Condorcet Voting

Condorcet voting is another type of voting that uses ranked ballots, but depending on who you talk to it may or may not be a type of ranked-choice voting. Condorcet voting is used to elect a single candidate.

Condorcet voting is quite different from instant runoff voting. Condorcet voting elects a candidate who beats all other candidates in pairwise elections. To figure out the Condorcet winner, we need to consider all pairwise elections. Consider two candidates A and B, if A is ranked higher than B on a majority of ballots, then A beats B, otherwise B beats A. A candidate who beats all other candidates in this way is the winner.

This is easiest to visualize this is using a table, and here is an example of Condorcet results generated by OpaVote. In the results, compare the candidate on the row with the candidate in the column. If a cell is green, that means that the candidate on the row beat the candidate on the column. If the cell is red, then the candidate on the row lost to the candidate on the column. The numbers in the cell show you the number of ballots where each candidate was ranked higher than the other. At the time of writing this, Cookies and Cream beat all other candidates and is the winner.

That seems pretty straightforward, but Condorcet has one complication, and it is a big one. It is possible that there is no candidate who beats all other candidates. For example, it is possible that candidate A beats candidate B, candidate B beats candidate C, and candidate C beats candidate A. Thus, all candidates have lost to at least one other candidate.

This is sometimes referred to as a Condorcet cycle, and the candidates in the cycle are referred to as the Smith set. You could think of it as a tie between the candidates in the Condorcet cycle. Like other types of ties, the tie needs to be broken and the different variants of Condorcet voting basically break this tie in different ways. For example, you could break the tie by running an IRV election among the candidates in the Condorcet cycle. Some Condorcet methods, such as Beatpath, have fairly complicated ways of breaking the tie.

No governments currently use Condorcet voting for elections.

OpaVote provides a few versions of Condorcet voting, such as Condorcet Beathpath, Condorcet IRV, Condorcet Borda, and Condorcet Copeland.

  • Condorcet Beathpath — See here.
  • Condorcet IRV — The winner is chosen from the Smith set using IRV.
  • Condorcet Borda — The winner is chosen from the Smith set using the Borda Count.
  • Condorcet Copeland — See here.