Prefer Accept Reject voting: Difference between revisions
Category:Graded Bucklin systems → Category:Graded Bucklin methods
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Prefer Accept Reject (PAR) voting works as follows:
# '''Voters
# '''Tally 1 point for each "Prefer"''' for each candidate.
# Out of the candidates (if any) with no more than 50% "Reject", find the one with the most points. '''For every ballot which doesn't "Prefer" this frontrunner, add 1 point for each "Accept".'''
# If the frontrunner still has the most points, they win. Otherwise, the winner is the candidate with fewest "Reject" ratings.
To express it in a single sentence: if the most-preferred non-majority-rejected candidate, X, has more non-reject votes than any other candidate has non-reject votes that aren't below X, then X wins; otherwise, the least-rejected candidate wins.
Note that the procedure above will always elect a candidate with no more than 50% "Reject", if any exist. This is because, if any exist, one of them will be the frontrunner, and they will thus score points equal to at least 50% of the voters.
Each candidate's score at the end can be seen as an approval total, and is thus suitable for combining with approval totals from other jurisdictions in a system like the National Popular Vote Interstate Compact.
A related system which passes [[FBC]] is [[FBPPAR]]. This has the same steps, except that voters can choose to mark any of their "preferred" candidates as "stand aside". "Stand aside" preferences are counted as rejections when finding the leader, but as preference when assigning points.
== Relationship to NOTA ==
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== Criteria compliance ==
PAR voting passes the [[majority criterion]], the [[mutual majority criterion]], the [[majority loser criterion]], [[Local independence of irrelevant alternatives]] (under the assumption of fixed "honest" ratings for each voter for each candidate), [[Independence of clone alternatives]], [[Monotonicity]], [[polytime]], [[resolvability]], and
There are a few criteria for which it does not pass as such, but where it passes related but weaker criteria. These include:
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* It fails [[Independence of irrelevant alternatives]], but passes [[Local independence of irrelevant alternatives]].
* It fails the [[Condorcet criterion]], but
* It fails the [[participation criterion]] but passes the [[semi-honest participation criterion]].
* It fails the [[later-no-help criterion]], but passes if there is at least one candidate rejected by under 50%.
It fails the [[consistency criterion]], the [[Condorcet loser criterion]], [[reversibility
▲It fails the [[consistency criterion]], the [[Condorcet loser criterion]], [[reversibility]], the [[majority loser criterion]], the [[Strategy-free criterion]], and the [[later-no-harm criterion|later-no-harm]] and [[later-no-help criterion|later-no-help]] criteria.
=== Favorite betrayal? ===
PAR voting fails the [[favorite betrayal criterion]] (FBC). For instance, consider the following "non-disqualifying center-squeeze" scenario: (
* 30: AX>B (That is, on 35 ballots, A and X are preferred, B is accepted, and C is rejected)
* 35: AX>B▼
*
* 10: B>AC
* 40: C>B
None are
* 30: AX>B (That is, on 35 ballots, A and X are preferred, B is accepted, and C is rejected)
*
*
* 10: B>AC
*
*
Now,
However, there are several ways to "rescue" FBC-like behavior for this system.
For another, the B>AC voters could simply reject C, the strongest rival of their favorite, and B would win with no need for favorite betrayal.
▲Third, note that in any scenario where it fails that for some small group, there is a rational strategy for some superset of that group which does not involve betrayal. For instance, in first scenario above, if 11 of the AX>B voters switch to >AXB, then A is eliminated without any betrayal.
== An example ==
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{{Tenn_voting_example}}
Assume voters in each city preferred their own city; rejected any city that is over 200 miles away or is the farthest city;
<div class="floatright">
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!City
!P
!(A)
!A
!(R)
!R
!tally
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!bgcolor="#fff"|Memphis
|bgcolor="#fff"|42
|bgcolor="#fff"|(0)
|bgcolor="#fff"|0
|bgcolor="#fcc"|(58)
|bgcolor="#fcc"|58
|bgcolor="#fcc"|
|-
!bgcolor="#fff"|Nashville
|bgcolor="#fff"|26
|bgcolor="#fff"|(42)
|bgcolor="#fff"|74
|bgcolor="#fff"|(0)
|bgcolor="#fff"|0
|bgcolor="#cfc"|100
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!bgcolor="#fff"|Chattanooga
|bgcolor="#fcc"|15
|bgcolor="#fff"|(43)
|bgcolor="#fff"|43
|bgcolor="#fff"|(0)
|bgcolor="#fff"|42
|bgcolor="#
|-
!bgcolor="#fff"|Knoxville
|bgcolor="#fcc"|17
|bgcolor="#fff"|
|bgcolor="#fff"|
|bgcolor="#
|bgcolor="#fcc"|68
|bgcolor="#fcc"|32
|}
</div>
Memphis is rejected by a majority, and is
(If Memphis voters rejected Nashville, then Chattanooga or Knoxville could win by conspiring to reject Nashville and accept Memphis. However, Nashville could stop this by rejecting them. Thus this strategy would not work without extreme foolishness from both Memphis and Nashville voters, ''and'' extreme amounts of strategy from the others.)
== Discussion ==
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=== Logic for 25%-preferred threshold (step 2) ===
The 25%-preferred threshold in step
[[Category:Graded Bucklin
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