First of all, I'd like to point out that, by destroying the world, my family would be destroyed as well.
But, assuming this means that my family will be able to live if the world is destroyed, then I'd have to go with killing my family. I think this because, looking at it from their point of view, they would be devastated if the entire world could have been saved if they just sacrificed themselves. I feel like the guilt alone would make them extremely depressed, maybe even to the point of suicide.
Furthermore, looking at this from the future's point of view, if you killed the family, the human race wouldn't be able to reproduce anymore without incest, and we all know what kind of problems that could cause.
My family would probably want to sacrifice if it meant to save the entire world, I would probably want to go down with my family. I mean if my family die, wouldn't we die anyways because the world would be gone? So yeah, I would totally sacrifice my family to save the world, and probably die with them.
Would I sacrifice my blood relatives to save the world? Oh yeah, in a heartbeat. Would I sacrifice my wife and child? I doubt it, unless it's impossible for us to continue living after the world is not saved. Since I don't know what will happen to the world, it would be impossible to make that decision before hand.
I'll just expect that everybody love their family like nothing else in the world, if you love someone you just don't sacrifice it for people you don't even know, we live in a world that is completely lost, drugs, sex, we've lost the real concept of love, and the thing is that we are selfish at some point, no matter how kind a person is nobody would put the whole world above their own family,
Firstly, how exactly would I be "sacrificing" my family? I certainly wouldn't kill them. Now, if they voluntarily did it that would be their choice but I probably do my best to talk them out of it.
Furthermore, I can't imagine a situation where sacrificing one family would save the entire world. But again, no I couldn't do it. I don't even think I could sacrifice anyone.
The world didn't do anything for me, why should i do anything for them? I understand that life is like a mirror and if i do good, i'll get good, but if we go extreme like this, i would go with my family (also if we are talking like zombie apocalypse or some kind of war, anarchy scenario) i would rather safe my family, at least i would die with my relatives, my friends and all. The world is a big challenge, but with the support of your family and friends, the challenge becomes easier. Even if there's something like apocalypse.