Prefer Accept Reject voting: Difference between revisions

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PAR voting fails the [[favorite betrayal criterion]] (FBC). For instance, consider the following "non-disqualifying center-squeeze" scenario:
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>A
* 5: AX>C
⚫
* 15: B>A
* 10: B>AC
* 10: B>AC
* 5: B>C
* 40: C>B
* 40: C>B


None are disqualified, 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:
None are disqualified, and C is the leader. Points are: A, 60; B, 55; C, 55; X, 35. C wins. However, if 6 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)
* 29: AX>B
* 6: X>B
* 5: AX>C
* 10: B>A
* 15: B>A
* 10: B>AC
* 10: B>AC
* 5: B>C
* 34: C>B
* 40: C>B
* 6: B


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


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


For one, we could add a "compromise" option to the ballot, as described in [[FBPPAR]].
For one, we could add a "stand aside" option to the ballot, as described in [[FBPPAR]].


For another, we could restrict the domain to voting scenarios which meet the following restrictions:
For another, we could restrict the domain to voting scenarios which meet the following restrictions:
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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.
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 disqualified without any 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 ==
== An example ==
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