We might not even have socialism etc.
If you accept the logic of absolute property rights, even if you havent got anything you could really call property, then you'll have to accept it when the rich buy up absolutely everything and you are left totally propertyless.
Sure you could buy the junk and commodities that are produced to pacify the people who've really got nothing but you'll always be a tenant in someone elses houes, on someone elses land, using someone elses transport.
There are three people, there is one orange, they all have equal right to that orange but if they dont share it and one person eats it the rights of everyone to that orange wont mean anything in real terms to the two who havent got the orange.
Absolute Property rights lead to the deprivation of property for all but a select few, what you could call the new fuedal lords.