Well, democracy answers this by asking people directly. So one way to do it is poll the sub's members. Or, you could see whether the stuff that gets deleted was highly voted before it was deleted. If people don't like certain content, it won't get voted up.
I'm not sure which cases of hostile takeovers they're referring to, so I don't know what happened there, but presumably they either had a mod on their side, or got an admin to step in. The mod's behavior must have been pretty bad if an admin intervened.
If you pull the "the majority decides" card then there is no decision necessary. Each subreddit is defined by the majority of its users. Simple as that.
Not necessarily. The algorithms that do the sorting might be biased toward certain content (for instance, if it highly values quickly upvoted content, it would be biased toward short memes and against long-form articles). Reddit voting isn't just a straight majority vote.
A subreddit is not a democracy. As a moderator, I can do mostly whatever I please and you're welcome to stay or start your own subreddit.
I don't understand why you'd say that if an admin did something then the mod's behavior must have been pretty bad. Define bad? Bad for reddit's public image? Bad for monetization?
I'm not sure which cases of hostile takeovers they're referring to, so I don't know what happened there, but presumably they either had a mod on their side, or got an admin to step in. The mod's behavior must have been pretty bad if an admin intervened.