Ranked Robin

Ranked Robin is a Condorcet 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 round-robin tournament. A strict series of tie-breaking mechanics are defined.

History

Ranked Robin was invented by Sass on 30 September 2021 and named by Sara Wolk on 7 November 2021. As an enthusiast of cardinal voting methods and a strong advocate for voter empowerment, Sass saw a timely need for a sufficiently-accurate 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, which was similarly replicated by Marquis de Condorcet centuries later, and then again by 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. 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 preference matrix can be overwhelming for most voters. This innovation can likely be adapted to simplify the results of other ranked voting methods.

Balloting

Voters may rank as many candidates as they would like. Voters are free to rank multiple candidates equally. Skipped ranks are ignored and will neither hurt nor help a voter's vote. All candidates left unranked are considered tied for the last rank, below the lowest rank marked on a voter's ballot.

Local counting

Ranked Robin is precinct summable through the use of 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 vote selling and 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 Ranked Choice (Instant Runoff) Voting and many expressive 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 $A_{w}$ be the number of ballots on which finalist ${\textstyle A}$ beats each other finalist (equivalent to the sum of the values in ${\textstyle A}$'s row in a preference matrix consisting only of finalists) and let $A_{l}$ be the number of ballots on which ${\textstyle A}$ loses to each other finalist (equivalent to the sum of the values in '${\textstyle A}$s column in preference matrix consisting only of finalists); ${\textstyle A}$'s total difference is $A_{w}-A_{l}$. This is mathematically equivalent to the 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 ${\textstyle A}$, ${\textstyle B}$, and ${\textstyle C}$ are tied after Level 2, then $A_{w}-A_{l}=B_{w}-B_{l}=C_{w}-C_{l}$ (where wins and loses are calculated across the entire field of candidates), but it's likely that $A_{w}\neq B_{w}\neq C_{w}$ (and by proxy that $A_{l}\neq B_{l}\neq C_{l}$). 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.