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Prefer Accept Reject voting: Difference between revisions
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# '''Voters can Prefer, Accept, or Reject each candidate.''' Default is "Reject" for voters who do not explicitly reject any candidates, and "Accept" otherwise.
# '''Candidates with a majority of Reject, or with under 25% Prefer, are disqualified''', unless that would disqualify all candidates.
# Each voter gives 1 point to each non-
== Relationship to NOTA ==
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* It fails the [[participation criterion]] but passes the [[semi-honest participation criterion]].
* It fails O(N) [[summability]], but can get that summability with two-pass tallying (first determine who's
* It may pass the majority Condorcet loser criterion (?).
* It fails the [[later-no-help criterion]], but passes if there is at least one candidate above the
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.
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* 40: C>B
None are
* 29: AX>B
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* 40: C>B
Now, A is
However, there are several ways to "rescue" FBC-like behavior for this system.
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If the above restrictions hold, then PAR voting would meet FBC. It is arguably likely that real-world voting scenarios will meet the above restrictions, except for a negligible fraction of "ideologically atypical" voters. For instance, in the first scenario above, the categories appear to be {XA}, {B}, and {C}, so the B>AC voters would probably actually vote either B>A or B>C.
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 11 of the AX>B voters switch to >AXB, then A is
== An example ==
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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 2 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
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