Condorcet loser criterion facts for kids

The Condorcet loser criterion is a rule used to check if a voting system is fair. Imagine an election where people vote for one winner. This rule helps us compare different ways of voting.

A voting system that follows the Condorcet loser criterion will never let a "Condorcet loser" win the election. So, what's a Condorcet loser? It's a candidate who would lose if they went head-to-head (one-on-one) against every other candidate in the election.

Sometimes, an election might not have a Condorcet loser. This happens when every candidate would lose to at least one other candidate in a head-to-head match.

What is a Condorcet Loser?

A Condorcet loser is a candidate who is less popular than everyone else. If you compared them to every other candidate one at a time, they would always lose.

For example, imagine an election with three candidates: Alice, Bob, and Carol.

• If Alice ran against Bob, Alice would lose.
• If Alice ran against Carol, Alice would lose.

In this case, Alice is the Condorcet loser because she loses to everyone else in a one-on-one contest.

The Condorcet loser criterion says that a good voting system should prevent this "least popular" candidate from winning.

Why is this Criterion Important?

This rule is important because it helps make sure that the person who wins an election is someone who is generally liked, or at least not disliked by most people. If a Condorcet loser won, it would mean the person who is least preferred by the voters ended up in charge.

Voting Systems That Pass This Rule

Many voting systems follow the Condorcet loser criterion. This means they are designed so that a Condorcet loser can never win. Some of these systems include:

• Two-round system: This is where voters choose candidates, and if no one gets a majority, the top two candidates go to a second round.
• Instant-runoff voting (also called AV): Voters rank candidates in order of preference. If no one has a majority, the candidate with the fewest votes is eliminated, and their votes are given to the voters' next choice. This continues until someone has a majority.
• Borda count: Voters rank candidates, and points are given based on their rank. The candidate with the most points wins.
• Schulze method and Ranked pairs: These are more complex systems that use head-to-head comparisons to find the best candidate.

Any voting method that uses a "runoff" round (where the top candidates face off again) usually passes this criterion. This is because the Condorcet loser would likely lose in any head-to-head competition, including a runoff.

Voting Systems That Don't Pass This Rule

Some voting systems do not pass the Condorcet loser criterion. This means it's possible for a Condorcet loser to win under these systems. Examples include:

• First-past-the-post voting (also called plurality voting): In this system, the candidate with the most votes wins, even if they don't have a majority. This is common in many elections.
• Approval voting: Voters can vote for as many candidates as they "approve" of. The candidate with the most approvals wins.
• Range voting: Voters give each candidate a score (like 1 to 10). The candidate with the highest total score wins.

These systems might allow a candidate who would lose to everyone else in a one-on-one contest to still win the election.

Related pages

• Condorcet method
• Condorcet criterion