Mutual majority criterion facts for kids

The mutual majority criterion is an idea used to check how fair different voting systems are. It helps make sure that if most voters clearly prefer a certain group of candidates over everyone else, then one of those candidates from that group should win the election. Think of it as a rule that helps elections truly reflect what the majority wants, especially when voters have similar favorites.

What is the Mutual Majority Criterion?

This rule says that if a majority (more than half) of voters like a specific group of candidates more than all other candidates, then one person from that preferred group must win. It's like saying if 51% of people want a dog from a specific breed, then the winner must be a dog from that breed.

How is it Different from the Majority Criterion?

The regular Majority criterion is simpler. It only applies if there's just one candidate that a majority of voters prefer over everyone else. The mutual majority criterion is broader. It applies even if the majority likes a group of candidates, not just one specific person. For example, if most people prefer any of the "Team A" candidates over any "Team B" candidates, then a "Team A" candidate should win.

Why is This Criterion Important?

This rule helps make sure that elections are fair and truly represent the voters' wishes. If a voting system passes this criterion, it means it's good at picking a winner that a large group of voters supports. This can help prevent situations where a candidate wins even if most people would rather have someone else from a specific group.

Voting Systems That Pass This Rule

Many voting systems are designed to meet the mutual majority criterion. This means they are good at picking a winner from a group that the majority supports.

• The Schulze method
• Ranked pairs
• Instant-runoff voting (also called ranked-choice voting)
• Nanson's method
• Bucklin voting

Also, all Condorcet methods that are "Smith-efficient" pass this rule. Condorcet methods are types of voting systems where the winner is the candidate who would beat every other candidate in a head-to-head contest.

Voting Systems That Don't Pass This Rule

Some common voting systems do not pass the mutual majority criterion. This means they might sometimes pick a winner that is not from the group most voters prefer.

• Plurality vote (the most common system, where you vote for one person, and the one with the most votes wins)
• Approval voting (where you can vote for as many candidates as you approve of)
• Range voting (where you give each candidate a score)
• The Borda count (where you rank candidates, and points are given based on rank)
• Minimax

What is the "Spoiler Effect"?

When a voting system passes the simple majority criterion but fails the mutual majority criterion, it can lead to something called the "spoiler effect." This happens when a candidate who is not widely preferred by the majority can still win. If many similar candidates split the votes of the majority, a less popular candidate might sneak in and win. If some of those similar candidates then leave the election, the remaining majority-preferred candidate might suddenly win instead. This shows how important it is for a system to consider groups of preferred candidates.

See also

• In Spanish: Criterio de mayoría mutua para niños