The people, acting through government, grants specific people, monopolies over particular property. That's all that property rights are--my community, acting through government, agreeing to come to my aid if I'm dispossessed of my property outside the framework of rules we have collectively established. That agreement is what distinguishes property rights from mere posession.
Gotcha - I grant myself my property, which I already had, by way of possession. :)
I see the subtlety of the point you are making - that property is defined collectively (otherwise it is mere possession) - but I am making an equally subtle point about the underlying meaning of that definition: that collective responsibility is just a statistic on a population of individuals, not a statistic about an entity.
