Ranked Choice Including Pairwise Elimination: Difference between revisions

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Mutual majority: add link to sequential loser-elimination method article for mutual majority proof
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'''Ranked Choice Including Pairwise Elimination''' (abbreviated as '''RCIPE''' which is pronounced "recipe") is an election vote-counting method that uses ranked ballots and eliminates '''pairwise losing candidates''' (elimination-round-specific [[Condorcet loser criterion|Condorcet losers]]) when they occur, and otherwise eliminates the candidate who currently has the smallest top-choice count.
 
 
This method modifies [[Instant-Runoff Voting|instant runoff voting]] (IRV) by adding the elimination of relativepairwise Condorcetlosing loserscandidates. This addition reduces the failure rate for the [[Independence of irrelevant alternatives|Independence of Irrelevant Alternatives]] (IIA), which is the kind of failure that occurred in the the [https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election[2009 Burlington mayoral election|2009 mayoral election in Burlington, Vermont]].  This check for pairwise losing candidates considers all the marks on all the ballots, which contrasts with the IRV method, which does not consider all the marks on all the ballots.
 
This method further modifies simple IRV by specifying how to handle ballots on which the voter has marked more than one candidate at the same ranking level.
 
The RCIPE STV method extends the single-winner RCIPE method to fill multiple equivalent seats.
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Unlike instant-runoff voting, which ends when a candidate reaches majority support, the eliminations continue until only a single candidate remains.
 
The last candidate to be eliminated is the runner-up candidate. If this counting method is used in the primary election of a major political party, and if the runoff or "general" election is counted in a way that is not vulnerable to vote splitting, then ideally the runner-up candidate would move to the runoff or general election along with the primary-election winner. SmallVery small political parties would not qualify to move their runner-up candidate to the runoff or general election.
 
Importantly, the runner-up candidate does not deserve to win any kind of elected seat. ThisInstead, meansthe thisRCIPE methodSTV isversion notshould suitablebe used for fillingelections that fill multiple seats, such as on a non-partisan city council or in a multidual-member legislative district.
 
=== Ballot Robustness ===
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Also to avoid spoiled ballots, if a voter marks more than one ranking level for the same candidate, only the highest-marked ranking level is used during counting.
 
IfThe thechoice of how to handle a ballot on which a voter does not mark any ovals for a candidate depends on how write-in candidates are handled. If write-in candidates are not allowed, thatan unmarked candidate iscan be ranked at the ranking level ''below'' the lowest ranking level, asshown ifon the voterballot. markedIf thewrite-in ovalcandidates forare allowed, an unmarked candidate can be ranked ''at'' the lowest ranking level shown on the ballot, and that level also would be used for a write-in candidate whose name does not appear on that ballot.
 
The ranking level below the lowest ranking level is reserved for write-in candidates whose names do not appear on the ballot being counted.
 
== Tie breaker ==
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* [[Condorcet loser criterion|Condorcet loser]]: pass
* [[Majority criterion|Majority]]: failpass
* [[Majority loser criterion|Majority loser]]: failpass
* Mutual majority: [[Sequential loser-elimination method#Criteria|pass]]
* Resolvable: pass
* Polytime: pass
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* [[Condorcet criterion|Condorcet]]: fail
* [[Majority criterion|Majority]]: fail
* [[Majority loser criterion|Majority loser]]: fail
* Mutual majority: fail
* [[Smith criterion|Smith]]/[[ISDA]]: fail
* Cloneproof: fail
* LIIA: fail
* IIA: fail
* Cloneproof: fail
* Monotone: fail
* Consistency: fail
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* Participation: fail
* No favorite betrayal: fail
It is* [[Summability criterion|summableSummable]]: with O(N<sup>2</sup>).fail
 
It is [[Summability criterion|summable]] with O(N<sup>2</sup>).
 
