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. 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 [https://en.wikipedia.org/wiki/Round-robin_tournament round-robin tournament]. A strict series of tie-breaking mechanics are defined.
== History ==
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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 and eliminate all other candidates. For each finalist, subtract the number of ballots on which they lost to each other finalist from the number of ballots on which they beat each other finalist. The finalist with the greatest total difference is elected. For example, let <math>A_w</math> be the number of ballots on which finalist <math display="inline">A</math> beats 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 ballots on which <math display="inline">A</math> loses to each other finalist (equivalent to the sum of the values in
* ''If there is a tie, then for each tied candidate, subtract the number of voters who prefer each other tied candidate from the number of voters 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 candidate with the best average rank.''
'''2<sup>nd</sup> Degree:''' For each tied finalist, subtract the number of ballots on which they lost to each other candidate (including eliminated candidates) from the number of ballots on which they beat each other candidate (including eliminated candidates). The tied finalist with the greatest total difference is elected.
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Eli won 2 matchups (against Deegan and Fabio)
Fabio lost all matchups</blockquote><blockquote>Ava vs. Bianca: -
Ava vs. Cedric: +20% points
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Cedric is elected!</blockquote>In the rare case of a '''2<sup>nd</sup> Degree''' tie and there are many candidates, it is recommended to focus on who the tied finalists are and their Total Advantages over all other candidates (which will not sum to 0).
== Criteria ==
=== Passed: ===
* [https://en.wikipedia.org/wiki/Unrestricted_domain Unrestricted domain]
* [[Arrow's impossibility theorem|Non-imposition]] ([https://en.wikipedia.org/wiki/List_of_acronyms:_A#AK a.k.a.] [[Arrow's impossibility theorem|citizen sovereignty]])
* [https://en.wikipedia.org/wiki/Dictatorship_mechanism Non-dictatorship]
* [[Homogeneity criterion|Homogeneity]]
* [[Condorcet criterion]]
* [[Majority criterion]]
* [[Arrow's impossibility theorem|Pareto criterion]] ([https://en.wikipedia.org/wiki/List_of_acronyms:_A#AK a.k.a.] [[Arrow's impossibility theorem|unanimity]])
* [[Monotonicity criterion]]
* [[Majority loser criterion]]
* [[Condorcet loser criterion]]
* [[Reversal symmetry]]
* [https://en.wikipedia.org/wiki/Resolvability_criterion Resolvability criterion]
* [https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time Polynomial time]
* [[Mutual majority criterion]]
* [[Smith criterion]]
* [[Independence of Smith-dominated alternatives]]
* [[Independence of Irrelevant Ballots]]
=== Failed: ===
* [[Participation criterion|Participation]]
* [[Independence of irrelevant alternatives]]
* [[Consistency criterion|Consistency]]
* [[Independence of clones criterion|Independence of clones]]
* [[Sincere Favorite criterion|Sincere Favorite]]
=== A note on cloneproofness ===
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.<references />
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