Mutual majority criterion
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.
Contents
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