Condorcet Voting

Americans need their elected officials to represent the people as a whole, rather than a small handful of individual voters. We need to elect by common consensus.

For single-seat elections, that’s a Condorcet method, which elect from the smallest set of candidates who would themselves win a majority vote against each single candidate not in that set, called the Smith set. When this is one candidate—a candidate who would defeat every other candidate one-on-one—it is called the Condorcet winner.

Voting Rules

Condorcet voting rules include Schulze, Tidemann’s Ranked Pairs, Benham Instant Run-off Vote, Tidemann’s Alternative Smith, and Tidemann’s Alternative Schwartz.

Ranked Pairs elects the candidate with the strongest overall support from the Smith Set.  Schulze elects from a subset of the Smith set, called the Schwartz set, and attempts to find the best candidate by avoiding those with particularly bad pairwise losses.  Either system can sum pairwise races to combine reporting precincts quickly.

Benham IRV and Tidemann’s Alternative Smith and Schwartz strongly resist strategic voting.  Benham IRV simply moves ballots from the candidate with the least votes to the next-ranked candidate on each ballot.  Tideman’s Alternative Smith elects the Condorcet candidate or, if there is none, eliminates all candidates outside the Smith set and then eliminates the one with the fewest votes.  Tidemann’s Alternative Schwartz does this with the Schwartz set.

Implementation

A State implementing a consensus voting method should follow the following criteria.

Ranked ballots should allow gaps, only counting sequence.

States must select an official ballot counting method—we recommend Tidemann’s Alternative Smith or Schwartz, due to their simplicity and resistance to strategic voting.  They should nevertheless publish the ballot rankings for public review and independent comparison against other voting rules.  The voters may decide if they prefer the alternate system.

Parties should nominate two or three candidates, rather than one, with the State specifying the exact maximum.  States should require Single Transferable Vote primaries for parties wishing to nominate multiple candidates.

Sheer Brute Force

States should consider voting rule constriction by sheer brute force rather than simply by trusting a voting rule to always elect the correct candidate.  Such constriction could follow:

  1. Condorcet:  If any Candidate tallies a pairwise majority victory against all other candidates, that Candidate is the winner.
  2. Smith:  If no Condorcet candidate exists, construct the smallest set of Candidates whom no Candidate outside the set has defeated and carry out the election as usual, considering only those candidates.

Smith constriction has no effect on rules compliant with Independence of Smith-Dominated Alternatives (ISDA):  the results of Ranked Pairs and Schulze do not change when throwing out the non-Smith candidates.

Tidemann’s Alternative Smith and Schwartz, as well as the Benham rules, incorporate these rules into the voting rule and so can and in fact must be implemented on their own. Tidemann’s Alternative Smith and Schwartz, in particular, either immediately elect the Condorcet candidate or eliminate all non-Smith or non-Schwartz candidates and continue from there.

These rules diminish the importance of technical questions, such as how to measure the strength of a pairwise victory.  The two primary methods are by number of winning votes and by percentage of votes earned; these have interesting impacts on some modes of strategic voting.

More-importantly, these rules force the election to the Condorcet candidate if and when a voting rule set fails.  Such failure occurred when Burlington, VT implemented Instant Run-off Voting, a non-Condorcet method, and elected neither the Plurality nor the Condorcet candidate.  Such constraint to the bona fide Condorcet candidate and to the Smith set allow us to see failure while not suffering from post-election controversy.