Majority criterion facts for kids

The majority criterion is a rule used to check how fair different voting systems are. It says that if more than half of the voters (a "majority") clearly prefer one candidate over all others, then that candidate should be the winner.

Some voting methods that follow this rule include Condorcet methods, instant-runoff voting, Bucklin voting, and plurality voting.

Some people who support other voting systems believe the majority criterion isn't always the best idea. They worry it can lead to a "tyranny of the majority." This happens when a candidate wins with just over half the votes, but many people strongly dislike them.

Other voting systems try to pick "consensus candidates." These are candidates who might not be loved by a majority, but are generally liked by a wider group of people. Supporters of these systems believe they do a better job of representing everyone. They aim for candidates who have broader support, rather than just strong support from a small majority.

The mutual majority criterion is a broader version of the majority criterion. It says that if a majority of voters prefer a group of candidates over all other candidates, then one of those preferred candidates should win. Voting methods that meet the majority criterion but not the mutual majority criterion can sometimes cause a "spoiler effect." This means that if too many similar candidates run, they might split the votes of the majority, allowing a less popular candidate to win. For example, in First-past-the-post elections, major political parties often hold primary elections. This helps them choose just one strong candidate to avoid splitting their votes.

Majority vs. Condorcet Criterion

The majority criterion asks: "Does a candidate win if a majority of voters like them more than every other candidate?"

The Condorcet criterion is a stronger rule. It says that a candidate should win if they would beat every other candidate in a head-to-head contest. This means if you compare candidate X to candidate Y, more voters prefer X. And if you compare X to candidate Z, more voters prefer X, and so on.

If a voting system meets the Condorcet criterion, it will also meet the majority criterion. However, the opposite is not always true. The Condorcet criterion looks at many different majorities (X vs. Y, X vs. Z). The majority criterion only applies when there's one clear candidate that a single majority prefers over everyone else.

When we say the Condorcet criterion is "stronger," we are talking about the rules a voting system follows. We are not talking about what a candidate needs to do to win an election.

Related pages

• Mutual majority criterion
• Voting system
• Voting system criterion
• Condorcet criterion

Images for kids

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  Systems that meet the majority criterion (like plurality, Condorcet, and IRV) elect the Red candidate when they receive a majority of the vote. Borda count does not meet the majority criterion and does not select Red.