You want accuracy. We can just ignore this false dichotomy about letting guilty people go to protect the innocent. If you are jailing the innocent, then you still have guilty parties going free anyways since the wrong person is convicted.
It's not like the only two possible outcomes of a criminal investigation are that a guilty person gets convicted or an innocent person gets convicted. You can also convict both (eg, if there is evidence that multiple people were involved), or neither.
> you still have guilty parties going free anyways since the wrong person is convicted
which is a non sequitur.
The whole premise of this one or the other thing is flawed. You can increase conviction of the guilty while also protecting the innocent depending on the procedures taken. The "how" matters at lot. So when you ask people stuff like how many guilty men should go free, it's a complete farce that is easily manipulated based on how you pose the question, methods, and outcomes in the fictional scenario. It takes away focus from the actual policies/solutions.
Edit: why disagree?
Loosening rules is in fact likely to result in MORE guilty parties running around not less because it makes it easier to stick SOMEONE with the crime whereas accountability makes it more likely that you stick the right guy with the crime.
I don't think it's a false dichotomy. I think roughly speaking you calibrate the standard of evidence for a conviction and a good approximation to how that is calibrated is the ratio of guilty man set free to innocent men jailed. This is calibrating the ratio of false negatives to false positives. To avoid false positives you want fewer convictions which is generally going to result in more false negatives. Yes every time you get a false positive, you also have a guilty person go free, but chances are that person was always going free, since they were never the most likely suspect and were unlikely to ever be tried in court.