Instant-runoff voting: Difference between revisions
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In normal [[runoff voting]], D and E are the two candidates with the most votes, preventing the majority's preferred candidates from entering the runoff. In FPTP, D has the most votes. But with IRV, first C is eliminated, and then E, and then B, resulting in A having 51 votes and winning. Note that though the 49 voter-minority preferred B to A, B didn't win; this is an example of IRV ignoring voter preferences in a way that can lead to some majorities (when looking at [[Head-to-head matchup|head-to-head matchups]]) having less power. However, the majority still got a better result than it would've had in some other methods.
IRV passes [[clone independence]] while [[FPTP]] doesn't. This is because if a candidate would receive a majority of votes, then [[Clone|cloning]] them will not allow any other candidate to receive a majority, because when all but one of the clones is eliminated, the remaining clone will have the same number of votes as if all of the clones hadn't run in the first place.
IRV is equivalent to [[runoff voting]] (supposing no change in preferences) when there are 3 or fewer candidates. This is used to argue both for and against it; advocates claim it is cheaper and easier for the voters to vote once, while opponents argue that a delayed runoff actually gives voters a second look into the candidates in the runoff, potentially improving the quality of their decision-making, and that because ranking candidates is harder than picking one candidate, that runoff voting is actually easier for voters. Note that though IRV is called instant runoff, this is more because it elects a candidate who could win or tie a runoff ([[pairwise beat]] or tie) against at least one other candidate, rather than because it is equivalent to runoff voting in all cases.
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Several variations of IRV have been proposed to meet the [[Condorcet]] and [[Smith criterion|Smith]] criteria. The simplest of these are to either (elect the [[Condorcet winner]] if one exists), or (eliminate all candidates not in the [[Smith//IRV|Smith set]]), and then run IRV. ▼
Note that when the top candidate doesn't have a majority, but the top two candidates each have over 1/3rd of the active votes (i.e. they combinedly have over 2/3rds), they are guaranteed to be the two final remaining candidates in IRV, so all other candidates can be eliminated (or equivalently, the pairwise matchup between the two can be tallied) to find the result. This explains why some criticize IRV as mathematically inducing two-party domination, since often it does result in two mainstream factions vying to be pairwise preferred to each other.
▲Several [[:Category:Condorcet-IRV hybrid methods|variations of IRV]] have been proposed to meet the [[Condorcet]] and [[Smith criterion|Smith]] criteria. The simplest of these are to either (elect the [[Condorcet winner]] if one exists), or (eliminate all candidates not in the [[Smith//IRV|Smith set]]), and then run IRV.
== Presentation of procedure ==
There are two ways to make a diagram detailing an IRV result. The first is generally to create a [[W:Sankey diagram|Sankey diagram]] showing votes transferring, at least until some candidate has a majority of active votes. The other is to show a flow diagram where, for either of the two candidates with the most votes in a round, it is shown whether they have over 1/3rd of the active votes, and how many of the other uneliminated candidates they pairwise beat. Here is a visualization example of IRV (it should be read as "Voter 1 ranks Candidate A 1 i.e. 1st, etc.): ▼
{| class="wikitable"
|+Rankings of the candidates
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Note that this form of visualization becomes harder when allowing for equal-ranking.
=== "Condorcet winner with over 1/3rd of votes" presentation ===
The "A Condorcet winner with over 1/3rd of 1st choice votes is guaranteed to win" [[Dominant mutual third|factoid]] can be used to speed up the counting; in the above example, when the votes were 8 B 9 D 5 C, D was a Condorcet winner:
{| class="wikitable"
Line 571 ⟶ 578:
|}
D [[Pairwise beat|pairwise wins]] against all others, and had 9 out of the 22 active votes = 40.9%, greater than 1/3rd, at that time. So there was no need to eliminate C at that point to find the winner.
▲There are two ways to make a diagram detailing an IRV result. The first is generally to create a [[W:Sankey diagram|Sankey diagram]] showing votes transferring, at least until some candidate has a majority of active votes. The other is to show a flow diagram where, for either of the two candidates with the most votes in a round, it is shown whether they have over 1/3rd of the active votes, and how many of the other uneliminated candidates they pairwise beat.
▲Note that when the top candidate doesn't have a majority, but the top two candidates each have over 1/3rd of the active votes (i.e. they combinedly have over 2/3rds), they are guaranteed to be the two final remaining candidates in IRV, so all other candidates can be eliminated (or equivalently, the pairwise matchup between the two can be tallied) to find the result. This explains why some criticize IRV as mathematically inducing two-party domination, since often it does result in two mainstream factions vying to be pairwise preferred to each other.
== Variants ==
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