Condorcet IRV: Difference between revisions
Content added Content deleted
No edit summary |
(Remove incorrect reference to C-IRV passing every criterion passed by IRV. See Condorcet-IRV hybrid methods article, and Benham's post linked in the DMTBR article.) |
||
| Line 1: | Line 1: | ||
'''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) 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 [[IRV Prime]] |
It is a simplification of more complex Condorcet-IRV hybrids like [[Benham's method]] or [[IRV Prime]], and 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 == |
== Procedure == |
||
Find the [[Condorcet winner criterion|Condorcet winner]] |
Find the [[Condorcet winner criterion|Condorcet winner]] and elect them; if there is no Condorcet winner, proceed with [[instant-runoff voting]]. |
||
== 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 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). |
|||
== External Resources == |
== External Resources == |
||
* [https://www.daneckam.com/?p=374 The Condorcet-IRV Voting Method] |
* [https://www.daneckam.com/?p=374 The Condorcet-IRV (Benham) Voting Method] |
||
[[Category:Single-winner voting methods]] |
[[Category:Single-winner voting methods]] |
||
Latest revision as of 09:02, 31 July 2021
Condorcet IRV is a Condorcet-IRV hybrid that elects the Condorcet winner if one exists, and otherwise performs instant-runoff voting.
It is a simplification of more complex Condorcet-IRV hybrids like Benham's method or IRV Prime, and 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 and elect them; if there is no Condorcet winner, proceed with instant-runoff voting.