Democracies not fighting each other? That's news to me.
There are no pure democracies, and some imperfect democracies surely waged war against each other.
The Greeks were the first with a (well-documented) kind of democracy, and they understood peace to be the exception, not the rule.

The Americans attacked the constitutional monarchy of Spain in 1898.
Germany fought against the French Republic and the British constitutional monarchy during the First World War while having a powerful parliament (the emperor was merely head of state, incapable of enacting laws or defining budgets himself).
Lots of republics faced each other in Latin American wars.

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I suppose that the characteristic "democratic" is often overpowered by nationalism in regard to your topic and that the relative scarcity of wars between democracies is probably rather a result of democracies becoming more common during the period of impractical wars between great powers than democracies working for peace.

Just look at how the war of 1898 came into being - you may be reminded of 2003.