Bucklin voting: Difference between revisions

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'''Bucklin''' is a [[voting system]] that can be used for single-member districts and also multi-member districts. It is also known as the Grand Junction system after Grand Junction, Colorado, where it was first proposed. It is closely related to the class of [[:Category:Graded Bucklin methods|graded Bucklin systems]], in which equal and/or skipped rankings are allowed, which includes such systems as [[Majority Choice Approval]] (MCA). Modern theorists tend to prefer graded Bucklin systems over ungraded ones, as they usually comply better with criteria such as [[FBC]].
 
== How did it work? ==
In the above example, Memphis voters have the most first place votes and might not offer a second preference in hopes of winning, but this attempted strategy fails because they are not a second favorite from competitors.
 
== Fallback voting ==
'''Fallback voting''' ('''FV''') is a voting method strongly related to [[Bucklin voting]], invented by Brams and Sanvers.<ref name="Brams Sanver 20062">{{cite web | last=Brams | first=Steven | last2=Sanver | first2=Remzi | title=Voting Systems that Combine Approval and Preference | website=Archive ouverte HAL | date=2006-12-07 | url=https://hal.archives-ouvertes.fr/hal-00119047 | access-date=2020-01-30}}</ref> It is a ranked method which (with a slight modification) works by examining the 1st rank, and electing the candidate with the largest majority of voters ranking them 1st, if such a candidate exists. If no such candidate exists, then it examines both the 1st and 2nd ranks, and elects the candidate ranked either 1st or 2nd by the largest majority of voters. If none exists, the procedure continues to sequentially examine an additional rank at a time until either some candidate has the largest majority of ballots ranking them within the examined ranks, in which case they win, or until all ranks have been added in, at which point the candidate ranked on the most ballots wins.
 
Fallback voting is equivalent to the [[Expanding Approvals Rule]] in the single-winner case under certain conditions.<blockquote>Remark 3 [...] For k = 1 and under linear orders for all but a subset of equally least preferred candidates applying the tweak in Remark 2 leads to the EAR [Expanding Approvals Rule] being equivalent to the Fallback voting rule (Brams and Sanver, 2009). <ref name="Aziz Lee 20172">{{cite web | last=Aziz | first=Haris | last2=Lee | first2=Barton | title=The Expanding Approvals Rule: Improving Proportional Representation and Monotonicity | website=arXiv.org | date=2017-08-25 | url=https://arxiv.org/abs/1708.07580v2 | access-date=2020-01-30|page=19}}</ref></blockquote>
== Notes ==
Example where the [[Condorcet winner]] and Bucklin winner diverge:<blockquote>40 B>A>V