A good social democracy checks a lot of the boxes mentioned above, and presumably where it falls short it could be improved without completely doing away with private ownership.
To what end would we suffer the ills of any private ownership at all? For what possible gain would we subject any person to the misery of a wage earner? Could there be some need for private ownership to generate the wealth needed to pay the taxes needed to provide the benifits needed to those who enjoy their socialist freedoms.
