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]]. In [[Election-methods mailing list#Notation|the notation typically used on the EM-list]], Ranked Robin is roughly "[[Copeland]]//[[Borda]]" with the addition of tiebreakers.
 
== History ==
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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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=== 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 ===
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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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== 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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* [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]]