If there is not enough money for law enforcement then more money has to be raised, encouraging vigilantism just leads to worse problems, popular as the "get yourself an AR-15" may be. Civilization will only work there where citizens refrain from vengeance because they know that the government will do it for them.
It doesnt matter how much money you throw at the situation, it still remains the same. Unless they spend so much where they can asign a cop to stand watch over say every 5 houses, and are present at all times. And that would bring more problems then it would solve. It would be a police state.