Condorcet Voting

Condorcet is a family of voting methods where the candidate who is preferred over all others always wins. If a candidate who is preferred over all others doesn't exist, ballots are looked at more closely to find the most preferred candidate.

Condorcet can be tallied with either ranked ballots or score ballots as long as the method allows voters to show their preference order. If ranked ballots are used, Condorcet is almost universally regarded as the most fair, representative, and accurate version of Ranked Choice Voting for single winner elections. 

 

Voting:

Voters rank candidates in order of preference. Equal rankings and skipped rankings* are allowed. Candidates left blank are ranked last. 

 

Note: Condorcet voting only takes into account preference order, so a ranking of 1st, 2nd, 3rd is counted the same as 1st, 3rd, 6th. 

 

Tabulation:

Step 1. For each pair of candidates, add up the number of voters who preferred each. 

The full preference data for the election can be recorded in a preference matrix:

In the example above Allison is the Condorcet winner because she is preferred over all others. Doug is a Condorcet loser because he isn't preferred over anyone. 

 

2. Elect the Condorcet winner if possible. 

3. Eliminate all Condorcet losers.

If the steps above didn't narrow it down to only one winner you have a Condorcet cycle, or rock-paper-scissors type tie. 

  • Eliminate any candidate who lost all of their head-to-head matchups. Repeat until all Condorcet losers have been removed. 

4. Calculate each remaining candidate's largest loss. The candidate with the smallest largest loss wins:

The example above shows a Condorcet cycle between Allison, Bill, and Carmen. Allison is preferred to Bill, Bill to Carmen, and Carmen to Allison. Doug is the Condorcet loser so he can be eliminated, but each of the others wins two match-ups and loses one. 

In this case the tie can be broken by calculating each candidates largest loss: 

  • In each match-up a candidate lost, calculate the margin they lost by. Allison lost to Carmen by 2 votes, Bill lost to Allison by 4 votes, and Carmen lost to Bill by 2 votes. This tiebreaker eliminates Bill, but Allison and Carmen are still tied. 
  • If there was still a tie after the step above, you can then calculate the total number of winning votes for each candidate. Allison's winning vote total is 15 and Carmen's is 14. Allison wins. 

Note: It's very important to do the steps above in the same order every time as changing the order can change the winner in close races. 

 

Condorcet Advantages:

  • Highly accurate at electing representative winners. 
  • Highly resistant to strategic voting.
  • The ranked ballot with equal rankings allowed means that it's easy for voters to express a nuanced opinion.
  • No wasted votes. All rankings are counted. It would be very difficult to accidentally void or spoil your ballot. 
  • Fair and equal. The system doesn't play favorites and ensures an equally weighted vote. 
  • Condorcet voting was invented hundreds or even thousands of years ago and it has been studied extensively. Peer review and other study consistently backs up claims made by Condorcet advocates. 

Condorcet Disadvantages:

  • While the general concept of electing the candidate who was preferred over all others or who is most preferred is quite simple, ranked Condorcet methods are the most complex single-winner methods to explain in detail or tabulate. In the modern age this is much less of a barrier than it used to be, and tabulation can be coded and automated, but some expertise is needed to fully understand the details of the method or to verify that it's been coded correctly. 
  • A ranked ballot doesn't allow voters to express their level of support and thus a 2nd choice ranking could be almost as good as your favorite or almost as bad as your worst case scenario.

Note: Both of the issues above are eliminated if a score ballot Condorcet method like Smith Score is used. 

Other Condorcet Methods:

There are a number of Condorcet voting methods with different variations on the tie breaking protocol including ranked options such as Minimax, Ranked Pairs, Schulz, and variations of each. Among experts and advocates in the field including Dr. Nicolaus Tideman, Department of Mathematics, Virginia Tech, and Professor Emeritus Richard DarlingtonDepartment of Psychology, Cornell University, there seems to be a growing consensus around the Smith Minimax option, which is the method described above. For a rated or 5 star ballots Smith Score is another great option. Keep in mind that regardless of the Condorcet variation you prefer, the winners for most of these will be the same the majority of the time. 

 

Condorcet as a metric for measuring voting method accuracy:

The Condorcet method is often used to measure the accuracy of other voting methods because it takes into account all the voter preferences from all ballots. For ranked methods preference data is all you have to work with, so the Condorcet winner is always the correct winner. For methods that use score ballots, preference order and also level of support is shown, so Condorcet is still one good metric, but strength of support can also be taken into account. Regardless of the metrics used to measure accuracy Condorcet methods tend to come out in the top tier. 

 

Condorcet as a tiebreaker:

Condorcet and in particular the Minimax method described above was designed to be a highly effective and fair tiebreaker. If there is any possible way to use the ballots themselves to find a candidate who deserves to win Minimax is a great tie breaking protocol to adopt if the voting method allowed voters to show their preference order. 

 

The case for Condorcet Voting:

Condorcet Voting was first invented in the 13th century and is the original Ranked Choice Voting method, but in modern times the voting reform movement has been largely focused on the Instant Runoff Voting (IRV) version. In 1870 when IRV was invented, computers were not an option and tabulating Condorcet elections was time consuming. In contrast IRV was easy to hand count and was logistically much more viable, despite the fact that Condorcet voting is significantly more accurate and more resistant to strategic voting. While both methods start with the same ballots, Condorcet voting counts all ballot data and does not ignore or discard any rankings or any ballots. IRV on the other hand only counts some of the rankings given and up to a 1/3 of ballots may not be counted at all in the deciding round, which can skew election results. 

While this compromise may have been necessary in 1870, we do not believe it's worth it anymore. For voters who are sold on the idea of ranked ballots we are recommend the above method as a now viable option which offers much more fair and representative outcomes than the Instant Runoff method. 

 

Try Condorcet:

To try Condorcet voting for yourself you can host elections online using the Condorcet Internet Voting Service.