Ranked Robin: Difference between revisions

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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]]. AIn strict[[Election-methods seriesmailing oflist#Notation|the tienotation typically used on the EM-breakinglist]], mechanicsRanked areRobin is roughly "[[Copeland]]//[[Borda]]" with the addition of definedtiebreakers.
 
== 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>=Bianca>=Cedric>Eli>Deegan
 
6:Eli>Ava>Bianca>=Cedric>=Deegan
 
6:Deegan>Bianca>=Cedric>Eli>Ava
 
4:Bianca>Ava>Eli>Deegan>Cedric
 
3:Eli>Deegan>Bianca>=Cedric>Ava
 
2:Deegan>=Eli>Bianca>=Cedric>Ava}}
Create a [[Pairwise comparison matrix|preference matrix]] from the ballots.
{| class="wikitable"
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== Tie-breaking mechanics ==
 
=== 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'''
|'''5256'''
|'''188204'''
|-
|'''Bianca over'''
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|''31''
|'''46'''
|'''4751'''
|'''188204'''
|-
|'''Cedric over'''
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|—
|'''30'''
|'''38'''
|'''175'''
|-
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|''16''
|''24''
|''3539''
|''35'39'''
|''2832''
|—
|'''138150'''
|-
|''Column total (votes against)''
|''149''
|''149''
|''169181''
|''156168''
|''178190''
|''224232''
|'''10251069''' - ''10251069'' = <u>0</u>
|}
'''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>188204-149=3955</math>).
 
'''3<sup>rd</sup> Degree:''' Ava and Bianca tie for the least ''losing'' (and '''winning''') votes between them, ''149'' (and '''188204''').
 
'''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 a certain races. Ranked Robin can satisfy many of these majority clauses in a single election, allowing municipalities to eliminate an election if so desired, helping to offset the costs of implementing Ranked Robin, typically entirely within one election cycle.
 
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.
Under Ranked Robin, parties do not gain an advantage from running clones whether the clones are frontrunners or not. A frontrunner can only gain an advantage from running inferior clones that are able to beat other frontrunners, which is incredibly difficult in practice. For elections where many clones run, the only advantage gained is if they are all frontrunners, in which case voters arguably benefit from a competitive election of many candidates close to the center of public opinion. Because Ranked Robin does not have vote splitting, the effects of clones are minimized.
 
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]]