I find that a horrible thought.
I believe No human death should be deliberate, especially if done the state.

This was also at a time with a higher birthrate, and society and life was more violent. We were not killing 1% of the people through execution for crimes. People were dying as victims of crime.
US Birthrate today is about 1.2%. Killing off of 1% of the population is not going to lead to a good outcome.

We don't kill that many people worldwide from execution -- Amnesty says 2707 across 17 countries in 2025. By advocating for killing more criminals you are proposing lower criminal charges to meet some kind of capital punishment threshold.

1. In order to kill 1% of society a year, what would be the minimum crime to attract death by the state? Would this lead to higher false positives and execution of innocent people?

Use of lethal force by law enforcement is not considered the death penalty for the debate and out of scope. I'm talking about the state enacting Justice by deliberately executing an inmate by decree.

Assume society wants less criminals, and wants broad agreement and social policy to optimize for this.

Consider criminality as an attribute of a human that we want to optimize to 0.

Consider how criminality is derived in the human, there has to be some source -- nature, nurture, otherwise. Assuming that there is some 'criminality gene' to be found to in the class of nature; eg: MAOA "Warrior Gene" and CDH13 for hyperactivity/impulse control.

2. What ratio of criminality is inherited, genetic vs organic damage later through disease or parasite?
   Something like Lead or Toxoplasma gondii exposure can have can behavioral effects that creates criminals, which would not be an inherited trait. The phasing out of lead fuel in the 20th century increased IQs, which should presumably decrease criminality.
3. How much does the upbringing and youth experience of a person impact criminality independent of their genes - the nurture class? A person in an abusive or violent environment may develop criminality through learned behavior. If one gets sent to a place where teenagers are stabbing each other, maybe they will become more criminal. This is independent of the gene pool.

Even if we consider that epigenetic inheritance, generational trauma, where environment switches off genes that impacts criminality in offspring as something to prevent, epigenetic changes are reversible. There may be treatment that reduces criminality in offspring and would not be inherited by future generations.

Executing people, or even executing 1% of the population for crimes is a highly inefficient way to reduce criminality in society with way too many false positives, which are abhorrent.

i am not pro crime! that has nothing to do with capital punishment.
capital punishment 'doesn't work', as in its so called positive incentives - crime deterrence - doesn't exist. as a tool of instilling fear in society, it doesn't work either, and is likely to build resentment for the state in the families of the inmate. its a flex by the state that often has negative results.
its hard to justify in the true positive case, and abhorrent when the inmate is actually innocent in the false positive case. Negative justice.

not wanting to kill other murderers does not mean one likes murderers!

homicide is abhorrent, by individuals or by the state. its negatives outweigh any perceived fictional benefit.

for the safety of others in society, we exclude people who kill other people and this is generally acceptable. she has been locked up for 30 years, since age 20.

what does killing her now achieve anyway?

lol. If peter gets his way, I'm sure you would fall into the 1% soon enough.