What is the acceptable rate of mistakes for the judiciary system? Death is an irreversible punishment, so I can understand that it seems incompatible with a wr

What is the acceptable rate of mistakes for the judiciary system? Death is an irreversible punishment, so I can understand that it seems incompatible with a wrong judge decision, but the alternative, that is for instance perpetual incarceration, is only reversible on a very theoretical basis (if an innocent is in prison, his case will be reviewed only if he's very lucky). So arguably, any sentencing is unfair when it's wrong. Death only makes it more obvious. Then, what's the acceptable error rate in a judiciary system? The author mentions 4% being unacceptable. What about 0.1%? 0.0001%? Crime can not be left unpunished, can it? And yet I doubt it is possible to always be absolutely sure of either guilt or innocence. After all, doesn't the Law talk about "reasonable doubt"? Doesn't that also mean by contraposition that below a certain threshold, it becomes unreasonable to consider unlikely circumstances or extraordinary events that would prove a defendant non-guilty?