 10,000 sent into home isolation (a week should be plenty here, no need for 14 days – we aren’t shooting for perfect anyways) versus 81 million with strong measures.
Obviously the app isn’t the perfect solution here. Much more important is thorough and swift real contact tracing (followed by quarantine irrespective of diagnostics, so quite similar to how the app would work with many false positives). But I wouldn’t reject the app out of hand.