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
# '''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 [[
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
=== Favorite betrayal? ===
▲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.
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)
* 5: AX>C
* 15: B>A
* 10: B>AC
* 40: C>B
None are majority-rejected, and C is the frontrunner. Points are: A, 60; B, 55; C, 55; X, 35. A wins. However, if 11 of the last group of voters strategically betrayed their true favorite C, the situation would be as follows:
* 30: AX>B (That is, on 35 ballots, A and X are preferred, B is accepted, and C is rejected)
* 5: AX>C
* 15: B>A
* 10: B>AC
* 29: C>B
* 11: B
Now, C is not viable with 51% rejection; so B is the leader. Since C is no longer the leader, B gets the 34 points from C voters, and wins. The strategy succeeded; the strategic voters are better off.
However, there are several ways to "rescue" FBC-like behavior for this system.
For one, we could add a "stand aside" option to the ballot, as described in [[FBPPAR]].
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.
And finally, 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 16 of the C>B voters switch to CB, then B is the leader and wins without them having to rate C below their true feelings.
== 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
Line 47 ⟶ 82:
!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
Line 59 ⟶ 98:
!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 ==
=== Logic for 25%-preferred threshold (step 2) ===
The 25%-preferred threshold in step 1 is not purely arbitrary; it is exactly enough so that, in a 3-candidate election where all voters give all three grades, there will always be at least 1 candidate who passes the thresholds to not be disqualified. In other words: if a minority supports a rejected candidate, while a majority divides preferences between two candidates while accepting the other, then at least one of those two will not be disqualified. This does not hold for an election with 4 or more candidates, because the majority could split its preferences more than two ways; but even in those cases, it is usually reasonable to hope that the top 3 candidates combined will get enough preferences to ensure that at least one of them is above the 25% threshold.
▲(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.)
[[Category:Graded Bucklin
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