old posts on this subject that got alot of attention
the posts are pretty hostile to the claims though
/u/ainrialai seemed to have alot to say on this matter
followup question: how to DPT advocates treat/deal with the war of 1812?
Political scientist here- I can tell you that this claim comes from the democratic peace theory which really has two different claims depending on who you ask: 1) democracies NEVER fight wars with one another or 2) democracies TEND not to fight wars with each other. One is static and the other is probabilistic. These are very different claims and the evidence for each one is highly sensitive to the data and definitions used for both democracy and war.
Generally speaking, the statistical evidence is very strong for the second claim that two states who are both democracies will have the least likelihood of fighting a war (versus pairing a democracy-autocracy or autocracy-autocracy). This result of democracies tending not to fight one another is robust over multiple different measures of democracy. Two commonly used definitions are from the Polity IV project and Adam Przeworski's "Democracy and Development". No matter what measure is used for democracy (within academic reason) the second claim has found consistent support - albeit other factors are also important such as the depth of two states' trading relationship.
The first claim, that democracies NEVER fight one another, is a bit more contested and very sensitive to the definition of democracy and war. The UK and Finland did indeed fight during WWII, but some academics wiggle out of this by showing that the actual military engagements between the two were very limited, not reaching the threshold of the academic concept of "war". There is also the Kargil war between Pakistan and India, in which both were considered democracies but still fought a war. Though again, there's plenty of people who would debate whether Pakistan was truly a democracy at the time- even if their head executive was civilian.
It should be said that the definition of war comes from the Correlates of War project- which has a high threshold for a conflict being considered an interstate war, which is what the democratic peace is all about. There are other data projects (Uppsala/PRIO) that code violence with a lower threshold for being considered a war, but to my knowledge there's still the same support for claim 2 using these data.
Another thing to point out is that when this claim is made, it typically only applies to the 1900s to the current day. Even more frequent is that the study is looking at the period after 1945. So the claim we're talking about is for a certain conception of democracy not engaging in a certain conception of war from 1945 to present day. So while comments about ancient or pre-1945 democracies that may have gone to war are useful, most democracies before that time would not count as democracies in the modern sense (i.e. universal suffrage, no restrictions to voting rights, alternation of powers, more than one party, elected leaders, elected legislatures etc.)
Weren't England and Finland technically at war in WW2 although not actively engaged in warfare? I've heard it but can't recall if the source was credible so would be interested to know if it is verified.
Let's remind ourselves that the theory of democratic peace exists within the parameters of international relations, which is a branch of political sciences. As it is, international relations describe interactions of post 1648 unitary entities known as States. Also, in this context, the notion of war is exclusively the domain of interstate violence.
Athens' Sicilian expedition comes to mind. Though as I understand it this would have been towards the end of both Athens' and Syracuse's democracies.
The 2008 Russo-Georgian war springs most readily to mind. One would have to stretch the definition of either war or democracy pretty far not to count it.
Carthage vs Rome is another one from the past. Both were republics at the time though the Carthaginian system is not as well documented.
War between Republic of Genoa and Venice spring to mind, though that depends how you see democracy in this case.