What is the difficulty with that? It's the difference between what you are able to use alone, and what you need other people in order to be able to use. I don't think that is workable distinction. Private property may be a small worthless (trade value...) rock that has some special meaning to you, an that you will defend with force if necessary. I don't think you should have to negotiate the private possession of that rock with everyone else you met. And I don't think anyone else would begrudge you the exclusive use of it. Obvious other cases are the use of a home. Having several homes though would create an issue because you'd not be able to use them all continuously - that you'd be forced to negotiate. And in fact we do negotiate property now. We just do it within a framework where some are believed powerful and others are believed (and believe themselves) near powerless.