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How are you determining you got a false positive? The app alerts you if you were exposed to someone with COVID while out and about in your day. Just because you didn't catch COVID from your exposure does not mean the app gave you a false positive. Just that you weren't close to them long enough and/or your immune system, hygiene, or luck fought it off.
Only way you could really say you got a "false positive" was if you got an alert, for a certain day but knew that you had 0 interaction with people (you never left the house and no one came over during your alert).
I think there probably can be adjustments made with more research, which at the time was unrealistic, since we were in the middle of it. For the alerts to be meaningful, they should be actionable, and receiving an alert should tell the person they should take a test. If 9 times out of 10 the alert turns up a negative covid test, then it's not really reliable, and people won't see use in taking them seriously (aka Alarm Fatigue). Fine tuning the parameters of the alert can improve this rate, for example requiring longer durations in close proximity and/or closer distance between devices.
Of course dialing things too extreme would lead to "false negatives" which would be even harder to test for and validate, because of the nature of the recorded history on the device. Ideally there'd be 0 false negatives and 0 false positives, where every alert resulted in a positive covid test, and no positive covid test wasn't prompted by an alert. This is obviously unrealistic, but finding a good balance would make the alerts reliable, and useful. Since this system is going away, it doesn't really matter, but the principals of alerting are still important to consider in any system, especially where health & safety are involved.