It is difficult for me to stay objective when it comes to gun possession, because I'm strongly anti-guns, and I can't seem to even begin to understand Americans' attitudes on the subject, but I'll give it my best shot:
Remember what was the "cause"[1] for these riots? A person got shot. The situation is already out of control, but if half the rioters and half the citizens and all of the police were carrying guns, I honestly think London would be a war zone right now.
One thing that - to me, at least - has always been obvious is a direct proportional relation between guns and violence. Less guns, less violence; more guns more violence. Weapons are a catalyst for violence.
These are people fighting people. Any guns would be evenly distributed among the defenders and the attackers, and thus not serve to end or cool the conflict, but further exacerbate the situation.
Any mob is better than an armed mob. Arming the citizens would be arming the mob, since the mob actually consists of citizens. I do not think guns would help anybody.
I don't even think that guns would help the police. I'm glad the police are not using arms against the mob.
And yes, if I had to choose between somebody breaking into my house and stealing/breaking everything, and having a gunfight with said person, I'd choose the former, without even blinking. Call me meek, but I'd rather lose my livelihood than my life. Where I come from, health is always valued more than possessions.
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[1] I know "cause" is not the right word. The shot drug dealer wasn't any more a cause for the riots than Helena's rapture by Paris was a cause for the Trojan siege. Doesn't mean that the Trojans would have been wise to counteract the Greeks by abducting more women. The mob is taking it as a primary reason to run amok, and more people getting killed would add more anger.