*Or "initiate" coercion, even though adding the concept of initiation creates more problems than it solves.
What makes ethics and political science interesting is that we can consider many different questions at different meta-levels, i.e. levels of generality and different levels of abstraction. The concept of free speech makes a particularly clear example. Suppose Andrew (a minority of one) is saying something that most people (the majority) dislike (e.g. "Kill all the redheads!"). We can look at the specific person and his specific speech, or we can look at people in general and speech in general. The question, "Should we permit Andrew to say, 'Kill all the redeads!'?" is a special case of "Under what circumstances should we tell people not to say what they please?" The majority may have very different opinions without contradiction at different meta-levels. At the specific, concrete level, the majority might have the opinion that Andrew's speech is objectionable, but at the general, abstract level, the majority might have the opinion that people should say what they please, even if it is specifically objectionable. Thus we can conclude that even if there were some institutional arrangement that prevented the majority from coercing Andrew (or even coerced the majority into giving Andrew some sort of platform for his speech), it would not be a case of the minority (the members of the institution) coercing the majority, but rather the majority at the abstract coercing itself at the concrete level.
Obviously, ethics and politics gets a lot more complicated when we try to reconcile our abstract opinions with our concrete opinions, especially when some of the abstract opinions take generations to construct. C'est la vie. We have seven billion people on this Earth, in a complex, interdependent technological society. If you want to kill five or six billion of them, and revert to a simple, agrarian society, feel free to try... and I'll feel free to try and stop you. Hard problems are indeed hard, but I have no patience for simplistic, moralistic ideologies.
At the ideological, theoretical level, democracy defines legitimacy as being grounded in some majority opinion. At the practical level, however, all societies can be viewed in some sense as "democratic". If, for example, the majority of the people were to assent to being ruled by an emperor with near-absolute power, then we could say that the emperor's decisions were fundamentally grounded in some majority decision. The emperor obviously cannot rule without an army, and the people must be willing to join, feed and socialize with the army. The emperor must have substantial popular support to rule. Thus "democracy" acts not to differentiate actual societies, but rather to differentiate between the underlying narratives of different societies. In two different hypothetical societies, we might have the same emperor, the same laws, the same army and police, the same territory, but one society has a democratic narrative and another a non-democratic narrative: in the former, the emperor rules because the people want to be ruled by an emperor, that emperor; in the latter, the emperor rules because e.g. the god(s) have chosen him to rule.
We can look at any ethical or political ideology as a "lens", as the underlying theme of the narrative we use to justify the use of coercion. We can construct a narrative of any society using any ideological theme. The narrative might be... strained... but it can be made logically coherent. (If Christianity can be made logically coherent, and it can, anything can be made logically coherent.) That we can narrate any society in terms of any ideology does not, however, mean that ideology is entirely useless. We can, most obviously, look for the strains in the narrative. If some ideological justification for an institution or social practice appears rococo, over-complicated, or just plain weird, narrating a society in terms of that ideology makes that strain explicit and a candidate for amendment. Alternatively, an ideological narrative will highlight areas where the ideology itself seems undesirable or absurd; it is, for example, absurd to construct Libertarianism to the extreme of permitting a person to sell himself into chattel slavery*. Ideology is not useful for distinguishing between societies, but ideology is very useful for directing the future evolution of a society.
*I want to be clear: I think that most self-identified Libertarians would not take Libertarianism to the extreme of permitting slavery (at least not publicly). The objection that the "purest" form of Libertarianism would permit slavery is a weak political objection; it is an objection only to claims of the absolute, objective truth of Libertarianism.
Assuming all societies construct a democratic narrative (and almost every human society in the 21st century does so), we can use democratic ideology to differentiate between societies in practice by determining to what degree the will of the majority directly influences public policy, i.e. the legitimate exercise of coercion. We can construct a completely democratic narrative for an emperor or monarch, but it is of course a very indirect form of democracy: the will of the people does not have any direct effect on public policy, and the acceptance of a particular monarch is infrequent and passive. A republic (such as the United States) is more directly democratic than a monarchy: the government is chosen more frequently and more actively than in a monarchy, and chosen more directly on the promised policies of the candidates. But a republic still interposes the will of the electors between the people and actual public policy. An Athenian* or town hall democracy is about as direct as possible.
*Ignoring, of course, women, slaves, and immigrants.
More democracy is not necessarily better. We intuitively feel, as in the example of free speech above, that simply putting every individual decision to a simple majority vote would not result in a society that we want to live in. An intellectual must I think, not advocate the purest form of any political ideology, but carefully and intelligently examine the ideological narrative of various societies to identify strains and absurdities; her task is to make not a "purer" society, but a better society. Indeed, I myself identify as a communist precisely and only because I (presently) believe that communism is not the purest but the best way to institutionalize a democracy.