Ranked Robin: Difference between revisions

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.

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]].

{{Definition|Elect the candidate who pairwise beats the greatest number of other candidates.}}

==== Tie-breakingExample methodselection ====

'''1^st Degree:''' Declare the tied candidates finalists. For each finalist, subtract the number of ballotsvotes on which they lost topreferring each other finalist from the number of ballots onvotes whichpreferring theythem beatover each other finalist. The finalist with the greatest total difference is elected. For example, let <math>A_w</math> be the number of ballotsvotes on whichpreferring finalist <math display="inline">A</math> beatsover each other finalist (equivalent to the sum of the values in <math display="inline">A</math>'s row in a preference matrix consisting only of finalists) and let <math>A_l</math> be the number of ballotsvotes onpreferring whicheach other finalist over <math display="inline">A</math> loses to each other finalist (equivalent to the sum of the values in <math display="inline">A</math>'s column in a preference matrix consisting only of finalists); <math display="inline">A</math>'s total difference is <math>A_w-A_l</math>. This is mathematically equivalent to the [https://en.wikipedia.org/wiki/Borda_count#Tournament-style_counting_of_ties tournament-style of the Borda count] (among only the finalists), where candidates get, per ballot, 1 point for each candidate they beat and ½ point for each candidate they tie. There are two alternate, more concise ways of describing the '''1^st Degree''' tiebreaker.

* ''If there is a tie, then for each tied candidate, subtract the number of votersvotes who preferpreferring each other tied candidate from the number of votersvotes with the opposite preference. Elect the tied candidate with the greatest total difference.''

* ''Among the candidates who tie for winning the most head-to-head matchups, elect the tied candidate with the best average rank.''

'''2^nd Degree:''' For each tied finalist, subtract the number of ballotsvotes on which they lost topreferring each other candidate (including candidates who are not finalists) from the number of ballots onvotes whichpreferring theythem beatover each other candidate (including candidates who are not finalists). The tied finalist with the greatest total difference is elected.

'''4^th Degree:''' If there is still a tie after the '''3^rd Degree''' tiebreaker, it is unlikely that the '''4^th Degree''' tiebreaker will break that tie, as it will only work if the tied candidates have matchup losses against other candidates. Find the shortest [[beatpath]] from each tied candidate to each other tied candidate. For each tied candidate, for each shortest beatpath to another tied candidate, for each pairwise victory in the beatpath, subtract the number of ballotsvotes on whichpreferring the losing candidate was preferred over the winning candidate from the number of ballotsvotes on whichpreferring the winning candidate was preferred over the losing candidate. Sum these differences within each selected beatpath to get the total strength of each selected beatpath. Sum each tied candidate's total beatpath strengths over other tied candidates. Elect the tied candidate with the greatest sum of beatpath strengths. If there are multiple shortest beatpaths from one tied candidate to another, select the one with the lowest total strength.

==== Example of a ballot set that requires all 4 tie-breaking degrees: ====

|'''5256'''

|'''188204'''

|'''4751'''

|'''188204'''

|'''38'''

|''3539''

|''35'39'''

|''2832''

|'''138150'''

|''169181''

|''156168''

|''178190''

|''224232''

|'''10251069''' - ''10251069'' = <u>0</u>

'''2^nd 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^rd Degree:''' Ava and Bianca tie for the least ''losing'' (and '''winning''') votes between them, ''149'' (and '''188204''').

'''4^th 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 votersvotes who preferpreferring Ava over Deegan and the number of voters whovotes preferpreferring 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.

If there is a [[Condorcet winner criterion|Condorcet Winner]], then simply show each of the winner's pairwise matchups against other candidates. This can either be shown as percentage of total votes for each candidate in a given pairwise matchup, or as the percentage point difference in favor of the winner if there's a desire to show less information. If there is no Condorcet Winner but a single candidate wins without any tie-breaker, show how many matchups each candidate won in addition to each of the winner's pairwise matchups. These two scenarios will cover the vast majority of real-world elections.

==== Two different ways to present the results of the same election with Condorcet Winner Ava: ====

==== Example of how to present the results of an election where the winner Ava is not a Condorcet Winner: ====

==== Example of showing Level 4 with 3 finalists in a Condorcet cycle: ====

==== Example of showing Level 5 with 3 finalists in a Condorcet cycle: ====

</blockquote>In the rare case of a '''2^nd Degree''' tie, if there are many candidates, it is recommended to focus on who the tied finalists are and their Total Advantages over all other candidates (which likely will not sum to 0).

=== Passed: ===

=== Failed: ===