Yes, executioners do proliferate this way. They tend to run out of murderers quickly though, then use any other excuses to execute.

Only if they haven't yet reproduced.

I doubt it. The fraction of population that is murderers is quite small.

If so, you don't have to execute a lot of them to affect the murder rates!

The question wasn't changing the murder rate now, but changing "the population over a few centuries". If it doesn't change the population genetics significantly it won't do that.

If 1% of men are potential murderers, and we execute 10% of them in each generation, it will have huge a impact on the murder rate over a few centuries, even though not a lot of people got executed, and the overall genetics of the population hasn't changed much.

Well, no, that presumes "murderosity" is due to rare genes concentrated in murderers, not unfortunate combinations of genes widely spread in the population. Experience with "disease genes" has been they mostly of the latter type, with each gene having a minor effect.

The rate of the effect is probably unknowable. I think we agree that it exists.

It is now. OTOH I have read that an estimated 1/4 of male chimpanzees die at the hands of other chimps (whether murder or war). So it’s not implausible.