A majority-minority district is one in which a racial or ethnic minority makes up a large-enough share of the electorate to assure that the community has a reasonable chance to elect the candidate of their choice.t began with the redistricting following the 1990 census. BEfore that, some majority-minority district existed, but out of geographical happenstance (not intentionally). The number of Majority-Minority districts increased with the 1991 redistricting.