Maximum Constrained Approval Bucklin: Difference between revisions
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Determining which voters to eliminate to maximize the support of a candidate subject to earlier constraints is relatively simple to do by linear programming, but hard to do by hand; FAB can't be counted entirely by hand. |
Determining which voters to eliminate to maximize the support of a candidate subject to earlier constraints is relatively simple to do by linear programming, but hard to do by hand; FAB can't be counted entirely by hand. |
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What ended up as FAB was initially proposed in 2017<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-January/001276.html|title=Bucklin multiwinner method|website=Election-methods mailing list archives}}</ref> and simplified in later that year<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html|title=A simpler vote management-resistant Bucklin LP|website=Election-methods mailing list archives}}</ref>. The method detailed here has been further modified from the EM posts to resist Woodall free riding. |
What ended up as FAB was initially proposed in 2017<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-January/001276.html|title=Bucklin multiwinner method|website=Election-methods mailing list archives|date=2017-01-06}}</ref> and simplified in later that year<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html|title=A simpler vote management-resistant Bucklin LP|website=Election-methods mailing list archives|2017-09-15}}</ref>. The method detailed here has been further modified from the EM posts to resist Woodall [[free riding]]. |
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<<TBD, below this point, particularly the handling of epsilons>> |
<<TBD, below this point, particularly the handling of epsilons>> |
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* Droop proportionality criterion |
* Droop proportionality criterion |
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* Invulnerability to Woodall free riding |
* Invulnerability to [[free riding|Woodall free riding]] |
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FAB fails the following criteria: |
FAB fails the following criteria: |
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* Weak invulnerability to Hylland free riding |
* Weak invulnerability to [[free riding|Hylland free riding]] |
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* Monotonicity |
* Monotonicity |
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=== Monotonicity === |
=== Monotonicity === |
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Like BTV, FAB fails the monotonicity criterion due to a lookahead problem<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2018-February/001682.html|title=Path dependence monotonicity failure in BTV|website=Election-methods mailing list archives}}</ref>. However, FAB passes the two criteria above as long as the candidate to elect in a round is chosen (by some method) from the set of candidates with above Droop quota support for that round. Thus, it is possible that a variant that uses a yet unknown lookahead criterion instead of electing the candidate with the greatest support, could pass monotonicity. |
Like BTV, FAB fails the monotonicity criterion due to a lookahead problem<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2018-February/001682.html|title=Path dependence monotonicity failure in BTV|website=Election-methods mailing list archives|date=2018-02-18}}</ref>. However, FAB passes the two criteria above as long as the candidate to elect in a round is chosen (by some method) from the set of candidates with above Droop quota support for that round. Thus, it is possible that a variant that uses a yet unknown lookahead criterion instead of electing the candidate with the greatest support, could pass monotonicity. |
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== References == |
== References == |
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