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Bottom-Two-Runoff IRV: Difference between revisions
Suggesting renaming this from "Bottom-Two-Runoff IRV" to "Bottom-two-runoff-instant-runoff-voting method to give the article a name more likely to be accepted on English Wikipedia
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(Suggesting renaming this from "Bottom-Two-Runoff IRV" to "Bottom-two-runoff-instant-runoff-voting method to give the article a name more likely to be accepted on English Wikipedia) |
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The '''"bottom-two-runoff-instant-runoff-voting method'''" (or "'''BTR-IRV method'''") is an [[election method]] that selects a single winner using votes that express ranked preferences.
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 BTR-IRV method 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]].
A benefit of BTR-IRV is that first choices are honored in the elimination process, so that a polarizing candidate can survive to later rounds until they have a single opponent who they can be individually compared to. This attribute and ease of explaining the system makes it less prone to claims of fraud than other systems for resolving the [[Condorcet paradox]].
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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''', though the multi-winner variant was not originally recommended by LeGrand.<ref name=":0" />
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{{Tenn_voting_example}}
<div class="floatright">
{| border="1"
!City
!Round 1
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!Round 3
|-
! bgcolor="#ffc0c0" |Memphis
| bgcolor="#ffc0c0" |42
| bgcolor="#ffc0c0" |42
| bgcolor="#ffc0c0" |42
|-
! bgcolor="#ffc0c0" |Nashville
| bgcolor="#ffc0c0" |26
| bgcolor="#ffc0c0" |26
| bgcolor="#ffffc0" |<strike>26</strike> 58
|-
! bgcolor="#ffc0c0" |Chattanooga
| bgcolor="#ffc0c0" |15
| bgcolor="#ffc0c0" |<strike>15</strike> 32
| bgcolor="#e0e0ff" |<strike>32</strike> 0
|-
! bgcolor="#ffc0c0" |Knoxville
| bgcolor="#ffc0c0" | 17
| bgcolor="#e0e0ff" |<strike>17</strike> 0
| bgcolor="#e0e0ff" |0
|}
</div>
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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.
==
BTR-IRV only requires eliminations to be done until one candidate remains who [[Pairwise counting#Terminology|pairwise beats]] all other uneliminated candidates, at which point that candidate can be declared the winner; this is because that candidate is guaranteed not to be eliminated in any remaining BTR-IRV pairwise matchups. This trick can be used to save time in counting if a pairwise comparison table has already been made, and also means BTR-IRV can be phrased analagously to [[Benham's method]], though in terms of BTR-IRV itself instead of IRV.
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|-
|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
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|4
|A>C>B>D<sub>2</sub>>D<sub>1</sub>
|}
|}
Note that the example requires two cases of the [[Condorcet paradox]] in the base case: b>a, a>c, c>b and also c>b, b>d, d>c, so it is unlikely to occur in practice.
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Variations of BTR-IRV could be considered to parallel other [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]]; one such variation would be "Repeat both steps until only one candidate remains: Eliminate everyone not in the Smith set, then do a pairwise elimination between the two candidates with the fewest 1st choices".
==
*
==
<references />
[[Category:Condorcet-reducible PR methods]]
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