There already is chaos on the roads - WITH consequences.
Those with the least amount of regard for others would then become the dominant players(alpha males if you will). Since there are no rules to constrain them, they will only be constrained by their morality or sensibility. Since these same people were devoid of both when they were mandated upon them, it would be foolish to have the slightest hope they they would have the ability to constrain themselves.
So you claim the arms will even things out. No, again they will skew the odds in the favor of those devoid of self constraint put upon themselves by morals and values. A moral man will look to other ways to solve such a dispute - the alpha male will look for ways to exert his dominance upon the others.
No need for a grand human experiment - just look to nature where anarchy rules. It only works out for the most vicious and strong of the species.