The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win".
The criterion was originally defined in relation to methods which rely only on ranked ballots (voted preference orders of the candidates), so while ranked methods such as the Borda count fail the criterion under any definition, its application to methods which give weight to preference strength is disputed. For these methods, such as STAR voting, Score (Range) voting, Approval voting and Majority Judgment, the system may pass or fail depending on the definition of the criterion which is used.
Advocates of other voting systems contend that the majority criterion is actually a flaw of a voting system, and not a feature, since it can lead to a tyranny of the majority where a polarizing candidate is elected who is loved by a little over half of the population and hated by everyone else. Other systems may be better at electing consensus candidates who have broader appeal, which is claimed to make them better representatives of the population as a whole. These are described as "utilitarian" or "consensus-seeking" rather than "majoritarian". Peter Emerson advocates for Borda count variants, arguing that majoritarianism is fundamentally flawed, and leads to bitterness, division, and violence, citing Northern Ireland and Bosnia as examples. Note however that in a utilitarian system, when no consensus candidate exists, a minority's preference can beat a majority's preference by offering only slightly higher utility; thus, utilitarian methods need not always increase consensus.
Note that the mutual majority criterion is a generalized form of the majority criterion meant to account for when the majority prefers multiple candidates above all others; voting methods which pass majority but fail mutual majority can encourage all but one of the majority's preferred candidates to drop out in order to ensure one of the majority-preferred candidates wins, creating a spoiler effect. The common choose-one first-past-the-post voting method is notable for this, as major parties vying to be preferred by a majority often attempt to prevent more than one of their candidates from running and splitting the vote by using primaries.