k = killers, i = innocents, p = total population, r = killer ratio
p = k+i
r = k/(k+i) = k/p
If an innocent kills a killer: (+1 killer, -1 innocent) from becoming a killer; -1 killer from killing a killer; -1 innocent net change, so r goes up (bad)
Now that you’re a killer, any time you kill another killer, it’s just -1 killer. r goes down (because the numerator gets smaller faster than the denominator) (good).
This means that the first time you kill someone is always bad, but it gets better if you kill more people. You can offset the net cost of the first kill this way; if r <= 0.5, killing two people will do it. So you’re right that if everyone kills one person, the world will be full of killers. But this also suggests that the best course of action is for one person to go around and kill every killer, and then themselves, leaving the world temporarily killer-free!
Your analysis is correct but I’m so tired of this line in popular discourse and the media. See also:
But if everyone killed killers then the relative number of killers go up and you only succeed when everyone is dead.
Wait, is that true?
k = killers, i = innocents, p = total population, r = killer ratio
p = k+i
r = k/(k+i) = k/p
If an innocent kills a killer: (+1 killer, -1 innocent) from becoming a killer; -1 killer from killing a killer; -1 innocent net change, so r goes up (bad)
Now that you’re a killer, any time you kill another killer, it’s just -1 killer. r goes down (because the numerator gets smaller faster than the denominator) (good).
This means that the first time you kill someone is always bad, but it gets better if you kill more people. You can offset the net cost of the first kill this way; if r <= 0.5, killing two people will do it. So you’re right that if everyone kills one person, the world will be full of killers. But this also suggests that the best course of action is for one person to go around and kill every killer, and then themselves, leaving the world temporarily killer-free!
Let me simplify your math a bit
Currently there are people who are not killers.
If everyone kills then everyone would be a killer
Some < All
I just wanted to do some stats tbh I was getting rusty