Prefer Accept Reject voting: Difference between revisions
Category:Graded Bucklin systems → Category:Graded Bucklin methods
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# '''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.
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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 O(N²) [[summability]]. (It is also possible to run it in no more than 3 counting rounds, each of which is O(N) summable.)
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
It fails the [[consistency criterion]], the [[Condorcet loser criterion]], [[reversibility]], the [[Strategy-free criterion]], and the [[later-no-harm criterion
=== Favorite betrayal? ===
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* 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
* 30: AX>B (That is, on 35 ballots, A and X are preferred, B is accepted, and C is rejected)
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* 15: B>A
* 10: B>AC
*
*
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.
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=== Logic for 25%-preferred threshold (step 2) ===
The 25%-preferred threshold in step
[[Category:Graded Bucklin
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