New RCTab Option Named “Eliminate Pairwise Losing Candidates”

This document describes a new counting option for the open-source RCTab software, which is maintained by the Ranked Choice Voting Resource Center (RCVRC).

This new option eliminates pairwise losing candidates when they occur.  A pairwise losing candidate is a candidate who would lose every one-on-one contest against every other continuing (not-yet-eliminated) candidate.

The code is here: https://github.com/cpsolver/RCTabPlus/tree/feature_issue_984_eliminate_pairwise_losing_candidates

A few quick clarifications

• When there are just two remaining candidates, the standard RCTab counting method is used.  (Both methods yield the same result.)
• When a counting round doesn't have a pairwise losing candidate, the standard RCTab counting method is used.
• As a reminder, the default RCTab counting method assumes the candidate with the shortest line of supporting voters is always least popular.
• Pairwise counting is delayed until there are fewer not-yet-eliminated candidates.  This delay simplifies the process of manually counting paper ballots during an audit.

Why should pairwise losing candidates be eliminated?

• The winner is virtually always supported by more than half the voters.  This fairness is not affected by the number of candidates, nor their similarities, nor their differences.  The standard RCTab counting method does not always achieve this higher level of fairness.
• The fairness of this refinement is easy for voters to understand using a sports metaphor.  (See below)
• The increased fairness will speed up adoption of ranked choice voting, especially by reducing valid criticisms from fans of competing vote-counting methods.
• Although the vote-counting process becomes slightly more complicated if a manual recount is needed, the change will simplify voting from the voter's perspective.
• This counting refinement enables a voter to rank candidates in the voter's honest order of preference, without concern about how other voters will rank the candidates.  (To achieve this advantage, the new overvote rule named “count when single continuing” also must be chosen.)
• This counting refinement will allow a second Republican and second Democrat to also appear on the general-election ballot.  In the meantime, the current limit of one nominee from each party is easy to exploit using money-based tactics during primary elections.

Detailed advantages

• A simple sports metaphor makes it easy for voters to understand the fairness of eliminating pairwise losing candidates.  When there is a soccer team that loses against every other soccer team still in the playoffs, that pairwise losing soccer team does not deserve to win the playoffs, and clearly deserves to be eliminated.  Similarly, when there is an election in which there is a candidate who loses every one-on-one contest against every other candidate, that pairwise losing candidate clearly does not deserve to get elected.
• This counting refinement prevents a voter's ballot from getting “stuck” supporting a candidate who cannot win, while the voter's next-favorite candidate is eliminated.
• The fans of Condorcet voting methods correctly criticize the RCTab counting rules as too easily failing to elect the Condorcet winner in elections that have a Condorcet winner.  (A Condorcet winner is the candidate who wins every one-on-one contest against every other candidate.)  Eliminating pairwise losing candidates when they occur almost always elects the Condorcet winner.  (When the Condorcet winner does not win, there are valid reasons that candidate does not deserve to win.)
• In the controversial 2022 Alaska congressional special election, when counting reached the top three candidates, Sarah Palin (a Republican) was a pairwise losing candidate.  If she had been eliminated as the pairwise losing candidate, the final count between Mary Peltola (the Democrat) and Nick Begich (a second Republican) would have correctly identified Begich to be more popular than Peltola.  Instead, Begich was eliminated early because he had the fewest transferred votes at that top-three round.  In hindsight, some voters who ranked Palin as their first choice realized they should have voted tactically by ranking Begich first.  This vote-counting refinement would have correctly identified the most popular candidate as Begich, without the need for tactical voting.
• The Alaska election demonstrated that voters should be able to rank their favorite candidate as their first choice, without concern about how other voters will be marking their ballots.
• In the controversial 2009 Burlingtion (Vermont) mayoral election, Kurt Wright (the Republican) was a pairwise losing candidate during the top-three counting round.  If Wright had been eliminated as the pairwise losing candidate (in this counting round), the winner would have been Andy Montroll (the Democrat) instead of Bob Kiss (the Progressive).  The ballot data revealled that Montroll would have won against both Bob Kiss and Kurt Wright if one-on-one contests had been done.
• The fans of STAR voting correctly criticize RCTab counting rules as creating a "center squeeze effect" that gives an advantage to extremist candidates, even when there is a clearly more-popular centrist candidate.  Eliminating pairwise losing candidates eliminates the center squeeze effect.
• Mathematical measurements confirm that tactical voting becomes more difficult, and less effective, when pairwise losing candidates are eliminated when they occur.
• This counting refinement defeats advanced vote-marking tactics that otherwise allow savvy voters to gain increased influence over who wins.
• Portland (Oregon) might have chosen this better counting rule when we adopted ranked choice voting for our mayoral and city-council elections.  If the winning candidate, Keith Wilson, had not achieved widespread name recognition, the likely winner of our first mayoral election (without this pairwise counting option) could have been one of the two strongly disliked former city-council members, or possibly Liv Osthus who had achieved name recognition as a stripper.  Specifically, a majority of Portland voters would have been likely to rank Wilson above one of the two strongly disliked former city-council members, yet the other three name-recognized candidates might have received more first-choice ranks if Wilson had not worked so hard to get ranked as first choice on a sufficient number of ballots.

The big picture is that voting is a form of communication between competing groups of voters who otherwise would resolve our conflicts through physical fighting.  Improving this currently primitive communication process will yield higher levels of democracy.  In turn, higher levels of democracy will yield less fighting, and more cooperation.  That higher level of civilization will make it much easier to reduce unnecessary economic suffering, dramatically improve healthcare and education, and better protect our fragile planet.

Detailed clarifications

• The words “pairwise losing candidate” are used instead of “Condorcet losing candidate” because an election can have only one Condorcet losing candidate, yet the election can have multiple pairwise losing candidates.
• The delay in looking for pairwise losing candidates is specified as the number of candidates who remain in the contest, which can range from 7 to 3.  The number 2 is not valid because that would specify only the final counting round (between the final two remaining candidates).
• The delay in looking for pairwise losing candidates reduces how much election data needs to be published.  Consider that pairwise counts must be supplied for every combination of every candidate pair involved in pairwise counting.  (Seven candidates yield 42 pairwise counts.)

Graphic summary

Here's a graphic that summarizes this refinement.



Software already written

Election software that implements this refinement is already available at https://github.com/cpsolver/RCTabPlus/tree/feature_issue_984_eliminate_pairwise_losing_candidates.  This software can be used as-is in a real election, or it can be used as a reference by an election system vendor that has been contracted to add this vote-counting refinement to their ranked choice voting software.