Ranked Robin: Difference between revisions
→Tie-breaking methods
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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.
'''1<sup>st</sup> Degree:''' Declare the tied candidates finalists. For each finalist, subtract the number of
* ''If there is a tie, then for each tied candidate, subtract the number of
* ''Among the candidates who tie for winning the most head-to-head matchups, elect the tied candidate with the best average rank.''
'''2<sup>nd</sup> Degree:''' For each tied finalist, subtract the number of
'''3<sup>rd</sup> Degree:''' It is highly unlikely that there will still be a tie after the '''2<sup>nd</sup> Degree''' tiebreaker, but if there is, it is not recommended to use tie-breaking methods beyond the '''2<sup>nd</sup> Degree''' tiebreaker for government elections as voter trust may be shaken more by using the '''3<sup>rd</sup> Degree''' tiebreaker and beyond than drawing lots or hosting another election. In the event that there is a tie after the '''2<sup>nd</sup> Degree''' tiebreaker, the differences for the tied candidates will be the same, but the values used to calculate them will likely be different. Elect the tied candidate whose values are closest to the tied differences. For example, if <math display="inline">A</math>, <math display="inline">B
</math>, and <math display="inline">C</math> are tied after the '''2<sup>nd</sup> Degree''' tiebreaker, then <math>A_w-A_l=B_w-B_l=C_w-C_l</math> (where wins and loses are calculated across the entire field of candidates), but it's likely that <math>A_w\neq B_w\neq C_w</math> (and by proxy that <math>A_l\neq B_l\neq C_l</math>). The tied candidate with the greatest loss margin will also have the greatest win margin, and the tied candidate with the least loss margin will have the least win margin. Elect the tied candidate with the least loss and win margins as that is the least polarizing tied candidate.
'''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
==== Example of a ballot set that requires all 4 tie-breaking degrees ====
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'''3<sup>rd</sup> Degree:''' Ava and Bianca tie for the least ''losing'' (and '''winning''') votes between them, ''149'' (and '''188''').
'''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
== Presentation of results ==
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
==== Two different ways to present the results of the same election with Condorcet Winner Ava ====
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Ava vs. Fabio: +51% points
</blockquote>If there is no Condorcet Winner but a single candidate wins without any tiebreaker, show how many matchups each candidate won in addition to each of the winner's pairwise matchups.
==== Example of how to present the results of an election where the winner Ava is not a Condorcet Winner ====
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Ava vs. Fabio: +51% points
</blockquote>These two scenarios will cover the vast majority of real-world elections.
=== If there's a tie ===
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Cedric is elected!
</blockquote>In the rare case of a '''2<sup>nd</sup> 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).
== Legal and economic viability ==
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