They could opt out. Nothing stops them in elective democracy (ie the US), and in states where voting is compulsory (compulsory democracy) like Australia, there are murderers and rapists still. Democracy has not a thing to do with preventing murder and rape. Honestly, neither does anarchy, in and of itself. If you are looking for a pat political program that will make the bad things end, I suggest you go talk to the LaRouche folks - they seem to have an answer for everything.
If, you want to talk about why anarchy (which is not compulsory democracy) might help reduce murder and rape (but probably not ever eliminate them) I think we want to look at the ways societies without laws work. There are plenty of examples of societies with much lower rates of person-on-person violence, and it often relates to the lack of things like private property and static power relations. [edit:] It also probably has something to do with the scale of the society - in a society where everyone knows everyone else, it is much harder for a perpetrator of violence to both other the potential victim (lots of overlapping social relations and shared history), and avoid social repurcussions. IT isn't perfect - rape and murder do exist even in small band societies, but the rates are much lower.
Additionally, if the commonly (not necessarily universally) held principles of mutual aid, affinity and free association were to actually be lived, as opposed to how we too often merely pantomime them currently, rape and murder wouldn't stop, but there would be much less opportunity. Most violence of that sort is between folks who are intimately related: friends, lovers, family, etc. Presumably with relations free of the social constraints that currently exist (capitalism, the nuclear family, add the things you hate to this list...) there would be both more actual interconnected relations that would serve to watch out for "bad people," and these "bad people" wouldn't be allowed to remain a part of social groups.
I don't really believe everything will be that clean. I think we will need knives and spears, but that is sort of an answer?
