You personally won't be executed. But your type will either be controlled, annihilated, or humanity as a whole will cease to be.
Psychopaths aren't parasites. A parasite doesn't threaten the life of the host, because the parasite's life depends on the host's life. If psychopaths were just parasites they would not be an issue.
When society uses competitions to pick leaders, many of the leaders will naturally be psychopaths because psychopaths will go to lengths that good people won't go to in order to win. It's that simple.
You have a contest. The winner gets a huge prize and becomes a leader of humanity. Good person could murder or blackmail to win the contest, but good person won't do that because he's not a psychopath. Psychopaths will do that, they win the contest, they take control of humanity and then run humanity into the ground because a psychopath only cares about satisfying their petty lusts.
All human problems right now are caused by the fact that our competitive systems of picking leaders always pick psychopaths.
If we murdered all the psychopaths when they were toddlers, today we would have a proper response to climate change. We would have a proper response to mass poverty. Corporations wouldn't look like they are actively TRYING to make our species go extinct.