Prefer Accept Reject voting: Difference between revisions

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There are a few criteria for which it does not pass as such, but where it passes related but weaker criteria. These include:

* It fails the [[favorite betrayal criterion]], but 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. (Also, the cases of such failure would arguably be quite rare in practice.) Also, in a 3-way election where all voters preferred at least 1 candidate and rejected at least 1 candidate, there is never a favorite-betrayal incentive unless there's a Condorcet cycle. (This holds even if you add weak also-ran candidates to such an election, because of the following property.)

* It fails [[Independence of irrelevant alternatives]], but passes [[Local independence of irrelevant alternatives]].

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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:

* 35: AX>B

* 10: B>A

* 10: B>AC

* 5: B>C

* 40: C>B

None are eliminated, so C wins with 40 points (against 35, 25, 35 for A, B, and X). However, if 6 of the first group of voters strategically betrayed their true favorite A, the situation would be as follows:

* 29: AX>B

* 6: X>B

* 10: B>A

* 10: B>AC

* 5: B>C

* 40: C>B

Now, A is eliminated with 51% rejection; so B (the CW) wins.

However, there are several ways to "rescue" FBC-like behavior for this system.

First, add a "compromise" option to the ballot, as described in [[FBPPAR]].

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 ==