Earlier quoted context omitted.
Even if there are 95% false positive: if you're able to test all those people and catch the 5% that might still be a net profit. It comes down to cost. Societies are spending thousands of billions to mitigate the problem, even a slight reduction of that number is a win.
As far as I understand, you would need to send everybody who might have been in contact with someone who's positive into quarantine, right away. You can also test them, but you need to quarantine them immediately, as the virus is transmitted before symptoms show. 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 bac…
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.