As such, there is necessarily a tradeoff between the rate of hits (correctly identifying "bad" parents) and false-alarms.
The question then becomes: what's an acceptable false-positive rate?
Even in other applications, you wouldn't just come up with an acceptable false-positive rate. You'd consider that as part of a larger process.
How often do you test? What other tests are available? What's the cost/benefit tradeoffs?
So for example in some medical tests they tell people of certain ages to just come in for tests. They review and change that age based on evidence. Some tests may give borderline results so people get asked to come back sooner than average if they only just pass. Better techniques for confirming or denying the conclusion may be developed for use before doing anything drastic and irreversible.
False-positive rates (of the multiple different tests available) are only one factor.
I would guess almost all of these things are already done in the current case under discussion, e.g. as mentioned before one case involved accusations from a husband. Now maybe that's just two false signals that happen to agree, but already you're talking about two false-positive rates you need to consider. Judges and social workers are probably making snap decisions based on gut instinct and rules of thumb as well that factor in. Presumably a case needs to be pretty serious before removal is even considered.
From just reading a libertarian blog that focusses on goverment intrusion into child-rearing though, you may think people are having their hair snipped randomly in the street and finding their children gone when they get home. A false-positive for that hypothetical case would obviously need to be much, much lower to be acceptable than in tests used as part of a bigger process.
I don't disagree wit you, but none of what you say gets around the fact that once you start removing children from the custody of their parents, a non-zero FA rate sets in.
>Better techniques for confirming or denying the conclusion may be developed for use before doing anything drastic and irreversible.
Case in point: this is also a signal-detection problem. You can certainly try to build a more sensitive detector, but the infamous tradeoff doesn't magically go away.
As such, you have to have at least some idea of what kinds of FA-odds you're wiling to tolerate, else you're just flying blind.
And I must insist on this point: the universe doesn't care how disturbing one finds the Hit/FA trade-off. It's still there, even if one doesn't want to look at it.
Then you cannot, under any circumstances, remove a child from his or her parents.
I mean this in the strictest, most mathematical sense.
Are you sure that's what you want?