I've been interested for quite a while in the theory that democracies don't fight wars with other democracies, but only recently learned that Spencer Weart, the historian-god of climate change science, also wrote a book in 1998 called Never at War: Why Democracies Will Not Fight One Another. (I'm shamefully cribbing off of wiki rather than his book, but I'll get around to the real thing sometime I swear).
Weart makes the maximalist argument, that any country sufficiently democratic to have let at least 2/3 of male adults to vote and control the government for at least three years will not go to war with a similar democracy. He includes many classic Greek city-states in this category. The book then discusses borderline cases and his theories about why democracies don't fight each other.
Wiki has a quite good general article on the democratic peace theory - as with any other field, you can find some expert who absolutely denies the consensus position, but it seems pretty clear that well-established democracies don't fight each other, and quite likely that even immature democracies are less likely to fight democracies. No consensus on why that's the case however.
My own view: I don't know enough about classical Greece to say anything relevant. I think democracy requires at least a certain level of organization and sophistication before the democratic peace kicks in. Hunter-gatherer and small-scale agricultural societies were reasonably democratic/anarchic and very often violent toward outgroups. Weart's maximalist position may or may not work - the 1999 Kargil War between India and Pakistan that started a year after Weart's book is a contrary example. OTOH, Pakistan's elected parliament didn't really control its military which initiated that war.
That Weart could even plausibly maintain his position suggests the overall strength of the democratic peace theory.
Israel's antipathy and fear of the Arab Spring is interesting in light of the fact that Israeli policymakers should know about democratic peace theory. Why Israelis thought their security was better protected by a hated 82-year old tyrant instead of a potential shot at Egyptian democratization isn't clear. I guess one response would be to look at how unpopular Israel is now with the average Egyptian, but I suspect that unpopularity itself could partially be a result of Israeli antipathy to Arab democracy.
I think the disinterest in Arab democracy in light of democratic peace theory suggests at least partially that Israel isn't all that worried about its security. It also suggests that Israel does not want democratically elected Arab leaders to be expressing grievances about West Bank and Gaza, because those leaders are much more persuasive that what Israel's had to deal with previously.
3. Labor unions.
Something of a tangent here, but one pithy statement I read somewhere about peace between democracies went to the effect of "yes it works in practice, but can you make it work in theory?" Weart isn't the only one who's tried to explain it, and no one's got a consensus theory for it.
I feel the same way about unions - the increasing inequality and declining middle class seems to be an effect of declining union power, but I don't think there's a good explanation about why unions benefit society generally, as opposed to just their members. I think the data is pretty good that they do benefit society, and there are plenty of theories why, but I'm not convinced as to why.
We'll just have to live with uncertainty.