A republic, or an oligarchy by any other name, even one ruled by law, is a notoriously indecisive form of organization. I do not see a better division of labor than the one we discovered by accident.
A republic is an excellent means of producing commons. A monarchy an excellent means of conducting war. And a democracy an excellent means of fooling the people into suicide.
The Optimum that I know of:
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Monarch, Military, and Militia for the defense of people, territory, routes, and trade.
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Independent Judiciary for the resolution of conflicts, Rule of law, Property en Toto.
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An independent treasury for the provision of credit (issuance and repurchase of shares)
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Houses for the Production of Commons with members drawn by lot.
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Families for the production of generations under voluntary selection of mates.
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Men and Women forming Militia and emergency services.
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Private provision of public goods.
We had it about right. If we had given women and the proletarians houses and maintained land and property requirements we would have created a market for commons, instead of the fallacy of majority rule (mob rule).