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Ranked Robin is a [[Condorcet method|Condorcet voting method]] focused on the presentation of the results such that everyday voters can understand them without extensive education. Ranked Robin uses a [https://electowiki.org/wiki/Ballot#Ranked_ballot ranked ballot]. Voters are free to rank multiple candidates equally on their ballots. The candidate who wins the most head-to-head matchups against other candidates is elected, much like a [[w:round-robin tournament|round-robin tournament]].
== History ==
Ranked Robin was invented by [[User:Sass|Sass]] on 30 September 2021 and named by [[Sara Wolk]] on 7 November 2021. As an enthusiast of [[Cardinal voting systems|cardinal voting methods]] and a strong advocate for voter empowerment, Sass saw a timely need for a sufficiently-accurate [[Ranked voting|ranked voting method]] that was on par with the simplicity of voting methods like [[STAR Voting]] and even [[Approval Voting]], particularly in the [[United States]]. Ranked Robin is nearly identical to the earliest known Condorcet method, invented by [[Ramon Llull]] in his 1299 treatise ''Ars Electionis''<ref name="Hagele">{{cite journal |author1=G. Hägele |author2=F. Pukelsheim |lastauthoramp=yes | title=Llull's writings on electoral systems | journal=Studia Lulliana | year=2001 | volume=41 | pages=3–38 | url=http://www.math.uni-augsburg.de/stochastik/pukelsheim/2001a.html }}</ref>, which was similarly replicated by [[w:Marquis de Condorcet|Marquis de Condorcet]] centuries later, and then again by [[w:Arthur Herbert Copeland|Arthur Herbert Copeland]]. A mathematically identical method to Ranked Robin including the first tie-breaking mechanic was described by Partha Dasgupta and Eric Maskin in 2004<ref>{{Cite journal|last=Maskin|first=Eric|last2=Dasgupta|first2=Partha|date=2004|title=The Fairest Vote of All|url=https://scholar.harvard.edu/maskin/publications/fairest-vote-all|journal=Scientific American|volume=|issue=290|pages=64-69|via=Harvard University}}</ref>. The primary innovation of Ranked Robin is the reduction and formatting of results in such a way that they are palatable to a general audience, as a full [[Pairwise comparison matrix|preference matrix]] can be overwhelming for most voters. This innovation can likely be adapted to simplify the results of other voting methods that use [[pairwise counting]], particularly those that first restrict the set of winners such as [[Smith-efficient|Smith-efficient voting methods]].
== Balloting ==
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==== Example election ====
{{Ballots|1=8:Ava>Cedric>Deegan>Bianca>Eli
6:Ava
6:Eli>Ava>Bianca
6:Deegan>Bianca
4:Bianca>Ava>Eli>Deegan>Cedric
3:Eli>Deegan>Bianca
2:Deegan
Create a [[Pairwise comparison matrix|preference matrix]] from the ballots.
{| class="wikitable"
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== Tie-breaking mechanics ==
Almost real-world elections using Ranked Robin will not have any ties for the winning candidate. However, ties under Ranked Robin may potentially be more common than ties under [[First Past the Post electoral system|Choose-one Voting]]. While there are 4 degrees of tiebreakers defined, ties after the '''1<sup>st</sup> Degree''' tiebreaker are about as rare as ties under Choose-one Voting, and ties after the '''2<sup>nd</sup> Degree''' tiebreaker are much rarer than that.▼
=== Frequency of ties ===
▲Almost all real-world elections using Ranked Robin will not have any ties for the winning candidate. However, ties under Ranked Robin may potentially be more common than ties under [[First Past the Post electoral system|Choose-one Voting]]. While there are 4 degrees of tiebreakers defined, ties after the '''1<sup>st</sup> Degree''' tiebreaker are about as rare as ties under Choose-one Voting, and ties after the '''2<sup>nd</sup> Degree''' tiebreaker are much rarer than that.
=== Degrees of ties ===
If there is a tie (including [[Condorcet paradox|Condorcet cycles]]), use the '''1<sup>st</sup> Degree''' tie-breaking method to resolve it. If there is still a tie, use the '''2<sup>nd</sup> Degree''' tiebreaker, and so on.
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4: Ava>Bianca=Fabio
4: Ava=Bianca>Fabio
2: Bianca=Fabio>Ava=Eli}}Here's the preference matrix:
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|'''39'''
|'''42'''
|'''
|'''
|-
|'''Bianca over'''
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|''31''
|'''46'''
|'''
|'''
|-
|'''Cedric over'''
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|—
|'''30'''
|
|'''175'''
|-
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|''16''
|''24''
|''
|''
|''
|—
|'''
|-
|''Column total (votes against)''
|''149''
|''149''
|''
|''
|''
|''
|'''
|}
'''Ranked Robin:''' Ava and Bianca tie for pairwise beating the greatest number of other candidates, '''3'''.
