While this may seem intuitively obvious, history does not seem to bear out the truth of this point. For example, one would expect that the Central Powers in WWI would have been an extremely strong coalition, given that the Germans and Austro-Hungarian ruling elites were largely from the same Teutonic stock. Yet, as it turns out, they were their own worst enemies. Each had very different war aims and very different plans for achieving those aims. The Austrians even started to negotiate a separate armistice. Another counterexample from WWI is the Western Front where a single country (the German Empire) was unable to beat a coalition that had centuries of animosity between its members (Britain and France).The more similar the coalition members are to each other, the stronger the coalition and the less vulnerable it is to the enemy's efforts to disrupt it.
The expressed example of Ike's greatest accomplishment also runs counter to the point it is supposed to support. I suspect that Eisenhower's greatest accomplishment in the WWII ETO was not keeping the US and British working together, but rather having the ability to give them diverse enough tasks that they did not have to work together very much. He kept the coalition together by keeping the partners apart, starting with the Normandy invasion--Brits in the north, Americans in the center and south. (Even the reduction of the Geman penetration in the Ardennes followed this pattern). A similar claim is worth making regarding his deployment of French forces late in the war.
I believe that the American desire to maintain separation of commands is also a legacy of the American experience from WWI. The French and British wished to commit US troops piecemeal, as battalion level replacements into British and French formations. Pershing fought against this effort, only allowing a small number of units to be so committed.
I think the truly important point to be made about coalitions is to recognize that there will always be areas of potential conflict between coalition partners. What effective leaders must do is prepare for that conflict and look for ways to mitigate it when it happens.
I suspect what is operative here is strongly akin to the tactical and operational problem of unit boundaries. One tries to hide one's boundaries from their opponents so the opponent cannot exploit those boundaries. Simultaneouly one seeks to find and exploit the boundaries of the opponent. These boundaries need not be an operational control measure or a line on a map. They can just as easily be alternative views on the nature of orthodox faith, the role of women, or the control of the means of production. Given the likelihood of discovrery of these boundaries, a good leader has a plan to mitigate the effects of their exploitation. For example, while on defense, one keeps a reserve to commit to threatened sectors; on offense one uses a reserve to exploit success (most often by splitting theopposing forces boundaries).
The hard part about coalition war is figuring out what to use as the reserve to commit when a cultural seam or boundary has been exploited (by us or by our oppoents). This work puts us squarely in the area of information operations (IO), and I submit that producing some answers to this issue could produce a very high payoff were it given a great deal of consideration by our IO wunderkind.
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