Ranked Choice Including Pairwise Elimination: Difference between revisions

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Line 1: '''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. Line 105 ⟶ 106: * [[Condorcet loser criterion\|Condorcet loser]]: pass * [[Majority criterion\|Majority]]: ~~fail~~pass▼ * [[Majority loser criterion\|Majority loser]]: ~~fail~~pass▼ * Mutual majority: [[Sequential loser-elimination method#Criteria\|pass]] * Resolvable: pass * Polytime: pass Line 111 ⟶ 115: * [[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 Line 126 ⟶ 127: * Participation: fail * No favorite betrayal: fail ~~It is~~* [[Summability criterion\|~~summable~~Summable]]: ~~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 RCIPE STV method modifies traditional STV in these ways.~~ 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. * A voter can mark two or more candidates at the same ranking level. 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. * Ties are resolved using pairwise elimination.▼ ~~Here are details that clarify how pairwise counts and shared preference levels are handled.~~ * 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. For example, in~~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. ~~Some~~If ~~jurisdictions~~a ~~may~~jurisdiction ~~have~~has laws that allow a ballot to have decimal influence amounts that range between zero and one~~. If this is allowed~~, the above rules can be ~~modified~~simplified to use decimal influence values~~. This approach eliminates the possibility that changing the ballot sequence can change the election results~~.▼ == External links == * [https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp RCIPE_STV software that calculates RCIPE and RCIPE STV methods] ▲Some jurisdictions may have laws that allow a ballot to have decimal influence amounts that range between zero and one. If this is allowed, the above rules can be modified to use decimal influence values. This approach eliminates the possibility that changing the ballot sequence can change the election results. [[Category:Sequential loser-elimination methods]] [[Category:Ranked voting methods]]