Condorcet IRV
Condorcet IRV is a voting method variation of instant-runoff voting (IRV) that selects a single winner using votes that express each voter's order of preference, like IRV. However, unlike IRV, it will select the Condorcet winner. Thus, unlike IRV, it satisfies the Condorcet criterion. It also satisfies later-no-harm, as well as all other criteria passed by IRV.
It is a simplification of IRV Prime which provides a simpler approach when there is a Condorcet winner.
Procedure
Find the Condorcet winner & elect them; if there is no Condorcet winner, proceed with IRV Prime.
Proof of satisfying Condorcet criterion as well later-no-harm
Suppose a classic IRV election looks as follows:
| Candidate | Votes |
|---|---|
| A | N |
| B | M (which is < N) |
| C | < M |
| Candidate | Votes |
|---|---|
| B | M' (which is > N) |
| A | < M' |
We now know that B is the winner & all other candidates (including A) will lose.
If we re-run the IRV eliminating all candidates except for B and Condorcet (who may be B), we know later-no-harm is preserved because all candidates were going to lose against B & thus are not being harmed (B is not harmed because all their votes are preserved)
| Candidate | Votes |
|---|---|
| Condorcet | P |
| B | < P |
By definition, Condorcet will always win this round, because by definition a Condorcet winner beats every other candidate in a pairwise match-up.
Thus, we can eliminate this B-preserving & Condorcet-preserving round, as we know the winner is guaranteed to be Condorcet, & simply pre-select the Condorcet winner (if there is one).