Plato makes the claim, somewhat capriciously, that all the wives of the rulers ought to be shared. Additionally, fathers ought not to think of a child as being their own son or daughter. Rather, the citizens should view all children of the state as being their own.
Taken literally, and Aristotle sees no other way to take it, this sort of thinking would effectively eliminate private property and would revert all things in the state, including women and children, to shared ownership.
But shared ownership simply is not the way to go, Aristotle tells us. The sharing of property and children will make the friendship in the city “watery”. It is human nature that when responsibility (the responsibility of raising child for instance) is divided among many (the entire state) the result is that nobody truly pays any attention to the responsibilities at hand.
Everybody simply assumes that somebody else will care for these matters and the people become lax, uninterested in managing any affairs. Aristotle compares this to a dinner party that runs more smoothly when there are a few servants attending to their own affairs rather than numerous servants attempting to tend to the entirety of the responsibilities.
The benefits of having private property are similar. For people are most interested in tending to and facilitating that which belongs to them or that which might benefit them. If all property is shared, there is no incentive for the citizens to maintain or develop the lands and properties of the society.
Self-interest, Aristotle tells us, is human nature. The philosopher writes as much in Nicomachean Ethics when he declares that the goal of a human life is to achieve our individual happiness through an understanding and application of virtue.
And so we see that the ownership of private property, as well as the self-interestedness of the citizens, is actually beneficial to the state as a whole.