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In general, a majority is a subset of a group that is more than half of the entire group. A plurality, the subset with the largest number of parts, is not necessarily a majority, as the largest number may be less than half.
For example, in a hypothetical group of 40 athletes there are:
A majority in this group would consist of one more than half the total number of athletes, or 21 athletes. Football players, 15 in number, comprise a plurality, but not a majority. The group of all ball sport players together (15 football players + 6 table tennis players = 21) comprise a majority, however.
In politics, there are several different kinds of majority:
Other kinds of majority are