Ranked Choice Including Pairwise Elimination: Difference between revisions
Ranked Choice Including Pairwise Elimination (view source)
Revision as of 10:18, 25 May 2022
, 2 years agoMutual majority: add link to sequential loser-elimination method article for mutual majority proof
(→Ballot Robustness: How to handle unranked candidate, affected by how write-in candidates are handled) |
m (Mutual majority: add link to sequential loser-elimination method article for mutual majority proof) |
||
(16 intermediate revisions by 2 users not shown) | |||
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 [
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 19 ⟶ 20:
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.
Importantly, the runner-up candidate does not deserve to win any kind of elected seat.
=== Ballot Robustness ===
Line 105 ⟶ 106:
* [[Condorcet loser criterion|Condorcet loser]]: 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
* [[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]] with O(N<sup>2</sup>).
== RCIPE 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. If there is no pairwise losing candidate, the candidate with the lowest vote transfer count is eliminated.
*
* 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.
*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.
== External links ==
* [https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp RCIPE_STV software that calculates RCIPE and RCIPE STV methods]
[[Category:Sequential loser-elimination methods]]
|