Summary: Two pages, with the simplest example I know of, to show what goes wrong when three candidates face each other under plurality or Instant Runoff; why a Condorcet rule is necessary. No mathematics is needed at all, only 500 words. If you are new to Instant Runoff or Condorcet methods, start with this.

Summary: The first of four linked papers A – D which analyze how best to take ranked-choice ballots and choose a single winner. The analysis includes the different incentives each method offers to candidates, causes, and voters, seeking to win, particularly to the tactics of bracketing and strategic nomination; presents examples and proofs of how the different methods perform when voters opinions are described as ranging along more than one political axis; and how the different systems rate against all the various abstract criteria used to assess the worth of election systems. In sum, any tournament method is decisively better than Instant Runoff (also known as the Alternative vote, or the Hare method); and the best of the tournament methods is Ranked Pairs; it is argued that any tournament method better than Ranked Pairs is unlikely to exist, which given its ease of implemen- tation, makes it the best choice if ranked-choice ballots are to be used. Ranked Pairs works whether voters preferences on their ballots are strict, or whether voters are permitted to rank candidates in equal groups. If Ranked Pairs is considered too different from Instant Runoff to adopt, two other runoff methods, the Direct Hybrid and the Benham method, may be used instead.

Summary The first of four linked papers A – D which analyze how best to take ranked-choice ballots and choose a single winner. The analysis includes the different incentives each method offers to candidates, causes, and voters, seeking to win, particularly to the tactics of bracketing and strategic nomination; presents examples and proofs of how the different methods perform when voters opinions are described as ranging along more than one political axis; and how the different systems rate against all the various abstract criteria used to assess the worth of election systems. In sum, any tournament method is decisively better than Instant Runoff (also known as the Alternative vote, or the Hare method); and the best of the tournament methods is Ranked Pairs; it is argued that any tournament method better than Ranked Pairs is unlikely to exist, which given its ease of implemen- tation, makes it the best choice if ranked-choice ballots are to be used. Ranked Pairs works whether voters preferences on their ballots are strict, or whether voters are permitted to rank candidates in equal groups. If Ranked Pairs is considered too different from Instant Runoff to adopt, two other runoff methods, the Direct Hybrid and the Benham method, may be used instead.

Summary: The first of four linked papers A – D which analyze how best to take ranked-choice ballots and choose a single winner. The analysis includes the different incentives each method offers to candidates, causes, and voters, seeking to win, particularly to the tactics of bracketing and strategic nomination; presents examples and proofs of how the different methods perform when voters opinions are described as ranging along more than one political axis; and how the different systems rate against all the various abstract criteria used to assess the worth of election systems. In sum, any tournament method is decisively better than Instant Runoff (also known as the Alternative vote, or the Hare method); and the best of the tournament methods is Ranked Pairs; it is argued that any tournament method better than Ranked Pairs is unlikely to exist, which given its ease of implemen- tation, makes it the best choice if ranked-choice ballots are to be used. Ranked Pairs works whether voters preferences on their ballots are strict, or whether voters are permitted to rank candidates in equal groups. If Ranked Pairs is considered too different from Instant Runoff to adopt, two other runoff methods, the Direct Hybrid and the Benham method, may be used instead.

Summary: The first of four linked papers A – D which analyze how best to take ranked-choice ballots and choose a single winner. The analysis includes the different incentives each method offers to candidates, causes, and voters, seeking to win, particularly to the tactics of bracketing and strategic nomination; presents examples and proofs of how the different methods perform when voters opinions are described as ranging along more than one political axis; and how the different systems rate against all the various abstract criteria used to assess the worth of election systems. In sum, any tournament method is decisively better than Instant Runoff (also known as the Alternative vote, or the Hare method); and the best of the tournament methods is Ranked Pairs; it is argued that any tournament method better than Ranked Pairs is unlikely to exist, which given its ease of implemen- tation, makes it the best choice if ranked-choice ballots are to be used. Ranked Pairs works whether voters preferences on their ballots are strict, or whether voters are permitted to rank candidates in equal groups. If Ranked Pairs is considered too different from Instant Runoff to adopt, two other runoff methods, the Direct Hybrid and the Benham method, may be used instead.

Summary:

Summary: Condorcet-compatible election methods are examined and compared. The Ranked Pairs method proves significantly better than Beatpath; that both are clone-free, and have other desirable properties, makes them much better than any alternative.

Summary: The concept of spoilers, as defined by Fairvote, is analyzed and demonstrated to be useless for deciding whether Instant Runoff or either of the clone-free, Condorcet methods of Beatpath or Ranked Pairs is a better method to decide elections that use ranked-choice ballots. The problem of finding all patterns of ballots that generate spoilers that are not merely clones is solved for the general case of 4 candidates, and for 4 candidates restricted to a spatial model in two dimensions.

Summary: Opportunities for tactical voting using ranked-choice ballots are examined for three-candidate elections under Instant Runoff, and under the Condorcet runoff method known as Benham. The Benham method is shown to have strictly fewer opportunities for unilateral tactical voting, as follows. If an election offers an opportunity under Benham, then it also offers an opportunity under Instant Runoff; but the converse is not true: there are elections that offer an opportunity under Instant Runoff that do not under Benham.

Summary: A verbatim copy of the material posted by Fairvote on why Instant Runoff (which they call Ranked Choice Voting, or RCV) is inferior to a Condorcet method, interlineated however with my analysis of all the errors, which when corrected reverse the Fairvote conclusion.