Ranked Choice Including Pairwise Elimination: Difference between revisions

* 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.

* 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.

* 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.

 

[[Category:Sequential loser-elimination methods]]

[[Category:Ranked voting methods]]