I voted no. Those that are advocating we stick with the traditional idea of a police force are thinking wrong. If roads were privatized, those that owned the roads would be responsible for providing a security force. If a murder (or something) occurred on their land, they would be held liable for it being on their land and not having an adequate security force; that would be the incentive to provide a security force. Those that own the road could also provide a contractual service to prevent crimes on your property while you're away (for example, in a neighborhood), or you could hire security for your property if it's too big (i.e., rural land).
It'd be dangerous to think that police could be trusted at your home while you're away. You can't have both property rights and a police force that is allowed to trespass on your property even to catch a criminal. I wouldn't be alright with this.
I don't have anyone who has influenced me in these thoughts: these are things that I have thought of on my own. Of course, these ideas also require free markets, a functioning economy and citizens who would be willing to privatize roads.