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'''1<sup>st</sup> Degree:''' Ava and Bianca tie for the greatest total difference in votes for and against other tied finalists (both <math>29-29=0</math>).
'''2<sup>nd</sup> Degree:''' Ava and Bianca tie for the greatest total difference in votes for and against all other candidates (both <math>
'''3<sup>rd</sup> Degree:''' Ava and Bianca tie for the least ''losing'' (and '''winning''') votes between them, ''149'' (and '''
'''4<sup>th</sup> Degree:''' The shortest beatpath from Ava to Bianca is Ava→Deegan→Bianca and the shortest beatpath from Bianca to Ava is Bianca→Cedric→Ava. The difference between the number of votes preferring Ava over Deegan and the number of votes preferring Deegan over Ava is <math>39-38=1</math>. From Deegan to Bianca, the difference is <math>37-31=6</math>. The sum of the differences in the beatpath from Ava to Bianca (the total beatpath strength) is <math>1+6=7</math>. From Bianca to Cedric, the difference is <math>35-28=7</math>. From Cedric to Ava, the difference is <math>33-26=7</math>. The total beatpath strength from Bianca to Ava is <math>7+7=14</math>. Bianca has the greatest (sum of) total beatpath strength(s) among tied candidates, so Bianca is elected.
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==== Two different ways to present the results of the same election with Condorcet Winner Ava ====
<blockquote>
Ava: 54%《》Bianca: 46%
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</blockquote><blockquote>
Ava vs. Bianca: +8% points
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==== Example of how to present the results of an election where the winner Ava is not a Condorcet Winner ====
<blockquote>
Ava won 4 matchups (against Cedric, Deegan, Eli, and Fabio)
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</blockquote><blockquote>
Ava vs. Bianca: -6% points
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==== Example of showing Level 4 with 3 finalists in a Condorcet cycle ====
<blockquote>
Ava, Bianca, and Cedric are finalists.
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==== Example of showing Level 5 with 3 finalists in a Condorcet cycle ====
<blockquote>
Ava, Bianca, and Cedric are finalists.
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== Legal and economic viability ==
When legally defined as ''always'' reducing to a finalist set first and then electing the finalist with the greatest total difference (Total Advantage) among finalists (as described in the '''1<sup>st</sup> Degree''' tiebreaker), Ranked Robin always elects a majority preferred winner, arguably including in cases of '''2<sup>nd</sup> Degree''' ties. This legal definition does not change the outcomes of Ranked Robin. Many municipalities in the [[United States]] are subject to a majority clause in their respective state's election code, often requiring those jurisdictions to run two or more elections for
If there is only 1 finalist, then they are voted for by a majority of voters who had a preference among finalists.
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=== A note on cloneproofness ===
Ranked Robin can fail clone independence in one of two ways: either by its Copeland component or by its Borda component.
The Copeland component fails clone independence by [[w:Independence of clones criterion#Copeland|crowding and teaming]]. It can be argued that a party stands nothing to gain (or lose) by running clones as far as the crowding vulnerability is concerned, because all a candidate A can achieve by triggering a clone failure is to change the candidate from some B to some other C, which doesn't help A since A lost anyway -- unless C just happens to be closer aligned with A's position than does B. However, the teaming incentive may be more conventionally exploitable, since it directly benefits a candidate who runs clones.
The Borda component fails clone independence by teaming. If the [[Copeland set]] consists of more than one candidate, as can happen with some Condorcet cycles, then this could expose the Borda component and allow teaming to succeed. For instance, consider this pre-cloning election:
{{ballots|
12: A>B>C>D>E>F
11: B>C>A>D>E>F
10: C>A>B>D>E>F
}}
The Copeland set is {A,B,C}. A and B tie for Borda score, but this can be shifted in favor of A by teaming, e.g.
{{ballots|
12: A1>A2>B>C>D>E>F
11: B>C>A1>A2>D>E>F
10: C>A1>A2>B>D>E>F
}}
after which A wins.
Ranked Robin passes vote-splitting clone independence: cloning a candidate can't make that candidate lose.
== External links ==
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* [https://www.reddit.com/r/EndFPTP/comments/qkamzm/new_condorcet_method_that_doesnt_require_a/ Ranked Robin thread on r/EndFPTP] (starting November 1, 2021)
* [https://www.votingtheory.org/forum/topic/136/new-simple-condorcet-method-basically-copeland-margins Ranked Robin thread on Voting Theory Forum] (starting October 25, 2021)
* [https://www.equal.vote/ranked_robin Explanation of Ranked Robin from the Equal Vote Coalition]
== References ==
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[[Category:Condorcet methods]]
[[Category:Smith-efficient Condorcet methods]]
[[Category:Condorcet-related concepts]]
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