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It's trivial to design an algorithm that's entirely unfair.
An algorithm which chooses the choice which it believes to cause the most deaths/cost the most money/etc.
Even if there is a limited number a A.I. in the gov., those A.I. could out perform humans on specific tasks easily. Examples are researching facts, bring up relevant information, hold persons accountable, and people could still make the important decisions A.I. couldn't.
Assuming it's true, an algorithmic gov't. capable of handling the complexity of human affairs "better" would be equivalent to strong A.I.; but our existing strong A.I.s (us) are demonstrably not capable of governing us as well as something algorithmic. Your premise is false by reductio ad absurdum.
Using humans as an example of AI would presume that another AI derived from algorithms would function the same way as the biological counterpart.
The AI of a chimpanzee governing us would also be a drastic difference and they are supposedly our closest relatives as well as biologic.
It is incoherent to say we are not capable of governing as well as something algorithmic just after saying we are strong A.I, and that A.I is algorithmic.