A common view about the relation between democratic governance and majorities is majoritarianism, which is that democratic governance occurs when decisions are made by the majority. It's so common that people slip into it without even thinking about it. And people in majorities tend to assume that this is the way things should work, no matter how many times they've been burned by it when they were in the minority. But there are many problems with it, not least in that, if the point of democratic governance is to represent and give power to the people, bare majority dominance does not do this well at all. This has been known for ages, but majoritarianism is the only view of democratic governance that one can always count on being accepted by people.
A more plausible account of how democratic governance and majorities should relate has no name, as far as I know, so I will just call it democratic generalism. The essential idea is that democratic governance should represent and give power to the people not partwise but generally or overall. More specifically, the idea is that in democratic governance, the goals of the majority should have greater weight, but minority goals should receive as much accommodation as is consistent with this. This guarantees, to the extent that it can be guaranteed, a bit of something for everyone, but the primary problems with it are (1) practical problems of guaranteeing it, given that majorities tend to take advantage of being the majority to ignore minority preferences, and (2) people are remarkably averse to it, and inclined to talk as if the only democratic thing were always winner-takes-all, despite that being the least democratic thing that can still reasonably be called 'democratic'. Institutions and practices whose very purpose for existence explicitly includes accommodation of minority goals are often vehemently attacked as being anti-democratic--- in the U.S., the obvious current examples are the Senate, the Electoral College, the filibuster, and any number of conscientious objection accommodations. I'm not sure what to make of this, beyond the rather commonplace point that people often participate in politics to get whatever they can get, and accommodating other people's differing goals is often not an obvious way to do that in the short run -- that is to say, democratic generalism, while having more claim to represent and give power to the Demos as a Demos, is just often not going to be popular with the Demos, which consists of people who prefer, if they can get it, that their own policies be enacted without negotiation, modification, or compromise.
