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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 pairwise losing candidates. 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 [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 IRV, 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.
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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 ==
 
RCIPE STV is the multi-winner version of the RCIPE method, which means it functions like the [[Single transferable vote|Single Transferable Vote]] (STV) for electing multiple legislators within the same district, and electing non-partisan members of a city council. RCIPE STV offers these advantages over plain STV:
The RCIPE method can be extended to elect multiple candidates, such as when electing non-partisan members of a city council, or when electing two (or more) representatives from the same district. This means the RCIPE STV method can be used as a direct replacement for the [[Single transferable vote|Single Transferable Vote]] (STV).
 
* 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 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.  andIf there is no pairwise losing candidate, then the candidate with the lowest vote transfer count is eliminated.▼
 
* During pairwise counting all the ballots are counted, but the ballots that have zero influence do not contribute any votes to either side of the one-on-one matches.
* 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.  The choice of which ballot transfers to which candidate must be handled so that supplying the same ballots in a different sequence is extremely likely to elect the same candidates.▼
*In Thea 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.  The goalThis ofrule thiscauses selectionthe process,calculations orto anyyield alternatethe selectionsame process,winners isif tothe ensuresame thatballots a differentwere supplied ballotin sequencea cannotdifferent change the resultssequence.▼
*Ties are resolved using pairwise elimination.
 
SomeIf jurisdictionsa mayjurisdiction havehas laws that allow a ballot to have decimal influence amounts that range frombetween zero toand one. If this is allowed, the above rules can be modifiedsimplified to use decimal influence amountsvalues.▼
 
== External links ==
The RCIPE STV method uses the following rules to elect two or more candidates to fill two or more equivalent seats:
 
* [https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp RCIPE_STV software that calculates RCIPE and RCIPE STV methods]
* At the beginning of all the counting rounds, each ballot has an influence amount equal to one vote.  During a counting round that elects a candidate, some ballots are given zero influence for future counting rounds.  This reduced influence increases the influence of the other ballots to compensate for their lack of support for already-elected candidates.  The result is that the elected candidates represent most of the voters, not just a majority of voters.
* At the beginning of each counting round, each candidate gets a transfer count of zero.
* During a counting round, each ballot that has full influence adds one vote count to the transfer count of the candidate who is ranked higher on that ballot than any other candidate who has not yet been elected or eliminated.  If a ballot has zero influence, it does not change the transfer count of any candidate.
* At the end of a counting round, the candidate with the highest transfer count is elected if that candidate's transfer count equals or exceeds the required quota count.
* The quota count can change after each candidate is elected.  Any reasonable formula for quota counts can be used.
* At the end of a counting round, if all the candidates have transfer counts that are less than the current quota count, and if there is a pairwise losing candidate during that round, the pairwise losing candidate is eliminated.  A pairwise losing candidate is a candidate who would lose every one-on-one match against every other remaining (not-yet-elected and not-yet-eliminated) candidate.  During pairwise counting all the ballots are counted, but the ballots that have zero influence do not contribute any votes to either side of the one-on-one matches.
▲* If a counting round does not elect a candidate and there is no pairwise losing candidate, then the candidate with the lowest transfer count is eliminated.
* When a counting round ends with a candidate getting elected, the ballots that contributed to the transfer count of that elected candidate are identified as the supporting ballots, and a quota count number of these supporting ballots are given zero influence for all future counting rounds.  All the supporting ballots do not get zero influence because the number of supporting ballots beyond the quota count is an excess level of support that must be allowed to contribute toward electing another candidate.
▲* 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.  The goal of this selection process, or any alternate selection process, is to ensure that a different supplied ballot sequence cannot change the results.
▲* 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.  The choice of which ballot transfers to which candidate must be handled so that supplying the same ballots in a different sequence is extremely likely to elect the same candidates.
 
▲Some jurisdictions may have laws that allow a ballot to have decimal influence amounts that range from zero to one. If this is allowed, the above rules can be modified to use decimal influence amounts.
[[Category:Sequential loser-elimination methods]]
[[Category:Ranked voting methods]]
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