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Well except crime doesn't seem to operate that way on a global scale. Sure on an individual level you would probably choose to commit crimes on people that don't have the ways to defend themselves, but if everybody has those ways, it seems crimes will happen anyway. And it doesn't even seem that there is a way to prove that gun ownership do end up detering crime on a large scale (if anything, the USA example seem to prove an inverse relation).
To go back to your illustration, if you're starving and can only find bear cubs, you will end up attacking them, even if they are all packing bear moms; you'll just make sure you have a big rifle beforehand.
Also utilitarian view matters because politics are not interested in individual preferences but about the well-being of the society as a whole. And what benefits the sum of the few does not necessarily align with what benefits the group (classic example being the prisonner's dilemma).