A Condorcet winner is defined as a candidate who wins every pairwise comparison against all other candidates in the election.

A candidate who is preferred by a majority over every other individual candidate satisfies the Condorcet winner criterion.

Condorcet methods are highly resistant to spoiler effects because altering preferences for non-Condorcet candidates does not change the outcome if a Condorcet winner exists.

The Condorcet criterion implies the majority criterion, meaning that any voting system satisfying the Condorcet criterion will also satisfy the majority criterion.

A Condorcet winner is also known as a 'tournament winner' or a 'beats-all winner'.

The Condorcet criterion is a stronger condition than the majority criterion.

The definition of a Condorcet winner requires them to receive more than 50% of the total votes cast in the election.

What is the fundamental characteristic of a Condorcet winner?

Which of the following is NOT an alternative name for a Condorcet winner?

The Condorcet criterion implies the majority criterion. This means:

Condorcet's voting paradox describes a situation where voter preferences form a cycle, preventing any single candidate from defeating all others in pairwise matchups.

Cyclical preferences, which lead to Condorcet paradoxes, are estimated to occur infrequently in real-world elections.

The participation criterion requires that a candidate's election outcome should not be negatively affected by the withdrawal of voters who do not support them.

The Smith set is defined as the smallest set of candidates where every candidate within the set is preferred, either directly or indirectly, over every candidate outside the set.

The mutual majority criterion ensures that if a set of candidates are mutually preferred over all candidates outside that set, then one of the candidates from that set must win the election.

The 'independence of clones' criterion ensures that a candidate's election outcome is not affected by the addition or removal of other candidates who have identical preferences to existing candidates.

The Smith set is guaranteed to exist even if a Condorcet winner does not.

Studies suggest that participation failures are empirically rare for modern Condorcet methods like ranked pairs.

Condorcet's voting paradox describes a situation where:

What is the 'Smith set' in the context of voting criteria?

What does the participation criterion for voting systems ensure?

Which criterion ensures that if a set of candidates are mutually preferred over outsiders, one of them must win?

According to the source, what is the relationship between the Smith set and a Condorcet winner?

Voting systems like Ranked Pairs and Schulze's method are designed to ensure the election of a Condorcet winner if one exists.

Most Condorcet methods satisfy the Smith criterion, ensuring a winner from the Smith set when no single Condorcet winner exists.

Copeland's method, Dodgson's method, and Kemeny method are examples of Condorcet methods.

The Smith criterion guarantees that the winner must come from the 'top cycle' or Smith set if no single majority-rule winner exists.

Which of the following voting systems is known to guarantee the election of a Condorcet winner when one exists?

Instant-runoff voting (IRV) is not guaranteed to elect a Condorcet winner, even when one exists.

Plurality voting often fails the Condorcet criterion due to its susceptibility to vote-splitting, which can result in a winner who loses pairwise contests.

Instant-Runoff Voting (IRV) eliminates the candidate with the fewest first-place votes and redistributes their votes.

The Borda count system assigns points to candidates based on their position in a voter's ranked preference list.

The Borda count system can elect a candidate who is not preferred by a majority in pairwise contests.

The highest medians system, also known as Bucklin voting, determines the winner based on the candidate with the highest median score.

Approval Voting does not require voters to rank candidates; instead, voters can approve of as many candidates as they wish.

Score Voting can fail the Condorcet criterion if a candidate's supporters are more enthusiastic (assign higher scores) than the supporters of the Condorcet winner.

Approval Voting can fail the Condorcet criterion because voters might approve of multiple candidates, potentially leading to a situation where a candidate with broad approval but not necessarily majority preference in pairwise contests wins.

Score Voting, also known as rating voting, requires voters to assign a score to each candidate from a predefined scale.

The highest medians system can fail the Condorcet criterion because it prioritizes overall ranking points over direct head-to-head majority support.

The source lists Coombs' rule and Bucklin voting as systems that satisfy the Condorcet criterion.

Plurality voting does not satisfy the mutual majority criterion.

Adding a runoff to score voting does not always guarantee compliance with the Condorcet criterion.

Why does plurality voting often fail to elect the Condorcet winner?

How does Instant-Runoff Voting (IRV) differ from Condorcet methods regarding winner guarantees?

Which voting system assigns points based on a candidate's position in a voter's ranked preference list?

The Borda count system fails the Condorcet criterion because:

The highest medians (or Bucklin) system determines the winner based on:

How does Approval Voting work?

Score Voting fails the Condorcet criterion primarily because:

Which of these voting systems is listed as NOT satisfying the Condorcet criterion?

What is the primary reason cited for plurality voting failing the Condorcet criterion?

The median voter theorem guarantees a winner under the specific condition of a single-dimensional political spectrum.

Ramon Llull, a 13th-century philosopher, is credited with the first detailed study of Condorcet methods.

Nicolas de Caritat, Marquis de Condorcet, rediscovered and advanced the study of these methods during the Age of Enlightenment.

The median voter theorem's conditions for a guaranteed winner are often not met in real-life political electorates due to their multidimensional nature.

Under what specific condition is a majority-rule winner guaranteed to exist, according to the median voter theorem?

The median voter theorem is based on the assumption of:

In the hypothetical government funds example, 'Spend more' was identified as the 'beats-all' winner.

In the hypothetical plurality failure example, Candidate B was the Condorcet winner but lost the election.

The 2000 United States presidential election in Florida is cited as a potential real-life example where IRV failed the Condorcet criteria.

In the hypothetical Borda count failure example, Candidate B won the Borda count but was not the Condorcet winner.

The hypothetical IRV failure example showed that the Condorcet winner could be eliminated early due to having fewer first-place votes.

The 2009 mayoral election in Burlington, Vermont, is cited as a real-life example where instant-runoff voting (IRV) failed to comply with the Condorcet criteria.

In the hypothetical Score Voting failure example, C won with a better median rating, while B was the Condorcet winner.

The hypothetical government funds example showed that 'Cut taxes' was preferred over 'Spend more' in pairwise comparisons.

The hypothetical scenario involving government funds and voting options used 'Pay debt' as the Condorcet winner.

In the hypothetical election scenario illustrating plurality failure (30% A>B>C, 30% C>A>B, 40% B>A>C), who was the Condorcet winner?

In the hypothetical Borda count failure example (3 voters A>B>C, 2 voters B>C>A), who was the Condorcet winner?

Which of the following is cited as a potential real-life example of plurality voting failure due to a spoiler candidate?

The 2009 mayoral election in Burlington, Vermont, is mentioned as an example where:

Why might Score Voting fail to elect the Condorcet winner, as illustrated in the example?