Centrally planned economies are NP-hard. That's the first argument against them. The second is probably the USSR. As you decentralize planning, you break the problem down into smaller and smaller problems, but lose the guarantee of global optimality (except under certain unrealistic conditions - Pareto efficiency, but then you might as well roll free-market anyway).
The justification for private ownership of capital is property rights. Whether you derive those rights from self-ownership or religion is irrelevant. What is lacking is justification for the theft of that private property, which you fail to supply.
Additionally, at the end of the day, social priorities - even if computationally ranked - are defined by the axiomatic system from which we derive our morality. The idea of computing axioms is kind of circular. What mathematical formula would you like to optimize to choose between libertarianism and communitarianism? What isGood() function do you propose?
According to the latest official figures, 43% of all statistics are totally worthless.