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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).
The RCIPE STV method modifies traditional STV in these ways.
The RCIPE STV method uses the following rules to elect two or more candidates to fill two or more equivalent seats:
* A voter can mark two or more candidates at the same ranking level.
* 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.
* AtVote thetransfer beginningcounts ofare eachre-calculated counting round,after each candidate gets a transfer count ofis zeroelected.
* DuringIf a counting round, eachdoes ballotnot thatelect hasa full influence adds one vote count tocandidate, the transferpairwise count of thelosing candidate who is ranked higher on that ballot than any other candidate who has not yet been elected or eliminated. If athere ballotis hasno zeropairwise influencelosing candidate, itthe doescandidate not changewith the lowest vote transfer count ofis any candidateeliminated.
* Ties are resolved using pairwise elimination.
* 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, which specifies how many votes are required to get elected, can be the Hare or Droop quota.
Here are details that clarify how pairwise counts and shared preference levels are handled.
* 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.
* 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.
*When a tie occurs among the highest or lowest transfer counts, the tie can be resolved using the pairwise counts. If there is still a tie and there are a large number of ballots, recounting the ballots is likely to break the tie.
* 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. ▼* 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.
* InThe 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 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 selection process protects the results from changing as a result of changing the sequence of the supplied ballot data.
▲* 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 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.
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