There is no correct answer to this question.
But. Yes, I would kill the 100 children, and then freeze them until a time in the future when we can bring them back to life. Win win situation right there.
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Ah, moral philosophy my favorite. I'll try keep it short and start by saying that there is an easy answer to this question and it is no. Here is why.
First of all, you did not specify "what is violence", but your word choices indicate to physical violence. So forth, leaving still attached to human nature as it is. Violence would continue in act, verbal, mind controlling way, and would even evolve much further. After all, violence and death are only there for a short period of time (even if abuse can leave big marks on a person). In other words, violence would evolve towards different kind of actions resulting in a catastrophic rise of mental problems.
It doesn't matter whether you have to kill one, hundred or million to save five, fifty or one billion. You can never justify when it is not in a stress situation in itself such as war, where a person has to sometimes sacrifice himself in order to save the others. Someone has to be last one to leave when retreating, someone has to be the first to scout etc. Even if the question would be sacrificing 100 deathly ill patients who were volunteering it would still be more than hard question based on, for instance, our moral beliefs and stands we have taken as a society.
Who would kill these one hundred people? How would select them? At what age would you make the selection? These are especially the two questions that lead the answer of this question incontrovertible one sided. Especially the picking point would the most troublesome part, a raffle? Or since you are referring to religion, it would be gods will as one says, as it was in many Indian cultures. This would mean that culture would have to develop these twisted affirmations that would confirm and make the ritual accepted and as a part of a normal society. It would twist our conception of believe science, culture, you name it. Not to mention it would once again create a class of people who have the right to decide life and death, which would result twisting society once again.
Not to mention the time span of 20 years you mentioned. Actually the shorter the time spawn would the better it is, unless we are talking something like over 100 years although it would still impose certain problems that I will next point out. First of all, if violence would be solved by someone just snapping their fingers. The problem of violence would be solved superstitiously as the Indians did to ensure their crop. In other words, we wouldn't learn the reasons, the psychology, that is behind the circumstances that lead to violence. After all everything in human nature is about evolving. It does not matter if it how we kill each other or how we live in peace. Not to mention, and here is why short time span is better, our coping mechanisms concerning violence would be deprived leaving us even further vulnerable to some who know how to use it, as it part of the human nature. In other words, after this time span of 20 years of artificial removal of violence would switch off, it would most probably result in enormous rise of violence compared to the period before violence was removed. Not to mention states control mechanisms would not be there. We once again have to train new kind of people for which there was no need for that 20 years, and for the past 20 years we would have trained those away from their original jobs.
If I wanted to take this even deeper I could evaluate the question based on your belief, for instance, are you liberal, conservative? Would you believe in utilitarianism?. What kind of religion would you believe in? What kind of moral ethic are we implementing? etc..
In a simplified way perceiving the matter that sacrificing this many people in order to get this many years of peace without violence is like saying, since the day that you were born, that the only way I can ever get wealthy is to win in a lottery. Predetermined mind sets that others have enforced, which actual limit us in an unimaginable ways, not just as a person but as society, nation, and as a human.
E: I did not read through what I wrote, so hopefully there are not too many spelling mistakes or too complicated sentences.
Violence is part of human's nature. If the world is like that today that's because species evolved throughout the millenium and we're the result. Erasing wars will never be possible. Erasing violence would be like erasing a part of us, not the best part but still a part of us and unfortunately I'm not sure the situation would get better, no worries, we still have egoism, greed etc. And humanity without that isn't humanity anymore, now who knows, maybe it would be better but 20 years c'mon
To resume : 1) 20 years isn't enough 2) Violence isn't enough 3) What's the point of being extremely violent to remove violence? It's like killing tons of people to get peace. Oh wait...
In case it wasn't clear enough, I wouldn't kill anyone
The unfortunate truth is that either way people die. As inhumane and depraved as it sounds, I would sacrifice the 100 children to end violence for 20 years.
In the US, there are around 16,000 homicides per year. 20 years of of no violence means ~320,000 people do not fall victim to homicide in the united states alone.
Think of the political impact as well. If violence was stopped, then war would no longer be a viable tactic for nations to solve disputes. Countries would be forced to use diplomacy to work through their problems. If nations were forced to work together instead of resorting to war, imagine the effect this would have on the global community.
On the other hand, if we took away violence, the movie and video game industries would tank. Tough call.