The right way to read Ranked-choice ballots: not Instant Runoff, but Ranked Pairs-D
Summary: The four linked papers A through D 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 implementation, 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.
Description: Following an introduction, paper D, in nine sections each of which can be read independently, proofs of points raised in papers A through C. Covered in section II is the phenomenon of bracketing, in 3, 4, and higher dimensions; in III that Condorcet methods and Instant Runoff extend to deal with ballots that can rank sets of candidate equally; in IV that for 3 or 4 candidates, the probabilities of different outcomes under Instant Runoff or Condorcet methods can be computed exactly; in V that the likelihood of outcomes under a Condorcet method when there is one axis of political opinion but many candidates is likewise solvable; in VI that under Instant Runoff, the defeat of a representative candidate by being bracketed by two other candidates can only rarely be averted by the presence of a fourth or fifth candidate on the ballot; in VII that under the Borda count a representative candidate can be defeated even if all his rivals are politically to his left or his right; in VIII, that if voters are chosen at random from a distribution of voters to run for office, that as the number of candidates increases, that the winning candidate becomes ever more representative under Borda or a Condorcet method; becomes less under plurality; and plateaus (ceasing to improve) under Instant Runoff; and in IX, that a simple comparison can be defined that sorts all possible rankings of candidates into a list, that has the Ranked Pairs ranking at its head. Section XI contains the history of the revision of papers A through D.
