I thought the crux of the question involved the fact that, when there are many possible options within a category, a situation may arise where no single option has more than 50%. ie a population separated along racial lines might have...

40% blue
25% pink
20% purple
15% green

The blue people might have the largest number, but they would not be called the majority, would they? I would say they're the largest minority, but I was hoping someone would have a sexy term to encompass that concept.