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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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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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* [[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:
 
* 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.
The RCIPE STV method modifies the [[Single transferable vote|Single Transferable Vote]] (STV) method in the following ways:
* 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 (not-yet-elected and not-yet-eliminated) candidates ranked higher on this ballot, then this ballot's is grouped with other similar (although not necessarily identical) ballots and their influence amountcounts isare 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 ifanother ballot ranks candidate B highest and ranks candidates A, C, and BD haveat beenthe electednext-highest or eliminatedlevel, then halfone of thisthese ballot'stwo influence amountballots transfers to candidate C and the other halfballot 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.
* During each round of counting either one candidate is elected, or one candidate is eliminated, but not both in the same round.
* At the beginning of each counting round, the transfer count for each candidate is reset to zero.
* At the beginning of all the counting rounds, each ballot has an influence amount equal to one vote.  During later counting rounds a ballot can have a reduced influence amount that is expressed as a decimal number that can range from zero up to one.  If a law makes it illegal for a ballot to have an influence amount other than zero or one, the counting process can be modified as described below.
* When counting a ballot, the ballot's influence amount is added to the transfer count of the candidate who is ranked highest after ignoring the marks for already-elected and already-eliminated candidates.
▲* If a ballot ranks two or more candidates at the same preference level, and if there are not any remaining (not-yet-elected and not-yet-eliminated) candidates ranked higher on this ballot, then this ballot's influence amount is equally split among the remaining candidates who are ranked at that shared preference level.  For example, if a ballot ranks candidate A highest, and ranks candidates B, C, and D at the next-highest level, and if candidates A and B have been elected or eliminated, then half of this ballot's influence amount transfers to candidate C and the other half transfers to candidate D.
* 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 is different for each counting round.  Any reasonable formula for quota counts can be used.
* If all the candidates have transfer counts that are less than the quota number, and if there is a pairwise losing candidate during that round, the pairwise losing candidate is eliminated.  During pairwise counting all the ballots are counted, but some ballots can have reduced influence.
▲* 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 candidate is elected, all the ballots that contribute full (not-reduced) influence to the candidate's transfer count have their influence reduced to the candidate's excess transfer count divided by the transfer count, where the excess transfer count equals the candidate's transfer count minus the quota count.  Of course decimal calculation results are rounded down, not up.
* When a candidate is elected, all the ballots that contribute reduced influence (less than full influence) to that candidate's transfer count are reduced to have zero influence in future counting rounds.
 
== External links ==
If decimal influence amounts are not allowed, the following modifications can be used:
 
* [https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp RCIPE_STV software that calculates RCIPE and RCIPE STV methods]
* Instead of giving a single reduced influence amount to ballots that support an elected candidate, some of the supporting ballots are given full influence and others are given zero influence.
* Selecting which ballots get full influence and which ballots get zero influence should make use of information about how many ballots share the same marking pattern.  For example, if 100 ballots have the same marking pattern and the decimal calculation method would reduce their influence to 0.8 of a vote each, then selecting any 80 of these ballots to get full influence and giving the remaining 20 ballots zero influence produces the same result as the decimal approach.
* Ballots that have unique or uncommon marking patterns must be selected semi-randomly, yet the total number of supporting ballots getting zero influence must equal the quota count, and the total number of ballots getting full influence must equal the elected-candidate's transfer count minus the quota count.
* Instead of using the same semi-random selections from one counting round to the next, the semi-random selection process should be done for each counting round.  This approach makes it unlikely that the same specific ballot will get zero influence significantly more than any other specific ballot that has similar markings.
* Ballots on which two or more remaining candidates share the same highest ranking level are distributed almost the same as in the decimal calculation method.  The significant difference is that ballots with zero influence (during that counting round) are not distributed among the shared-level candidates.
 
[[Category:Sequential loser-elimination methods]]
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