Worldwide anarchy is something to strive for. It would not be utter chaos, and to think so just shows how little real thought you put into this.
To describe anarchy as chaos means you had your first thought, "There would be no laws or authorities," and came to your first conclusion, "Everyone would run amok," and then just stopped thinking. There are still consequences to your actions in anarchy. Most people would still live peaceably, but everyone would be their own police. If someone decides there are no police, so they're going looting, raping, and killing, they would quickly learn how much more effective free people are at being their own police.
If there's one thing the government can do, it's mess everything up. Jobs would still be there, but you wouldn't have to work for less wages than you want, and you would not be obligated to "give" the authorities their "piece." If they were truly, inherently your authorities, then they wouldn't NEED anything from you to maintain their position. Thinking this way, you realize that all authority is illusory inasmuch as it is voluntary.
If anyone who voted no in the first place revisits this site, I hope you would take all of these things under consideration and think more than one move ahead about this.