Is Democracy when the Minority is subjected to the Tyranny of the Majority?

There are laws in place to protect a minority from the majority in most democracies- in the US it's called the Constitution. You know, "inalienable rights," etc. There are however, certain things that the majority has decided that one has to accept, or move somewhere else. It may not seem fair, but then life in general isn't always fair. Humans must treat each other with a sense of fairness, it's called civilization. Of course, then human beings don't always act civilized, do they?