Why States Exist: The Square Law Theory of The State

States—governments—exist because they can raise armies, by force if necessary, and the effectiveness of armies increases as the square of the number of men in arms. I shall prove, for example, that an army of 10,000 men can completely annihilate an army of 1,000 men while losing only 50 men, provided only that the average fighting ability of the men in the two armies is the same. To face the army of 10,000 men on equal terms, the army of 1,000 would have to be man per man 100 times more militarily efficient, so a huge army of unwilling draftees can generally outfight a small army of trained professionals. This is a precise formulation of the Principle of Concentration known to generals for millennia. It is also a military analogue, actually a special case, of Ronald Coase’s central idea in his The Nature of the Firm: business organisations exist because they can overcome the information costs that individual contractors would face operating alone. Anarchy is possible only if a means can be found to cancel the Principle of Concentration. I show that future technology may cancel it.