Bucklin voting: Difference between revisions
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{{Wikipedia}}
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 [[Majority Choice Approval]] (MCA), which can be considered a form of Bucklin in which equal rankings are allowed. Modern theorists prefer MCA for its greater compliance with criteria.▼
▲'''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 [[
== How did it work? ==
Line 26 ⟶ 28:
<div class="floatright">
{| class="wikitable" border="1"
!City
!Round 1
Line 49 ⟶ 51:
</div>
The first round has no majority winner. Therefore the second rank votes are added. This moves Nashville and
An alternative way to demonstrate it:
{| class="wikitable" border="1"
!City
!Majority
!Memphis
!Nashville
!Chattanooga
!Knoxville
|-
! bgcolor="#ffc0c0" |Round 1
|'''51'''
|<small>42</small>
|<small>26</small>
|<small>15</small>
|<small>17</small>
|-
! bgcolor="#ffc0c0" |Round 2
|'''51'''
|<small>42</small>
|'''<u><big>68</big></u>'''
|'''<big>58</big>'''
|<small>32</small>
|}
== Voter Strategy ==
Voters supporting a strong candidate have
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 Sanver.<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>
== Related systems ==
There are a number of variations of Bucklin voting such as [[Iterated bucklin|Iterated Bucklin]], [[Expanding Approvals Rule]], [[Maximum Constrained Approval Bucklin]], [[Venzke Bucklin Variant]] and [[Majority Choice Approval|Majority Choice Approval/ER-Bucklin.]] [[Majority Judgment]] is a cardinal voting system which is similar.
== Notes ==
Example where the [[Condorcet winner]] and Bucklin winner diverge:<blockquote>40 B>A>V
20 V>B
40 C>Z>V</blockquote>The Bucklin winner is B with 60 votes at the 2nd rank, while the Condorcet winner is V (V [[Pairwise counting|pairwise beats]] A, B, C, and Z with 60 votes to 40.)
Clone-proofness failure:<blockquote>
{| class="wikitable"
!Number
!Ballots
|-
|48
|A>C
|-
|40
|B>D>A
|-
|3
|C
|-
|9
|C>A
|}
Here, nobody has a majority in the first preferences, so when the next rankings are added in, C wins in both Bucklin and ER-Bucklin.
Create a clone of C, C'
{| class="wikitable"
!Number
!Ballots
|-
|24
|A>C>C'
|-
|24
|A>C'>C
|-
|40
|B>D>A
|-
|3
|C>C'
|-
|9
|C>C'>A
|}
A wins, having attained a majority on the third preferences (exceeding both C and C') in both Bucklin and ER-Bucklin.<ref>{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/eyjlja/the_new_hampshire_libertarian_primary_used_a/fgjpa4p|title=r/EndFPTP - Comment by u/curiouslefty on ”The New Hampshire Libertarian Primary used a hybrid of Bucklin and Approval Voting”|website=reddit|language=en-US|access-date=2020-04-06}}</ref></blockquote>
== See also ==
* [[ER-Bucklin]]
* [[Expanding Approvals Rule]]
* [[Maximum Constrained Approval Bucklin]]
* [[Venzke Bucklin Variant]]
* [[Majority Judgment]]
* [[Evaluative Proportional Representation]]
* [[Iterated bucklin|Iterated Bucklin]]
== References ==
[[Category:Single-winner voting systems]][[Category:Multi-winner voting systems]][[Category:Preferential voting systems]]▼
<references />
▲[[Category:Single-winner voting
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