Ranked Robin: Difference between revisions

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'''4<sup>th</sup> Degree:''' If there is still a tie after the '''3<sup>rd</sup> Degree''' tiebreaker, it is unlikely that the '''4<sup>th</sup> 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 ballots on which the losing candidate was preferred over the winning candidate from the number of ballots on which 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.
'''4<sup>th</sup> Degree:''' If there is still a tie after the '''3<sup>rd</sup> Degree''' tiebreaker, it is unlikely that the '''4<sup>th</sup> 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 ballots on which the losing candidate was preferred over the winning candidate from the number of ballots on which 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:''' ====
==== Example of a ballot set that requires all 4 tie-breaking degrees: ====
<blockquote>10: Eli>Deegan>Ava=Cedric>Fabio
<blockquote>10: Eli>Deegan>Ava=Cedric>Fabio


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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.
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:''' ====
==== Two different ways to present the results of the same election with Condorcet Winner Ava: ====
<blockquote>Ava: 54%《》Bianca: 46%
<blockquote>Ava: 54%《》Bianca: 46%