Be a bit careful of jumping to that conclusion. CvC was pretty sceptical of democracy and/or republics, as he saw them work in practice. Best to look back at Thucydides as a strong influence on Clausewitz, were the forces that drive nations or peoples to war, were Fear, Honour, and/or Interest.
CvC was describing the process as an observer. He saw no evidence that people, governments or armies were guided by rational thought - which is why he did not have much time for democracy!
He also had a number of trinities, and they were all context specific. Passion, reason and chance, for example are those he uses to describe the social nature of war.
I would submit that US Foreign Policy post -911 shows CvCs observation, as being correct.
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