In fact, that is exactly what democracy feels like! People have different preferences (as they always do) and so they take a vote, majority wins. It happens on every level, from national declarations of war to a bunch of people deciding on which movie to watch. And it has a very long track record of people dealing with it with no problem.
Every election in history on every level has had a loser. I know that personally: I didn't get to see the movie I wanted on Friday.
What is undemocratic is treating losing like a catastrophe or failure of the system - that is the system. That is democracy.