The "myth" dates back to Kant's "Perpetual Peace" published about 1795. Not everyone buys into it [Sebastian Rosato. The Flawed Logic of Democratic Peace Theory (2003). The American Political Science Review, Vol. 97(4)]. Probably the most common attack is based on the idea that the democratic peace, at least in recent history, was a byproduct of the Cold War [Farber and Gowa. Common Interests or Common Polities? Reinterpreting the Democratic Peace (1997). Journal of Politics Vol. 59]. And while it may be no more than myth what does seem to be true is that democracies prefer to fight against non-democratic states with at least part of the justification being the spread of democracy [Morgan and Campbell. Domestic Structure, Decisional Constraints, and War: So Why Kant's Democracies Fight? (1991) Journal of Conflict Resolution, Vol 35(2)]. The 'myth', or the perception, of the democratic peace is part of the logic of getting involved in those wars. So, as you say, perception is reality, or at least in this case, it justifies it.
Why should this matter? Because if we want to determine the type of war the US Army is most likely to engage in at some future date, then it is more likely to be against a non-democratic state justified, at least in part, on the idea that we are spreading democracy. And if spreading democracy is part of the justification, then it will be part of the requirements of victory.
I don't prescribe to the the maxim of a democratic peace, otherwise I would not be asking the question what surrender by a democracy might look like (or how might it be different from the surrender of the Japanese after WWII or even the German's for that matter).
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