View source for Bucklin voting

{{Short description|Class of electoral systems}}{{For|the modern [[graded voting]] variant with equal and skipped ranks|Graduated majority judgment}}
{{Electoral systems sidebar|expanded=Single-winner}}

'''Bucklin voting''' is a class of [[voting system|voting method]]s that can be used for single-member and multi-member [[Constituency|districts]]. As in [[highest median voting rules|highest median rules]] like the [[majority judgment]], the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the [[Georgist]] politician<ref>Hermann, J. R. "A Remembrance of James W. Bucklin". Single Tax Review, Vol. XIX, No.2, March-April 1919. http://cooperative-individualism.org/hermann-j-r_a-remembrance-of-james-bucklin-1919.htm</ref> [[James W. Bucklin]] of [[Grand Junction, Colorado]], and is also known as the '''Grand Junction system'''.

==Voting process==
Bucklin rules varied, but here is a typical example:

Voters are allowed [[Ranked voting systems|rank preference ballots]] (first, second, third, etc.).

First choice votes are first counted. If one candidate has a [[majority]], that candidate wins. Otherwise the second choices are added to the first choices. Again, if a candidate with a majority vote is found, the winner is the candidate with the most votes accumulated. Lower rankings are added as needed.

A [[majority]] is determined based on the number of valid ballots. Since, after the first round, there may be more votes cast than voters, it is possible for more than one candidate to have majority support.

== Variants and relationships to other methods ==
The term ''Bucklin voting'' refers to the process of counting all votes on all ballots that are above some threshold, and then adjusting that threshold down until a majority is reached. In some variants which have been used, equal ranking was allowed at some or all ranks. Some variants had a predetermined number of ranks available (usually 2 or 3), while others had unlimited ranks. There were also variants akin to [[Borda voting]] in that lower-ranked votes counted for less.

The Bucklin procedure is one way to ensure that the winning candidate will be among those with the highest median vote. When used with a [[cardinal voting]] scale instead of [[ranked voting|ordinal ranking]], Bucklin's balloting method is the same as that of [[highest median voting rules|highest median rules]] like the Majority Judgment. However, Bucklin's selection algorithm starts with the highest rated votes and adds lower ones until a median winner is reached, whereas Majority Judgment starts with the median votes and removes them until all but one candidate is eliminated. Due to this difference, Bucklin passes some [[Comparison of electoral systems#Comparisons under a jury model|voting criteria]] that Majority Judgment fails, and vice versa.

==Bucklin applied to multiwinner elections==
Bucklin was used for multiwinner elections. {{Citation needed|date=November 2008}} For multi-member districts, voters marked as many first choices as there are seats to be filled.  Voters marked the same number of second and further choices.  In some localities, the voter was required to mark a full set of first choices for his or her ballot to be valid. However, allowing voters to cast three simultaneous votes for three seats ([[Plurality-at-large voting|block voting]]) could allow an organized 51%, or the largest minority in a contest with three or more slates, to win all three seats in the first round, so this method does not give [[proportional representation]].

