Bottom-Two-Runoff IRV: Difference between revisions

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The process: take the two options with the fewest first preference votes. The pairwise loser out of those two options is eliminated, and the next preferences from those ballots are redistributed. This process repeats until there is only one option remaining, and that remaining option is the winner.
The process: take the two options with the fewest first preference votes. The pairwise loser out of those two options is eliminated, and the next preferences from those ballots are redistributed. This process repeats until there is only one option remaining, and that remaining option is the winner.


BTR-IRV was originally proposed by [[User:Legrand|Rob LeGrand]] in 2006.<ref name=":0">[https://election-methods.electorama.narkive.com/LKfc52OI/an-example-of-btr-stv#post4 election-methods mailing list: An example of BTR-STV]</ref><ref>[https://www.mail-archive.com/election-methods@electorama.com/msg01311.html <nowiki>[EM] DH3 - error by me - should prefer BTR-IRV to Schulze beatpaths?</nowiki>]</ref> It was conceived as a modification to standard [[Instant-runoff voting|Instant-runoff voting (IRV)]] which ensures the runoff doesn't ever eliminate a Condorcet Winner. Thus, the method passes the [[Condorcet Criterion]], ensuring it functions as a [[Condorcet method]].
BTR-IRV was originally proposed by [[User:Legrand|Rob LeGrand]] in 2006.<ref name=":0">[https://election-methods.electorama.narkive.com/LKfc52OI/an-example-of-btr-stv#post4 election-methods mailing list: An example of BTR-STV]</ref><ref>[https://www.mail-archive.com/election-methods@electorama.com/msg01311.html <nowiki>[EM] DH3 - error by me - should prefer BTR-IRV to Schulze beatpaths?</nowiki>]</ref> It was conceived as a modification to standard [[Instant-runoff voting|Instant-runoff voting (IRV)]] which ensures the runoff doesn't ever eliminate a Condorcet Winner (and in fact, never eliminates all candidates in the [[Smith set]], since a Smith set member can never be eliminated in a runoff against a non-Smith set member). Thus, the method passes the [[Condorcet Criterion]] and the [[Smith criterion]], ensuring it functions as a [[Condorcet method]].


This system is a form of [[Single transferable vote|single transferable vote (STV)]], and may be referred to by the more general name '''BTR-STV''', thought the multi-winner variant was not originally recommended by LeGrand.<ref name=":0" />
This system is a form of [[Single transferable vote|single transferable vote (STV)]], and may be referred to by the more general name '''BTR-STV''', thought the multi-winner variant was not originally recommended by LeGrand.<ref name=":0" />
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In a real election, of course, voters would show greater variation in the rankings they cast, which could influence the result.
In a real election, of course, voters would show greater variation in the rankings they cast, which could influence the result.

== Notes ==
BTR-IRV is not immune to clones. Example:
{| class="wikitable"
|Chris Benham's BTR-IRV cloning-failure example (before cloning D). Winner is '''A''' after B,C,D eliminated in that order.
{| class="wikitable"
!#voters
!their vote
|-
|2
|B>A>D>C
|-
|3
|D>C>B>A
|-
|4
|A>C>B>D
|}
|Benham's BTR-IRV cloning-failure example (after cloning D). Winner is '''B''' after C,D<sub>1</sub>,D<sub>2</sub>,A eliminated in that order.
{| class="wikitable"
!#voters
!their vote
|-
|2
|B>A>D<sub>1</sub>>D<sub>2</sub>>C
|-
|2
|D<sub>1</sub>>D<sub>2</sub>>C>B>A
|-
|1
|D<sub>2</sub>>D<sub>1</sub>>C>B>A
|-
|4
|A>C>B>D<sub>2</sub>>D<sub>1</sub>
|}
|}
There are likely to be many candidates tied for having the fewest 1st choices; one possible non-random tiebreaker is to look for those among the tied candidates that have the fewest 2nd choices, then 3rd choices, etc.


== External links ==
== External links ==
Retrieved from "https://electowiki.org/wiki/Bottom-Two-Runoff_IRV"