Majority criterion

The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win".

Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, and plurality voting.

The majority criterion was originally defined in relation to methods which rely only on voted preference orders of the candidates. Thus, its application to methods which give weight to preference strength is in some cases disputed. Some such methods, such as the Borda count and range voting, fail the criterion under any definition. For others, such as 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 are better at electing consensus candidates who have broader appeal, making them better representatives of the population as a whole. These are described as "utilitarian" rather than "majoritarian".

By the majority criterion, a candidate X should win if a majority of voters answers affirmatively to the question 'Do you prefer X to every other candidate?'.

The Condorcet criterion is stronger. According to it, a candidate X should win if for every other candidate Y there is a plurality of voters that answers affirmatively to the question 'Do you prefer X to Y?'.

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