== History and usage ==
The method was proposed by [[Marquis de Condorcet|Condorcet]] in 1793,<ref>{{cite book | last=Haines | first=C.G. | last2=Haines | first2=B.M. | title=Principles and Problems of Government | publisher=Harper and Brothers | year=1921 | url=https://books.google.com/books?id=gHkqAAAAYAAJ&dq=Bucklin+system&pg=PA162}}</ref> and was reported as having seen use by the Republic of Geneva later that year.<ref name="w947">{{cite journal | last=Lhuilier | first=Simon | title=Examen du mode d'élection proposé à la Convention Nationale de France en février 1793, et adopté à Genève | journal=Mathématiques et Sciences Humaines | publisher=Ecole Pratique des hautes études, Centre de mathématique sociale et de statistique | volume=54 | year=1976 | issn=0987-6936 | pages=7–24 | url=https://eudml.org/doc/94179 | access-date=2025-03-01 | orig-date=Composed 1794-07-07}}</ref> It was re-invented under its current name and used in many political elections in the United States in the early 20th century, as were other experimental election methods during the [[Progressive Era]]. Bucklin voting was first used in 1909 in [[Grand Junction, Colorado]], and then used in more than sixty other cities including Denver and San Francisco.<ref>{{Cite book|url=https://books.google.com/books?id=bDCwpD1RiocC&q=denver|title=A Right to Representation: Proportional Election Systems for the Twenty-first Century|last=Barber|first=Kathleen L.|author-link=Kathleen L. Barber|date=2000|publisher=Ohio State University Press|isbn=9780814208540|pages=167|language=en}}</ref><ref>{{Cite book|title=City government in the United States.|last=Kneier|first=Charles Mayard|date=1957|publisher=Harper|pages=365–370|oclc=610214970}}</ref>

In two states, it was found to violate the state constitution and overturned; in the remainder of states using it, it was repealed. In Minnesota, it was ruled unconstitutional, in a decision that disallowed votes for multiple candidates, in opposition to some voters' single expressed preference,<ref>Brown v. Smallwood, 130 Minn. 492, 153 N. W. 953</ref> and in a [[Oklahoma primary electoral system|variant used in Oklahoma]], the particular application required voters in multi-candidate elections to rank more than one candidate, or the vote would not be counted; and the preferential primary was therefore found unconstitutional. The canvassing method itself was not rejected in Oklahoma.<ref>{{cite web|url=http://www.oscn.net/applications/oscn/deliverdocument.asp?citeid=53555|title=Dove v. Oglesby|work=oscn.net}}</ref>
{| class="wikitable sortable mw-collapsible mw-collapsed"
|+Adoption by Location{{efn|All instances of this system were later abolished, but the dates are unknown.}}
!State
!Election
!Year Adopted
!Notes
|-
|Washington
|State Primaries
|1907
|Predates traditional Bucklin voting and is slightly modified: candidates could win with 40% of the vote. The idea may have been based on a proposed primary law for [[Wisconsin]] suggested by [[Robert M. La Follette|Governor La Follete]] a year earlier.<ref>{{Cite book|last=Merriam|first=Charles Edward|url=https://books.google.com/books?id=IR8SAAAAIAAJ&q=washington+plan+for+preferential+voting+1907&pg=PA79|title=Primary Elections: A Study of the History and Tendencies of Primary Election Legislation|date=1908|publisher=University of Chicago Press|language=en}}</ref>
|-
|Colorado
|[[Grand Junction, Colorado|Grand Junction]] 
|1909
|
|-
|Washington
|[[Spokane, Washington|Spokane]]
|1910
|
|-
|Colorado
|[[Pueblo, Colorado|Pueblo]]
|1911
|
|-
|Louisiana
|[[New Iberia, Louisiana|New Iberia]]
|1912
|
|-
|Minnesota
|[[Duluth, Minnesota|Duluth]]
|1913
|
|-
|Colorado
|[[Denver]]
|1913
|
|-
|Colorado
|[[Colorado Springs, Colorado|Colorado Springs]]
|1913
|
|-
|Oregon
|[[Portland, Oregon|Portland]]
|1913
|
|-
|New Hampshire
|[[Nashua, New Hampshire|Nashua]]
|1913
|
|-
|Ohio
|[[Cleveland]]
|1913
|
|-
|Colorado
|[[Fort Collins, Colorado|Fort Collins]]
|1913
|
|-
|Oregon
|[[La Grande, Oregon|La Grande]]
|1913
|
|-
|California
|[[Members_of_the_San_Francisco_Board_of_Supervisors#endnote_PreferentialVoteE|San Francisco]]
|1917
|
|-
! colspan="5" |Sources<ref>{{Cite book|last1=Mason|first1=Haven A.|url=https://books.google.com/books?id=1GKtAAAAMAAJ&q=preferential+voting+bucklin+adoption&pg=PA263|title=Pacific Municipalities|last2=Locke|first2=William James|date=1914|language=en}}</ref>
|}

