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'''Condorcet IRV''' is a [[Condorcet-IRV hybrid methods|Condorcet-IRV hybrid]] that elects the Condorcet winner if one exists, and otherwise performs instant-runoff voting.
'''Condorcet IRV''' is a [[voting method]] variation of [[instant-runoff voting]] (IRV) developed by Dan Eckam 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 criterion|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 more complex Condorcet-IRV hybrids like [[Benham's method]] or [[IRV Prime]], whichand provides a simpler approach when there is a Condorcet winner.
The term "Condorcet IRV" is also sometimes used to refer to Benham's method, or to an unspecified Condorcet-IRV hybrid..
== Procedure ==
Find the [[Condorcet winner criterion|Condorcet winner]] &and elect them; if there is no Condorcet winner, proceed with a normal/classic [[instant-runoff voting]] procedure.
== Proof of satisfying [[Condorcet criterion]] as well [[later-no-harm]] ==
Suppose a classic IRV election looks as follows:
{| class="wikitable"
|+Round N-1 IRV
!Candidate
!Votes
|-
|A
|<small>N</small>
|-
|B
|<small>M (which is < N)</small>
|-
|C
|<small>< M</small>
|}
{| class="wikitable"
|+Last Round IRV
!Candidate
!Votes
|-
|B
|<small>M' (which is > N)</small>
|-
|A
|<small>< M'</small>
|}
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)
{| class="wikitable"
|+Last Round of IRV preserving B & Condorcet
!Candidate
!Votes
|-
|Condorcet
|<small>P</small>
|-
|B
|<small>< P</small>
|}
By definition, Condorcet will always win this round, because [[Condorcet winner criterion|by definition]] a Condorcet winner beats every other candidate in a pairwise match-up.
Thus, we can eliminate this final B-preserving & Condorcet-preserving round, as we know who the winner will be, & simply pre-select the Condorcet winner (if there is one).
== External Resources ==
* [https://www.daneckam.com/?p=374 The Condorcet-IRV (Benham) Voting Method]
{{fromwikipedia}}
[[Category:Single-winner voting methods]]
[[Category:Plurality-runoff voting methods]]
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