Ranked Robin: Difference between revisions

== Local counting ==

Ranked Robin is [[Precinct-summable|precinct summable]] through the use of [[Pairwise comparison matrix|preference matrices]]. Full preference matrices can be created simply by hand if needed and then reported directly to the media and the public, allowing ballots and ballot data to remain local for recounts and risk-limiting audits without risking the threat of [https://en.wikipedia.org/wiki/Electoral_fraud#Vote_buying vote selling] and [https://ballotpedia.org/Intimidation_of_voters voter coercion]. This decentralization of tallying allows elections to remain robust against scaled election attacks, which is vital in jurisdictions that run geographically-spread or high-profile elections. In contrast, voting methods that are not precinct summable, like [[Instant runoff voting|Ranked Choice (Instant Runoff) Voting]] and many expressive [[Proportional Representation|proportional voting methods]], lose these benefits and can lead to distrust in election outcomes if fraud, attacks, or even simple mistakes happen under a centralized counting authority.

== Tabulation ==

Elect the candidate who pairwise beats the greatest number of other candidates.

=== Tie-breaking methods ===

If there is a tie, use the "Level 1" tie-breaking method to resolve it. If there is still a tie, use "Level 2", and so on.

'''Level 1:''' 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 '<math display="inline">A</math>s column in 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.

'''Level 2:''' 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.

'''Level 3:''' It is highly unlikely that there will still be a tie after '''Level 2''', but if there is, it is not recommended to use tie-breaking methods beyond '''Level 2''' for government elections as voter trust may be shaken more by using '''Level 3''' and beyond than drawing lots or hosting another election. In the event that there is a tie after '''Level 2''', 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 '''Level 2''', 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.

'''Level 4:''' If there is still a tie after '''Level 3''', it is unlikely that '''Level 4''' will break that tie, as it will only work if the tied candidates have matchup losses against different candidates.<references />