== Satisfied and failed criteria ==
Bucklin voting satisfies the [[Majority favorite criterion|majority criterion]], the [[mutual majority criterion]] and the [[monotonicity criterion]].<ref>[https://books.google.com/books?id=RN5q_LuByUoC&q=Bucklin Collective decisions and voting: the potential for public choice], Nicolaus Tideman, 2006, p. 204</ref>

Bucklin voting without equal rankings allowed{{Clarify|reason=MJ doesn't pass Condorcet|date=February 2019}} fails the [[Condorcet criterion]], [[independence of clones criterion]],<ref>Tideman, 2006, ibid</ref> [[later-no-harm]], [[participation criterion|participation]], [[consistency criterion for voting systems|consistency]], [[reversal symmetry]], the [[Condorcet method|Condorcet loser criterion]] and the [[independence of irrelevant alternatives|independence of irrelevant alternatives criterion]].

If equal and skipped rankings are allowed, Bucklin passes or fails the same criteria as highest median rules like the [[Majority Judgment#Satisfied and failed criteria|Majority Judgment]].

==Example application==
{{Tenn voting example}}

<div class="floatright">
{| border=1
|-
!City
!Round 1
!Round 2
|-
! Memphis
| 42
| 42
|-
! Nashville
| 26
| style="background:#00ff00;"|68
|-
! Chattanooga
| 15
| style="background:#ffff00;"|58
|-
! Knoxville
| 17
| 32
|}
</div>

The first round has no majority winner. Therefore, the second rank votes are added. This moves Nashville and Chattanooga above 50%, so a winner can be determined. Since Nashville is supported by a higher majority (68% versus 58%), Nashville is the winner.

== Voter strategy ==
Voters supporting a strong candidate have an incentive to [[bullet vote]] (offer only one first-rank vote), in hopes that other voters will add enough votes to help their candidate win. This strategy is most secure if the supported candidate appears likely to gain many second-rank votes.

In the above example, Memphis voters have the most first-place votes and might not offer a second preference in hopes of winning, but the strategy fails, unless other voters also bullet vote, because they are not a second-place choice of competitors.

If all Memphis voters bullet vote, Chattanooga voters could cause their city to win by all bullet voting. However, if all Nashville voters also do the same, Memphis would win on the fourth and final round.  In that case, Knoxville voters could do nothing to change the outcome.

In this particular example (but not always), bullet voting benefits one group of voters only if another group or groups do it as well.  The example shows that, depending upon who does it, bullet voting may distort the outcome and could be counterproductive for some voters who do it (here, those from Chattanooga and Nashville).

To prevent bullet voting, voters could be required to rank all candidates on the ballot. This would provide the voter with a disincentive to bullet vote, as the vote would not be counted unless all candidates are ranked.

==See also==
* [[List of democracy and elections-related topics]]
* [[Voting system]]
** [[Plurality voting system]]
** [[Instant-runoff voting]]
** [[Approval voting]]
** [[Score voting]]
** [[Borda count]]
** [[Expanding Approvals Rule]]

==References==
;Specific
{{reflist}}

;General
* [https://web.archive.org/web/20090204174848/http://www2.mnbar.org/benchandbar/2002/oct02/voting.htm Municipal Voting System Reform: Overcoming the Legal Obstacles (History of use of Bucklin voting in Duluth, Minnesota in 1912)]
* [https://web.archive.org/web/20080708181227/http://www.gjhistory.org/cat/main.htm Grand Junction people: James Bucklin]

== Notes ==
{{notelist}}

{{voting methods}}

{{DEFAULTSORT:Bucklin Voting}}
[[Category:Multi-winner electoral systems]]
[[Category:Single-winner electoral systems]]
[[Category:Preferential electoral systems]]