== RCIPE STV ==
 
TheRCIPE STV is the multi-winner version of the RCIPE method, canwhich bemeans extendedit tofunctions electlike the [[Single transferable vote|Single Transferable Vote]] (STV) for electing multiple candidates,legislators suchwithin asthe same district, whenand electing non-partisan members of a city council,. or whenRCIPE electingSTV twooffers (orthese more)advantages representativesover fromplain the same district.STV:
 
The RCIPE STV method modifies the Single Transferable Vote (STV) method in the following ways:
 
* During each round of counting either one candidate is elected or one candidate is eliminated, but not both in the same round.
 
* If more than one candidate has enough transferred votes to exceed the quota for that round, the candidate with the highest transferred-vote count is elected.
 
* A voter can mark two or more candidates at the same ranking level. This flexibility allows voters to fully rank all the candidates, including the ability to rank the voter's most-disliked candidate lower than all other candidates, even when the number of ranking levels is fewer than the number of candidates.
* The ballots that support an elected candidate with transferred votes are proportionally reduced in influence according to any excess beyond the quota. Specifically the reduced influence amount equals the number of votes beyond the quota vote count divided by the count of the supporting ballots. If decimal values are not allowed, these supporting ballots are reduced to zero influence. Any supporting ballots that already have reduced influence are reduced to zero influence after any secondary partial support.
*The counting process considers all the marks on all the ballots. This deeper counting is done when identifying pairwise losing candidates. It prevents a voter's ballot transfer from getting stuck on an unpopular pairwise-losing candidate while other ballots determine which other candidates win seats and which other candidates get eliminated.
*Changing the ballot-counting sequence does not change who wins. In contrast, plain STV can elect different winners if the ballots are supplied in a different sequence.
These advantages occur because:
* Vote transfer counts are re-calculated after each candidate is elected.
* If a counting round does not elect a candidate, the pairwise losing candidate is eliminated.  If there is no pairwise losing candidate, the candidate with the lowest vote transfer count is eliminated.
 
* AfterDuring eachpairwise counting round all the ballots are re-counted, and transferred tobut the highest-ranked candidate (onballots that ballot) who has not yet been elected or eliminated. Some ballots will have reducedzero influence, ordo nonot influence,contribute ifany theyvotes alreadyto contributedeither partialside supportof tothe one-on-one or two candidates who have been electedmatches.
* If a full-influence ballot ranks two or more remaining (not-yet-elected and not-yet-eliminated) candidates at the same preference level, and if there are not any remaining candidates ranked higher on this ballot, then this ballot is grouped with other similar (although not necessarily identical) ballots and their influence counts are equally split among the remaining candidates who are ranked at that shared preference level.  For example, if candidates A and B have been elected or eliminated, and a ballot ranks candidate A highest and ranks candidates B, C, and D at the next-highest level, and another ballot ranks candidate B highest and ranks candidates A, C, and D at the next-highest level, then one of these two ballots transfers to candidate C and the other ballot transfers to candidate D.
*In a counting round that ends with a candidate getting elected, the specific supporting ballots that are changed from full influence to zero influence are chosen to be equally spaced from one another in the supplied ballot sequence, without including the already-zero-influence ballots in the equal-spacing calculations. This rule causes the calculations to yield the same winners if the same ballots were supplied in a different sequence.
*Ties are resolved using pairwise elimination.
 
If a jurisdiction has laws that allow a ballot to have decimal influence amounts that range between zero and one, the above rules can be simplified to use decimal influence values.
* Ballots on which two or more remaining (not-yet-elected and not-yet-eliminated) candidates are ranked at the same preference level are temporarily categorized as "currently not available to be transferred" for the remainder of that counting round.
 
== External links ==
* If no candidate is elected during a counting round, and there is a pairwise losing candidate during that round, the pairwise losing candidate is eliminated instead of eliminating the candidate with the fewest transferred votes. During pairwise counting the ballots that have reduced influence are counted according to that reduced influence. When checking for a pairwise losing candidate, the ballots that are categorized as "currently not available to be transferred" are included in the pairwise count, but some of these ballots may have partial influence rather than full influence.
 
* [https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp RCIPE_STV software that calculates RCIPE and RCIPE STV methods]
Any reasonable quota can be chosen for the RCIPE STV method.
 
[[Category:Sequential loser-elimination methods]]
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